What is epistemology?

Epistemology is the investigation into the grounds and nature of knowledge itself. It is the study of the theory of knowledge. The study of epistemology focuses on our means for acquiring knowledge and how we can differentiate between truth and falsehood. Modern epistemology generally involves a debate between rationalism and empiricism, or the question of whether knowledge can be acquired a priori or a posteriori:

a priori - relating to or derived by reasoning from self-evident propositions (deductive)

a posteriori - relating to or derived by reasoning from observed facts (inductive)

Empiricism: knowledge is obtained through experience. Rationalism: knowledge can be acquired through the use of reason.

Why is Epistemology Important?:

Epistemology is important because it is fundamental to how we think. Without some means of understanding how we acquire knowledge, how we rely upon our senses, and how we develop concepts in our minds, we have no coherent path for our thinking. A sound epistemology is necessary for the existence of sound thinking and reasoning — this is why so much philosophical literature can involve seemingly arcane discussions about the nature of knowledge. Unfortunately, atheists who frequently debate questions that derive from differences in how people approach knowledge aren't always familiar with this subject.

The first problem encountered in epistemology is that of defining knowledge.

What is knowledge?

Much of the time, philosophers use the tripartite theory of knowledge, which analyses knowledge as justified true belief, as a working model.

the tripartite theory of knowledge - There is a tradition that goes back as far as Plato that holds that three conditions must be satisfied in order for one to possess knowledge. This account, known as the tripartite theory of knowledge, analyses knowledge as justified true belief. The tripartite theory says that if you believe something, with justification, and it is true, then you know it; otherwise, you do not. Belief The first condition for knowledge, according to the tripartite theory, is belief. Unless one believes a thing, one cannot know it. Even if something is true, and one has excellent reasons for believing that it is true, one cannot know it without believing it. Truth The second condition for knowledge, according to the tripartite theory, is truth. If one knows a thing then it must be true. No matter how well justified or sincere a belief, if it is not true that it cannot constitute knowledge. If a long-held belief is discovered to be false, then one

must concede that what was thought to be known was in fact not known. What is false cannot be known; knowledge must be knowledge of the truth. Justification The third condition for knowledge is justification. In order to know a thing, it is not enough to merely correctly believe it to be true; one must also have a good reason for doing so. Lucky guesses cannot constitute knowledge; we can only know what we have good reason to believe.

From where do we get our knowledge? A second important issue in epistemology concerns the ultimate source of our knowledge. There are two traditions: empiricism, which holds that our knowledge is primarily based in experience, and rationalism, which holds that our knowledge is primarily based in reason. Although the modern scientific worldview borrows heavily from empiricism, there are reasons for thinking that a synthesis of the two traditions is more plausible than either of them individually. empiricism - Empiricism is the theory that experience is of primary importance in giving us knowledge of the world. Whatever we learn, according to empiricists, we learn through perception. Knowledge without experience, with the possible exception of trivial semantic and logical truths, is impossible. Classical Empiricism Classical empiricism is characterised by a rejection of innate, in-born knowledge or concepts. John Locke, well known as an empiricist, wrote of the mind being a tabula rasa, a “blank slate”, when we enter the world. At birth we know nothing; it is only subsequently that the mind is furnished with information by experience. Radical Empiricism In its most radical forms, empiricism holds that all of our knowledge is derived from the senses. This position leads naturally to the verificationist principle that the meaning of statements is inextrically tied to the experiences that would confirm them. According to this principle, it is only if it is possible to empirically test a claim that the claim has meaning. As all of our information comes from our senses, it is impossible for us to talk about that which we have not experienced. Statements that are not tied to our experiences are therefore meaningless. This principle, which was associated with a now unpopular position called logical positivism, renders religious and ethical claims literally nonsensical. No observations could confirm religious or ethical claims, therefore those claims are meaningless. Radical empiricism thus requires the abandonment of religious and ethical discourse and belief. Moderate Empiricism More moderate empiricists, however, allow that there may be some cases in which the senses do not ground our knowledge, but hold that these are exceptions to a general rule. Truths such as “there are no four-sided triangles” and “7+5=12” need not be investigated in order to be known, but all significant, interesting knowledge, the empiricist claims, comes to us from experience. This more moderate empiricism strikes many as more plausible than its radical alternative. rationalism - Rationalism holds, in contrast to empiricism, that it is reason, not experience, that is most important for our acquisition of knowledge. There are three distinct

types of knowledge that the rationalist might put forward as supporting his view and undermining that of the empiricist.

First, the rationalist might argue that we possess at least some innate knowledge. We are not born, as the empiricist John Locke thought, with minds like blanks slates onto which experience writes items of knowledge. Rather, even before we experience the world there are some things that we know. We at least possess some basic instincts; arguably, we also possess some innate concepts, such as a faculty for language.

Second, the rationalist might argue that there are some truths that, though not known innately, can be worked out independent of experience of the world. These might be truths of logic or mathematics, or ethical truths. We can know the law of the excluded middle, answers to sums, and the difference between right and wrong, without having to base that knowledge in experience. Third, the rationalist might argue that there are some truths that, though grounded in part in experience, cannot be derived from experience alone. Aesthetic truths, and truths about causation, for instance, seem to many to be of this kind. Two people may observe the same object, yet reach contradictory views as to its beauty or ugliness. This shows that aesthetic qualities are not presented to us by our senses, but rather are overlaid onto experience by reason. Similarly, we do not observe causation, we merely see one event followed by another; it is the mind, not the world, that provides us with the idea that the former event causes the latter. How are our beliefs justified? There are better and worse ways to form beliefs. In general terms, it is important to consider evidence when deciding what to believe, because by doing so we are more likely to form beliefs that are true. Precisely how this should work, when we are justified in believing something and when we are not, is another topic in the theory of knowledge. The three most prominent theories of epistemic justification are foundationalism, coherentism, and reliabilism. foundationalism - If we think of epistemic justification in inferential terms, i.e. in terms of a belief being justified by being inferred from other justified beliefs, then we face a problem: on this account, for every justified belief there must be at least one other justified belief on which it is based, which must in turn be based on at least one other justified belief, and so on. If all of our beliefs are justified in this way, therefore, then there must be an infinite regress of justified beliefs. This implication of the idea that all of our beliefs are inferentially justified has struck many as implausible, if not incoherent. Clever though human beings may be, our intellects are finite; we do not seem to have the capacity to execute an infinite chain of inferences. The problem of avoiding this implication has become known as the regress problem of justification. Foundationalism is a response to this problem, an attempt to halt the regress of justification. The foundationalist seeks avoid the regress problem by positing the existence of foundational or “basic” beliefs. Basic beliefs are non-inferentially justified, i.e. they are justified without being inferred from other beliefs. As basic beliefs are justified, they are able to confer justification onto other beliefs that can be inferred from them. As basic beliefs are justified non-inferentially, however, they halt the regress of justification; we need not posit an infinite series of justified beliefs on which basic beliefs are based, because basic beliefs are self-justifying, and so need no such series. According to foundationalism, the justification for all of our beliefs is ultimately derived from the basic beliefs that act as the foundation for all that we know.

epistemic justification - Justification, according to the tripartite theory of knowledge, is the difference between merely believing something that is true, and knowing it. To have knowledge, on this account, we must have justification. How our beliefs are justified is among the central questions of epistemology. Inferential Justification Having justification for our beliefs is, plausibly, about having good reasons to think that they are true. For a belief to be justified, it seems, it must be inferred from another belief. This type of justification is called inferential justification. It seems that three conditions must be met for a belief to be inferentially justified. First, there must be some other idea that supports it. This other idea need not establish what is believed with absolute certainty, but it must lend some degree of support to it, it must render the belief probable. Without a supporting idea, there can be no inferential justification. Second, we must believe that this other idea is true. It is not enough for justification that there be another idea that supports our belief; if we thought that that other idea were false then it could not possibly help to justify our belief. Inferential justification, therefore, requires the existence of a supporting idea that is believed to be true. Third, we must have good reason for believing that this supporting idea is true. If we irrationally believe the supporting idea, then that irrationality will transfer to the belief that we base upon it; a belief can only be as justified as are the other beliefs on which it is based. For a belief to be inferentially justified, therefore it must be based in a supporting idea that is believed to be true with justification. coherentism - Coherentism is a rival theory of justification to foundationalism. Unlike foundationalists, coherentists reject the idea that individual beliefs are justified by being inferred from other beliefs. Instead, according to coherentism, whole systems of beliefs are justified by their coherence. What is Coherence? Coherence consists of three elements. A belief-set is coherent to the extent that it is consistent, cohesive, and comprehensive. Consistency A belief-set is consistent to the extent that its members do not contradict each other. Clearly a belief-set full of contradictory beliefs is not coherent. Consistency, however, need not be an all or nothing affair; beliefs may be in tension with each other, without being strictly speaking contradictory. Tensions of this kind, like contradiction, reduces the coherence of a set of beliefs. Cohesiveness Mere consistency is not enough for coherence. For a belief-set to be coherent, the beliefs that it contains must not only be mutually consistent, but must also be mutually supportive. A set of beliefs that support each other, where one belief makes another more probable, is more coherent than a set of unrelated, but consistent beliefs. Comprehensiveness Finally, coherence involves comprehensiveness. Comprehensiveness, of course, is a not a part of the meaning of coherence in the ordinary sense. In the context of coherentist

theories of justification, however, a belief-set increases in coherence as it increases in scope; the more a belief-set tells us about, the more coherent it is. reliabilism - Reliabilism is an alternative theory of justification to foundationalism and coherentism. According to reliabilism, whether or not a belief is justified is not determined by whether or not it is appropriately related to other beliefs. Rather, according to reliabilism, a belief is justified based on how it is formed. There are good and bad ways to go about forming beliefs. Beliefs based on reliable belief-forming mechanisms are likely to be true. Beliefs based on unreliable belief-forming mechanism are not. The reliabilist holds that a belief’s justification depends on whether it is formed using a reliable or an unreliable method: If perception is a reliable method for forming beliefs, then beliefs based on perception are justified. If wishful thinking is a reliable method for forming beliefs, then beliefs based on wishful thinking are justified. Conversely, if either of these methods of belief-formation is unreliable, then beliefs based on them will be unjustified. Reliabilism is an externalist theory of justification. Whereas internalist theories hold that justification is determined by states internal to the believer, states to which the believer has infallible access, externalism holds that it is not. If we cannot know whether a belief-forming method is reliable, then we cannot know whether our beliefs formed in that way are justified; nevertheless, on reliabilism, if it is then they are justified, and if it is not, then they are not. How do we perceive the world around us? Much of our knowledge, it seems, does come to us through our senses, through perception. Perception, though, is a complex process. The way that we experience the world may be determined in part by the world, but it is also determined in part by us. We do not passively receive information through our senses; arguably, we contribute just as much to our experiences as do the objects that they are experiences of. How we are to understand the process of perception, and how this should effect our understanding of the world that we inhabit, is therefore vital for epistemology. Do we know anything at all? The area of epistemology that has captured most imaginations is philosophical scepticism. Alongside the questions of what knowledge is and how we come to acquire it is the question whether we do in fact know anything at all. There is a long philosophical tradition that says that we do not, and the arguments in support of this position, though resisted by most, are remarkably difficult to refute. The most persistent problem in the theory of knowledge is not what knowledge is or what it comes from, but whether there is any such thing at all. philosophical scepticism - There is much in life that is open to doubt. Ordinarily, we confine our doubts to specific questions; though we may doubt particular beliefs and ideas, we generally take it for granted that the majority of our beliefs are accurate. Philosophical scepticism, unlike ordinary scepticism, doubts whole categories of beliefs. Most influential has been external-world scepticism, which doubts the existence of the physical world around us.

There are several different sceptical arguments, and a number of responses to scepticism, available. The problem of dismissing scepticism and vindicating common beliefs remains a live issue in philosophy, however.

sceptical arguments - The philosopher best known for his scepticism is Rene Descartes. Descartes’ main legacy to philosophy was doubt. Ironically, Descartes himself was not a sceptic; though he proposed various sceptical arguments that have subsequently proved difficult to refute, Descartes offered responses to each of them. These responses, however, have convinced few; it is his sceptical arguments that have had the greatest impact on philosophy. Descartes’ doubt, set out in his Meditations on First Philosophy, comes in three waves. In the first wave of doubt, Descartes advances the argument from error, arguing that as our senses have led us astray before we should not trust them in future. In the second wave, he advances the argument from dreaming, arguing that all of our experiences are as consistent with the hypothesis that we are dreaming as they are with the hypothesis that we are awake, and so we cannot know which hypothesis is true. In the third wave, he advances the argument from deception, invoking the idea of an evil demon constantly deceiving us as a troubling hypothesis that cannot easily be dismissed. responses to scepticism - Though sceptical arguments are very rarely judged to be persuasive, they are notoriously difficult to refute. Perhaps the most straightforward attempt to refute philosophical scepticism is GE Moore’s appeal to common sense. Moore’s attempt begins with a simple argument: (1) Here is a hand, (2) Here is another, therefore (3) External objects exist. This argument may appear to be question-begging, but there is more to it than meets the eye. Gilbert Ryle’s counterfeit coinage argument offers an alternative solution to the problem of scepticism. Ryle argues that scepticism, at least in its strongest forms, is incoherent. We can only make sense of the idea of false experience if there are also some true experiences to which they can be compared. JL Austin’s linguistic argument is a response specifically to the argument from dreaming. That argument assumes that we cannot tell the difference between dreaming experiences and waking experiences. Austin argues that the fact that we use the phrase “a dream-like quality” shows that this assumption is false. David Lewis’s contextualism makes a partial concession to scepticism. Contextualism suggests that the quality of evidence required for knowledge vary with context. Once sceptical doubts have been raised, it concedes, and the context changed, those doubts cannot be answered. This, however, doesn’t change the fact that in normal circumstances and by normal standards we do have knowledge.

What is Logic? The term “logic” came from the Greek term logike which means “thought” thus, etymologically, Logic means a “treatise pertaining to thought”. It was the Philosopher, Zeno the Stoic who first coined the word “Logic”. Aristotle in his books on Analytics considered Logic as the “organon” or the tool or instrument of the sciences. For him, Logic is the instrument for gaining knowledge or the tool for correct thinking. Real definition: Logic is commonly defined as the science of correct inferential thinking. It deals with the laws, methods and principles of correct thinking. It is the study of methods and principles used to distinguish correct reasoning from incorrect reasoning. Thus it provides us with the techniques for testing the correctness (also the incorrectness) of arguments. It is a science because it is a systemized body of knowledge about the principles and laws of correct inferential thinking. It follows certain rules and laws in arriving at valid conclusions. It is also considered as art, the art of reasoning. As a art it requires mastery of the laws and principles of correct inferential thinking. Through logic we acquire the techniques and skill of thinking correctly whereby our mind is able to proceed with order, ease and is able to avoid error. Aristotle – father of logic Formal logic- discusses the conceptual patterns or structure needed for a valid and correct argument or inference. Deals with correct and valid patterns of argumentation. Material Logic- deals with the nature of the terms and propositions that are used in the different types of inference. It discusses the types and meaning of the terms or words and sentences or propositions used tin the argument. Logic and the Intellect and its Operations Aristotelian Logic divided into three mental operations or acts of intellect: Simple Apprehension ; Judgment ; Reasoning The mental product of simple apprehension is the idea, while enunciation is the mental product of judgment and argumentation is the mental product of reasoning. These mental products are externally manifested or expressed by their externeal signs. External sign of idea is the term, while proposition manifests for enunciation and syllogism manifests for argumentation.

Reasoning It is the supreme or the highest operation of man, all his operations and powers reach their culmination in reasoning and it is this ability to think and to reason that differentiate man form other mortal beings.

2 Kinds of Reasoning: Deduction and Induction Deduction - is a process of reasoning which proceeds from universal or general laws and principles to specific or particular instances. Induction – is a process of reasoning which proceeds from specific or particular instances to the formulation of universal or general laws and principles. It concludes from particular to universal.

What is Deductive Reasoning? Is a process of reasoning which proceeds from universal or general laws, principles or statements to particular instances or propositions. An argument is deductive when the truth of its premises is intended to guarantee the truth of its conclusion. The conclusion is already implied in the premises, hence if the premises are true the conclusion becomes necessarily true. Eg.) All law school students are college degree holders, but high school students are not students of the law school, then they are not college degree holders.

What is Inductive Reasoning? A process of reasoning which proceeds from specific or particular instances to the formulation of general or universal principles or statements. When the truth of the premises is intended to make likely/probably the truth of its conclusion. Eg.) When Jane had a racquet in her hand, was coming from tennis court. Dressed in tennis outfit, was perspiring heavily and was talking about a game with somebody, then it is likely that she been playing tennis.

What is Modus Ponens?

Modus ponendo ponens, usually simply called modus ponens or MP is a valid argument form inlogic. It is also known as "affirming the antecedent" or "the law of detachment".

The form of modus ponens is: "If P, then Q. P. Therefore, Q." It may also be written as:

P → Q, P Q

Examples of modus ponens

The following are examples of the modus ponens argument form:

If the cake is made with sugar, then the cake is sweet. The cake is made with sugar. Therefore, the cake is sweet.

If Sam was born in Canada, then he is Canadian. Sam was born in Canada. Therefore, Sam is Canadian.

Conditional elimination

Modus ponens, as a valid argument form, also serves as the basic conditional elimination rule (→E), one of the basic rules of inference, and may be labeled as such where appropriate.

rules of inference - The rules of valid inference are a set of laws by which the syntax of statements in a system of logic, such as propositional or first-order logic, may be manipulated.

Rules of inference are, in themselves, simple valid argument forms. They may be divided into basic rules, which are fundamental to logic and cannot be eliminated without losing the ability to express some valid argument forms, and derived rules, which can be proven by the basic rules and serve as shortcuts for logicians when constructing a logical argument or proof.

valid argument forms - A valid argument form is one that produces true conclusions if the premises provided to it are true. In logic, argument forms serve to provide and verify the structures of arguments that are valid, in order to facilitate the formation of valid arguments in language.

What is a Proposition?

It is defined as a judgment expressed in sentence or a sentence pronouncing the agreement or disagreement between terms. A proposition as an assertion or statement always makes a claim about a subject matter.

A Proposition is always a sentence. A sentence is string of words constructed in accordance with grammatical rules of language, which can be used for such purpose as asserting, asking or commanding.

Types of Proposition (Aristotelian)

Categorical – expresses a direct judgment or a direct assertion of the agreement or disagreement of two terms in an absolute manner. It is regarded as assertoric.

Eg.) A book is useful. ; The weather is fine.

Hypothetical – does not express a direct judgment, rather a relation between two judgments, in which the truth of one depends on the other.

Eg.) If there is no typhoon the weather is fine.

What is Predicate Logic?

- also known as “first-order logic” - a statement has a specific inner structure, consisting of terms and predicates.

Terms denote objects in some reality, and predicates express properties of, or relations between those objects. For example, the same example as before might be expressed as Locked(d) → ¬At Home(a). Here, Locked and At Home are predicates ,and d and a are terms, all with obvious meanings.

- assumes that the world consists of individual objects which may have certain properties and between which certain relations may hold (the general name for a property or a relation is predicate). Besides, there are operations which may be performed on these objects, the result of which is an object in the world again. For example, if the objects in the world are individual human beings, then there might be predicates like “male”, “female”, “older-than”,“married-to”. Note that the first two examples are about one person, the others about two. An example of an operation on human beings is “father-of”. applying this operation to an individual delivers the father of that individual1 distinguishing separate objects in the world gives the possibility to quantify over these objects, i.e., to make statements about all or some objects. In higher order predicate logic it is also possible to speak about all (or some) sets of objects, such as all families, some school classes. We restrict ourselves to first order logic in which one can only quantify over the individual objects themselves.

What is Philosophical Logic?

Philosophical logic, despite its name, is not a kind of logic, nor is it simply to be identified with the philosophy of logic. The philosophy of logic (or logics) is the philosophical examination of systems of formal logic and their applications and although this overlaps with philosophical logic in certain ways, the two fields of study are nonetheless distinct in their subject matter and methods. The subject matter of philosophical logic is, indeed, hard to

define precisely, partly because it encroaches upon many other areas of philosophy�such as

metaphysics, epistemology, the philosophy of mind and the philosophy of language�and partly because it is not immediately obvious what connects all the topics that philosophers have traditionally addressed under the heading of 'philosophical logic'. However, one quite appealing way to unify these topics under this heading is to describe philosophical logic as the philosophical elucidation of those notions that are indispensable for the proper characterisation of rational thought and its contents. The notions in question are ones like those of reference, predication, identity, truth, negation, quantification, existence, necessity, definition and entailment. These and related notions are needed in order to give adequate

accounts of the structure of thoughts�particularly as expressed in language�and of the relationships in which thoughts stand both to one another and to objects and states of affairs in the world. However, it must be emphasized that philosophical logic is not really concerned

with thought insofar as thought is a psychological process�that, rather, is the province of

empirical psychology and the philosophy of mind�but only insofar as thoughts have contents which are evaluable as true or false. To conflate these two concerns is to fall into the error of psychologism, much decried by Gottlob Frege, arguably the founding father of modern philosophical logic.

Even if this definition of philosophical logic may be implicitly accepted by most of its current practitioners, no single way of dividing up its subject matter would be agreed upon by all them. However, one convenient division, which I shall adopt here, is the following. I propose to divide the subject.into five major areas, the first two of which, being the most fundamental, will occupy most of our time: (1) theories of reference, (2) theories of truth, (3) problems of logical analysis (for example, the problems of analysing conditional and existential statements), (4) problems of modality (that is, problems concerned with necessity, possibility and related notions), and (5) problems of rational argument. These areas inevitably overlap to some extent, but it is roughly true to say that topics covered later in the list presuppose those covered earlier to a greater degree than earlier ones presuppose later ones. This is because the order in which the areas are listed reflects a general progression from the study of parts of propositions, through the study of whole and compound propositions, to the study of relations between propositions. (Here and throughout I use the

term 'proposition' to denote a thought-content evaluable as true or false�something expressible by a complete sentence.) Let us make a start, then, with theories of reference.

Theories of reference

Theories of reference are primarily concerned with the relationships between sub-propositional or sub-sentential parts of thought or speech and extra-mental or extra-

linguistic entities�for instance, with the relationship between names and things named, and with the relationship between predicates and the properties they express or the items to

which they apply. These entities may accordingly be called the 'references' of the parts of thought or speech in question. Another term sometimes used in place of 'reference' in this sense is 'semantic value': this has the advantage of being less suggestive that a word or phrase must refer to a thing-like entity, in the way that names characteristically do. Clearly, names are amongst the earliest and most important words we learn to use, so it is unsurprising that philosophers sometimes fall prey to the temptation of modelling the function of other parts of speech upon names. But while this temptation must be resisted, it is still proper and natural for a theory of reference to begin with a theory of naming. According to some theories, as we shall see, a name refers to a particular thing by virtue of its being associated with some description which applies uniquely to that thing. Other theories hold that the link between name and thing named is causal in nature. Theories of both sorts are intimately bound up with questions concerning identity and individuation, to which we shall turn in due course. Shortly we shall examine theories of naming in some detail, but before doing so let us look briefly at predicates.

It has generally been accepted, following the seminal work of Frege (1892a) on the distinction between (what he called) 'concept' and 'object', that predicates need to be clearly distinguished from names in the way they function. A predicate may roughly be thought of as what remains when one or more names are deleted from a sentence. For instance, the

(monadic, or one-place) predicate '�is red' may be formed by deleting the name 'Mars' from

the sentence 'Mars is red', and the (dyadic, or two-place) predicate '�is north of ...' may be formed by deleting the names 'Edinburgh' and 'London' from the sentence 'Edinburgh is north of London'. Frege's point is that a predicate, unlike a name, is an 'unsaturated' expression (it has, as it were, one or more 'gaps' in it), and consequently it cannot function as the logical subject of a sentence. He held that names, and only names, refer toobjects. Indeed, in effect he defines an 'object' as something which can be referred to by a

name�understanding 'name' in a fairly broad sense to embrace all singular terms. By

contrast, he took the reference of a predicate to be a concept�which, for the anti-psychologistic Frege was not something mental, but rather an abstract entity, the sort of entity that other philosophers would call a property or universal. On this view, the reference

of the predicate '� is red' is the property of being red. An alternative view, favoured by some nominalistically minded philosophers, is to take the reference of a predicate to be

a class or set�namely, the class or set of things to which the predicate applies, or of which it is true, such as the class of red things. However, since classes or sets are themselves objects, this view may perhaps be criticized for assimilating predicates too closely to names. Another nominalistically acceptable alternative, which avoids this problem, is to take the reference of

a predicate to be, quite simply, all the things to which it applies, or of which it is true�thus,

all red things, in the case of the predicate '� is red' (cf. Quine 1995, p. 60). I shall not attempt to adjudicate between these alternatives here, though my own sympathies lie with Frege's view.

But let us now turn back to names. In a very broad sense of the term 'name', names

traditionally divide into two classes�proper names and common names, these being species of singular and general terms respectively. Proper names are names of individuals, examples being 'London', 'Mars' and 'Napoleon', whereas common names are naturally thought of as being names of kinds of individuals, examples being 'city', 'planet' and 'man'. Since Frege, however, orthodox logic has tended to assimilate common names to predicates, only

recognizing their occurrence in expressions of the form '� is an F' (where 'F' is a common

name), rather than allowing them (as Aristotelian logic did) to function as logical subjects in their own right. Thus, whenever a common name appears to function as a logical subject, as in the sentence 'Man is a rational animal', current logical orthodoxy holds that it may be

removed to predicate position by paraphrase�so that, for instance, the underlying 'logical form' of the sentence just cited is taken to be 'Anything which is a man is a rational animal',

in which the common name 'man' now only appears as part of the predicate '�- is a man'. This idea that the 'real' logical form of many sentences in natural language is not perspicuously displayed by their overt grammatical form is a persistent theme in modern

philosophical logic�though perhaps one that needs to be challenged more than it presently is (cf. Somers 1982).

Frege apart, most philosophers would not classify all singular terms indiscriminately as proper names (what he called Eigennamen). For instance, they would not describe pronouns such as 'I' and 'he' as being proper names, nor demonstrative noun phrases such as 'this city' and 'that man', nordefinite descriptions such as 'the Prime Minister

of the U.K'. Similarly, not all general terms are common names�for instance, adjectival or characterizing general terms such as 'red' and 'circular' are not, nor are abstract nouns such as 'redness' and 'circularity' (if indeed the latter are deemed to be general terms, for an alternative view is that they are singular terms referring to abstract individuals). The

distinguishing feature of common names�sometimes also

called substantival or sortal general terms�is that they have associated with them, as a component of their meaning, a criterion of identity for the individuals to which they apply (see Lowe 1989, Ch. 2). A criterion of identity for individuals of a kind K is a principle which determines, for any individuals x and y of kind K, whether or not x and y are one and the same K. Thus, the criterion of identity forcities tells us that Paris and London are different cities, since they occupy different locations; and the criterion of identity for rivers tells us that the Isis and the Thames are the same river, since they flow from the same source to the same mouth. Different kinds of individuals, denoted by different sortal terms, very often have

different criteria of identity governing them�and in some cases there is philosophical debate as to precisely what these criteria are (for example, in the case of persons). Credit is once more due to Frege for recognizing the important role that criteria of identity have to play in the semantics of sortal terms.

Recently, philosophical debate has focused on proper names much more than on common names (apart from the special case of natural kind terms). A prominent issue has been whether such names have not only references but also senses, as Frege believed, or whether they are purely referential devices, as John Stuart Mill held and as Saul Kripke now contends. An implication of the latter position is that proper names do not have linguistic meanings specifiable by way of definition. This would appear to be confirmed by the fact that one does not find proper names defined in dictionaries. As Mill pointed out, a proper name such as 'Dartmouth', even though its etymology implies that it denotes a town situated at the mouth of the river Dart, would continue to refer to that same town even if the river mouth were to move several miles further down the coast (Mill 1843, Bk I, Ch. II). Accordingly, 'Dartmouth' cannot be defined as meaning 'the town situated at the mouth of the Dart'. Mill consequently held that proper names have only denotation (that is, reference), whereas common names have both denotation and connotation, the latter being a set of defining characteristics for bearers of the name, such as might be found in a dictionary definition of that name.

Frege's claim that proper names have not only reference but also what he called 'sense' draws sustenance from the fact that a true identity statement involving two different proper

names�for instance, 'George Eliot is Mary Ann Evans'�can be informative, which seems to imply that it expresses a different proposition from that expressed when one of those names is merely repeated, as in the trivially true sentence 'George Eliot is George Eliot' (see Frege 1892b). Frege's explanation of this phenomenon is that although the names 'George Eliot' and 'Mary Ann Evans' have the same reference(they refer to one and the same person), they nonetheless have different senses, and according to Frege the proposition (or, as he called it, the 'thought') expressed by a sentence is a function of the senses of the words composing it. (Indeed, for Frege, a 'thought' just is the sense of a meaningful sentence.) By the 'sense' of a proper name, Frege means, as he puts it, that name's 'mode of presentation' of its reference. Often, this 'mode of presentation' will be captured by some definite description, or conjunction of definite descriptions, which a user of the name associates with it and which determines the reference of that name as used by that speaker. For example, speakers may associate with the name 'George Eliot' the definite description 'the author of the novels Middlemarch and Adam Bede', whereas with the name 'Mary Ann Evans' they may associate a quite different description, not realizing that the woman in question was an author who adopted a male pen name. So although these two descriptions may in fact be true of precisely the same individual, users of the two names need not be aware of this fact. This, then, according to Frege, is why a speaker can know that 'George Eliot is George Eliot' is true even while failing to know that 'George Eliot is Mary Ann Evans' is true: the two sentences, though both true, express different thoughts or propositions. Indeed, for Frege, the criterion of identity for thoughts is just this: two sentences express the same thought just in case no rational speaker who understands both of them can judge one to be true and the other false.

Against this Fregean position, Kripke (1980) plausibly argues that speakers can successfully use proper names to refer to individuals about whom they possess no uniquely identifying information. For instance, a speaker may know, and assert, that Kurt Gödel proved the incompleteness of arithmetic even though he or she cannot clearly differentiate in thought between Gödel and many other eminent logicians. However, a Fregean 'sense' is supposed to provide just such identifying information about, or a 'mode of presentation' of, its

reference�and the Fregean view is that if a speaker is to grasp the thought expressed by the sentence 'Kurt Gödel proved the incompleteness of arithmetic', then he or she must grasp the sense of the name 'Kurt Gödel', since the thought expressed contains that sense as a component. Hence Frege must say, implausibly, that a speaker who lacks uniquely identifying information about Kurt Gödel cannot so much as have the thought that Kurt Gödel proved the incompleteness of arithmetic. By this standard, it seems, very few of us have much in the way of historical or geographical knowledge, since we would be hard put to supply uniquely identifying information about many of the individual people and places we commonly seem to converse about. Kripke's conclusion is that knowledge of uniquely identifying information about the reference of a name, in the form of a definite description applying solely to that individual, is not necessary in order for a speaker to be able to use that name successfully in referring to that individual. This then raises the question of how proper names refer, if they do not refer in virtue of their references fitting descriptions associated with the names. It also raises the question of how Frege's puzzle about informative identity statements is to be solved, if not by maintaining that proper names have sense as well as reference.

For Kripke, the reference of a name is secured not by some Fregean 'sense' which a speaker attaches to it but rather by an external causal chain linking the speaker's use of a name to an original 'baptism' in which the name was first assigned to a certain individual. As the name is passed on from speaker to speaker, all that is required for a later recipient of the name to use it successfully to refer to the individual originally named by it is that each speaker in the chain should use it with the intention to refer to the same individual as it was used to refer to by the speaker from whom he received the name. Thus, if someone quite ignorant of the history of logic overhears some logicians in a restaurant talking about Kurt Gödel's achievements, that person may subsequently report, quite truthfully, that Kurt Gödel proved the incompleteness of arithmetic, provided only that she intends to use the name 'Kurt Gödel' to refer to the same individual as was being referred to by the logicians: she need not know anything further about Gödel, and in particular need not be able to identify him uniquely. It will not do to object here that she at least knows, now, that Kurt Gödel proved the incompleteness of arithmetic, and so can identify him uniquely: for more than one person can prove something like this, even though Gödel was in fact the first to do so, so far as we know.

Suppose, however, that the logicians in the restaurant had been overheard to say that Gödel was the first person to prove the incompleteness of arithmetic: in that case might not the person overhearing them be taken to understand the name 'Kurt Gödel' as having a Fregean sense captured by the definite description 'the first person to prove the incompleteness of arithmetic'? Kripke's answer to this question is 'No', for the following reason. Suppose, after all, that the widespread belief that Kurt Gödel was the first person to prove the incompleteness of arithmetic is mistaken, perhaps because Gödel secretly stole the proof from another, little-known logician, Schmidt. In that case, those who hold that the person overhearing the logicians' conversation now uses the name 'Kurt Gödel' as having a Fregean sense captured by the definite description 'the first person to prove the incompleteness of arithmetic' are compelled to say that when this person uses this name she refers to Schmidt rather than to Gödel, and this seems absurd. Thus, it seems, not only is a speaker's association of a name with a uniquely identifying description of a certain object not necessary for his or her successful use of that name to refer to that object, neither is it sufficient for this. For the speaker in our imagined case associates the name 'Kurt Gödel' with a definite description which in fact applies to someone else, the little-known Schmidt, and yet plainly does not refer to Schmidt when using that name.

Another important feature of Kripke's theory of names is that he holds them to be (what he calls) rigid designators. What he means by this is that they do not alter their reference when used in modal and counterfactual contexts. In the terminology of 'possible worlds' (of which more later), a proper name refers to the same individual in every possible world in which it refers to anything at all. Because definite descriptions are, for the most part, non-rigid designators, Kripke uses this difference between the logical behaviour of names and descriptions as further evidence against the view that names have descriptive 'senses'. For example, suppose it were maintained that the proper name 'Mars' has as its sense something like 'the fourth nearest planet to the sun'. Now, we can imagine a counterfactual situation in which, perhaps as a result of some cosmic catastrophe, Mars is pushed out of its present orbit to one beyond Jupiter's. In that case, however, Mars would not cease to be Mars, even though it would cease to be the fourth nearest planet to the sun, a description which would now apply to Jupiter instead. It is hard, then, to see how the proper name 'Mars' can simply

be identical in sense with the definite description 'the fourth nearest planet to the sun', since the latter, unlike the former, designates different objects in different possible worlds. Similar objections can be raised against identifying the supposed sense of the name 'Mars' with that of almost any other definite description. However, a proponent of the view that names have descriptive senses has a possible line of reply to this objection: one could urge that the

descriptions associated with names are always implicitly rigidified�that, for instance, the name 'Mars' has as its sense the sense of the definite description 'the planet which is actually (that is, in this possible world) the fourth nearest to the sun'. Then, even when we envisage a world in which Mars ceases to be the fourth nearest planet to the sun, we could still be thinking of it as the planet which in this, the actual world, is the fourth nearest. Consequently, Kripke's arguments against descriptive theories of names on the basis of the way in which names behave in modal and counterfactual contexts are not quite as compelling as his other arguments (cf. Dummett 1981, pp. 126-8, where much the same point is made in terms of the scope of a description).

Despite their intuitive plausibility, so-called 'causal' or 'direct' theories of reference like Kripke's are not without their problems. One important line of objection, made prominent by Gareth Evans (1973), is that such a theory cannot easily accommodate some of the ways in which names change their reference over time. Consider, for instance, the case of identical twin boys, baptized 'Thomas' and 'Henry' at birth, but a few weeks afterwards accidentally switched in their cots, so that the child baptized 'Thomas' is thought by everyone to be Henry and the child baptized 'Henry' is thought by everyone to be Thomas. Before the switch, the names 'Thomas' and 'Henry' were passed on from speaker to speaker in the way Kripke prescribes, that is, with each new speaker intending to use each name to refer to the same child as it was used to refer to by the speaker from whom he or she received the name, and this process carries on undisrupted after the switch. It seems, then, that according to Kripke's theory, whenever someone uses the name 'Thomas' after the switch, he or she is still referring to the child originally baptized 'Thomas'. Consequently, almost all of the beliefs that such a speaker expresses using the name 'Thomas' will be false, by Kripke's account, and this seems absurd. For instance, when the speaker asserts, on the basis of direct observation, that Thomas is sitting in a certain chair, this will be false, because in fact the child that was baptized 'Henry' will be sitting there. Surely there must come a point, sometime after the switch, at which 'Thomas' comes to refer to the child originally baptized 'Henry', even though no new baptismal ceremony has been performed? For Evans, the lesson to be drawn from this sort of example is that the link between a name and the thing named is mediated by information which a user of the name associates with the name, even if not in quite the way supposed by the 'descriptive' theory of names so forcefully attacked by Kripke. Evans's suggestion is that a speaker associates with a name a certain 'dossier of information'. More than one thing may in fact 'fit' this information (so the information need not take the form of a uniquely satisfiable definite description), but the thing which is referred to by the speaker when he or she uses the name is the thing which is the dominant causal source of that information for the speaker at the time of speaking. Thus Evans's account is neither purely descriptive nor purely causal, but appeals to both kinds of consideration. It is able to overcome the problem of reference-change, as presented in the example of Thomas and Henry, by pointing out that the dominant causal source of the information which a speaker associates with a name may change over time, even though the speaker himself may be unaware of this fact.

Another apparent difficulty for the 'direct' theory of reference is that it seems to leave Frege's puzzle about informative identity statements unresolved. Frege's explanation was that the identity statements 'George Eliot is George Eliot' and 'George Eliot is Mary Ann Evans' express different propositions, or 'thoughts', because the two different names involved have different senses, and the sense of a name is a component of the proposition expressed by a sentence containing that name. However, if names are denied to have 'senses', then it seems that we must say that these two identity sentences express the same proposition: but then how can a speaker who understands both sentences believe one to be true and the other false? It seems that a proponent of the 'direct' theory of reference must claim that a speaker who understands the linguistic meaning of a sentence need not thereby know what proposition that sentence expresses. This claim is not as implausible as it might first appear to be, as can be seen from a consideration of sentences containing demonstrative or indexical expressions, such as 'that' and 'I'. Consider the two sentences 'That person is fat' and 'I am fat'. One and the same speaker could, on the same occasion, assert the first sentence and yet deny the second, even while referring to the same thing by the expressions 'that person' and 'I'. For example, while thinking of himself as slim, the speaker might see a reflection of himself in a mirror and refer to the evidently fat person seen there as 'that person', not realizing it to be himself. There is no failure of linguistic understanding on the part of this speaker. What we perhaps have to say, along lines suggested by David Kaplan (1977), is that the proposition expressed by a speaker's utterance of a sentence on a given occasion is a function of both the sentence's linguistic meaning and the context of utterance. Hence, knowledge of a sentence's linguistic meaning alone need not suffice for knowledge of what proposition that sentence expresses on a given occasion of use. Frege would have to reply that, in the case just described, the two sentences 'That person is fat' and 'I am fat' express different propositions, or 'thoughts'. But the implication of this is that the first-person pronoun, 'I', as used by a given speaker, has a unique and incommunicable sense which is distinct from the sense of any other singular term which that speaker, or any other speaker, can use to refer to that speaker. For it is always possible for a rational speaker to deny 'I am fat' while asserting 'S is fat', for any singular term 'S' (other than 'I') which refers to that speaker. This is because it is always possible for such a speaker to be unaware that 'I am S' is true. Frege (1956) was himself prepared to accept that 'I' has a unique and incommunicable sense for each user of it, but this is a high price to pay for his conception of the identity-conditions of propositions, or 'thoughts'.

To conclude this discussion of theories of reference I should mention that the Kripkean account of proper names (and natural kind terms) as rigid designators is linked to certain

metaphysical doctrines of an essentialist character�notably, the theses of the necessity of

identity and of origin�because of the ways in which such names are thought to behave in modal contexts. For instance, Kripke (1980) holds that, given that George Eliot is Mary Ann

Evans, George Eliot could not have been different from Mary Ann Evans�though he deems this impossibility to be a posteriori rather than a priori. Similarly, given that George Eliot was in fact born of certain parents, he holds it be an a posteriori metaphysical necessity that she was born of just those parents. We shall return to these matters when we discuss theories of modality. Here, though, we may remark that Kripke can draw on such claims to respond to Frege's puzzle about identity in the following way: precisely because he does not think that all necessary truths are knowable a priori, he can allow that we know a priori that 'George Eliot is George Eliot' is true simply because this sentence is a logical truth, but at the same time he can allow that we at best only know a posteriori that 'George Eliot is Mary Ann

Evans' is true, even though the second sentence expresses the same necessary proposition as does the first sentence.

Theories of truth

Truth and falsehood�if indeed they are properties at all�are properties of whole sentences or propositions, rather than of their sub-sentential or sub-propositional components. Theories of truth are many and various, ranging from the robust and intuitively appealing

correspondence theory�which holds that the truth of a sentence or proposition consists in

its correspondence to extra-linguistic or extra-mental fact�to the redundancy theory at the other extreme, according to which all talk of truth and falsehood is, at least in principle, eliminable without loss of expressive power. These two theories are examples, respectively,

of substantive and deflationary accounts of truth�other substantive theories being the coherence theory, the pragmatic theory and the semantic theory, while other deflationary theories include the prosentential theory and the performative theory (which sees the truth

predicate, '�is true', as a device for the expression of agreement between speakers). However, a monolithic approach to truth, despite its attractive simplicity, may not be capable of doing justice to all applications of the notion. Thus the correspondence theory, though intuitively plausible in application to a posteriori or empirical truths, cannot be expected to accommodate a priori or analytic truths, since there is no very obvious 'fact' to which a truth such as 'Everything is either red or not red' can be seen to 'correspond'. Again, the performative theory, while attractive as an account of the use of a sentence like 'That's

true!'�uttered in response to another's assertion�has trouble in accounting for the use of the truth predicate in the antecedent of a conditional, where no assertion is made or implied. Similarly, it may be that a 'deflationary' account of truth, such as that provided by the redundancy theory, is quite well suited to explicating talk of moral or aesthetic 'truths', but less convincing when applied to talk of scientific truths, which seem to demand something more substantial (at least if one is a metaphysical realist).

The term 'truth' seems to denote a property, one which is also expressed by the truth

predicate, '�- is true'. But if so, of what is truth a property? What are the primary 'bearers' of truth, and of its counterpart, falsehood? (Whether truth and falsehood are indeed polar opposites, as the principle of bivalence implies, is itself a disputed issue.) At least three candidates can be put forward: sentences, statements and propositions. Loosely, a sentenceis a linguistic token or type, such as the string of written words 'This is red'. (The type/token distinction, which is very important for what follows, may be illustrated thus: the

next two words printed on this page�and, and�are two different tokens of the same word-type.) A statement is the assertoric use of a sentence by a speaker on a particular occasion.

A proposition is what is asserted when a statement is made�its 'content'. Thus two different speakers, or the same speaker on two different occasions, may assert the same proposition by making two different statements, perhaps using sentences of two different languages. And the same sentence (conceived of as a linguistic type) may be used in two different statements to assert two different propositions. (Here, though, we should recall from our discussion of theories of reference that there is considerable disagreement amongst philosophers concerning the identity-conditions of propositions.)

In addition to speaking of sentences, statements and propositions being true or false, we also speak of beliefs (and other so-called 'propositional attitudes') being true or false. So is the notion of truth multiply ambiguous, or is there a primary notion which attaches to just one of these classes of items? Opinions differ, but a broad division can be drawn between those theories of truth which regard truth as being primarily a property ofrepresentations of some

sort (whether linguistic or mental)�including, thus, sentences, statements and beliefs�and those which regard truth as being primarily a property of propositions, conceived of as items represented or expressed in thought or speech. Disputes between theorists of truth are sometimes confused by a failure to discern this division.

The best known theory of truth is the correspondence theory. On this view, in its classical form, a candidate for truth is true if and only if it 'corresponds to the facts'. Some objectors complain that the notion of a fact is itself only to be explained in terms of truth (suggesting, for instance, that a 'fact' can only be understood as the worldly correlate of a true sentence or proposition), so that the theory is vitiated by circularity. Others complain that the notion of 'correspondence' invoked by the theory is either vacuous or unintelligible. It is hard to say which philosophers have really held this theory. Aristotle is sometimes said to intimate allegiance to it in his famous remark in the Metaphysics that 'To say of what is that it is, or of what is not that it is not, is true', though nothing in this passage speaks directly of a 'correspondence' relation of any sort. Wittgenstein's Tractatus and Russell's lectures on logical atomism are often cited as endorsing a version of the correspondence theory, according to which 'correspondence' lies in a relationship of structural isomorphism between sentences constructed in a logically perfect language and states of affairs in the world. Even Tarski's so-called 'semantic' theory of truth (see below) has been described as a version of the correspondence theory. But in recent times one of its best-known advocates has been J. L. Austin (1970). He, however, carefully avoided stating it in terms of a correspondence between sentences or propositions and extra-linguistic facts, appreciating the philosophical difficulties which beset attempts to articulate a suitable 'correspondence' relation. But before looking at Austin's theory, something should be said about the equally grave difficulties which beset an ontology of facts. I shall restrict myself to examining what I think is the chief of these difficulties.

Facts will only serve as the truth-making correlates of sentences or propositions if they can be individuated and identified in a principled way. However, there is an important

argument�now often referred to as the 'slingshot' (Barwise & Perry 1981)�attributed by Alonzo Church (1956, p. 25) to Frege and subsequently espoused by such philosophers as Donald Davidson (1969, pp. 41-2) and W. V. Quine, the implication of which is that facts cannot be non-trivially individuated. The argument purports to show that if a 'fact' is what a true sentence or proposition 'corresponds' to, then all true sentences or propositions

correspond to the same fact�so either we should avoid an ontology of facts, or else we have to accept that there is only one fact, the 'Great Fact'. The latter position, however, is of no use to a proponent of the correspondence theory of truth, since it entirely trivializes that theory. The argument (or one version of it) goes as follows. If facts exist, and a certain sentence, P, is true, then it is surely undeniable that

(1) The fact that P is identical with the fact that P.

However, it is surely also the case that the singular term 'the fact that P' should not change its reference if we substitute for P another sentence Qwhich is logically equivalent to P, nor if we substitute for any singular term in P another singular term with the same reference. This being so, let Q be any true sentence distinct from P and let a be any arbitrarily chosen object. Then it is easily provable that P is logically equivalent to the following sentence: '{a} = {x: x = a & P}'. (This may be read in English as follows: 'The set whose sole member is a is identical with the set every member xof which satisfies the condition that x is identical with a andP is the case'.) Hence, from (1) we can deduce

(2) The fact that P is identical with the fact that {a} = {x: x = a & P}.

However, in exactly the same way it can be proved that Q is logically equivalent to '{a} = {x: x = a & Q}'. It follows that the two singular terms '{x:x = a & P}' and '{x: x = a & Q}' have the same reference, since both have the same reference as the singular term '{a}'. Accordingly, we can substitute the second of these terms for the first in (2) to give

(3) The fact that P is identical with the fact that {a} = {x: x = a & Q}.

Finally, using the already established logical equivalence between Q and '{a} = {x: x = a & Q}', we can deduce from (3)

(4) The fact that P is identical with the fact that Q.

Thus, starting out from some highly plausible assumptions and an apparently trivial premise, (1), we have been able to deduce that any two true sentences, P and Q, correspond to the same fact, if indeed facts exist. There are various ways in which one might attempt to block

this argument�for instance, by rejecting the assumption that so-called set-abstracts like '{x: x = a & P}' are genuinely singular referring terms, or by allowing that the substitution of one singular referring term for another co-referring one within P may alter the reference of the term 'the fact that P'. But none of these strategies is particularly compelling.

Frege's own conclusion from this line of reasoning (to the extent that Church is correct in attributing it to him) was that, rather than saying that every true sentence corresponds to a fact which makes it true, we should say that every true sentence has as its reference the True (and that every false one has as its reference the False). (See Frege 1892b, p. 63.) That is to say, the reference of every (assertoric) sentence is a truth value, of which there are just two. (The only exceptions to this rule, for Frege, would be assertoric sentences containing names lacking a reference, such as 'Zeus': such a sentence, he thought, must itself lack a reference and hence have no truth value.) Frege did not believe that one could define 'truth', holding it to be a primitive and irreducible notion. Of course, the idea that a sentence can have a 'reference' may seem odd, though only if we take names as our paradigms of expressions having a reference (this, then, is a case in which the term 'semantic value' may be less misleading than the term 'reference'). It should be pointed out here that between Frege's extreme of taking all true sentences to have the same reference and the opposite extreme of

taking all logically non-equivalent true sentences to 'correspond' to different 'facts' there are many intermediate positions. Consider, thus, the case of negative and disjunctive true sentences of the forms 'Not P' and 'P or Q', respectively. A correspondence theorist need not say that 'Not P' is made true by a negative fact, the fact that not P, nor that 'P or Q' is made true by a disjunctive fact, the fact that P or Q. He can say that 'Not P' is true because there is no fact that P for it to correspond to, and he can say that 'P or Q' is either made true by the fact that P or else made true by the fact that Q. Thus, on this view, logically non-equivalent true sentences can, but need not, have the same 'truth-makers'.

At this point we should advert briefly to Austin's version of the correspondence theory, which appeals to a distinction between two different kinds of linguistic conventions: descriptive conventions, which correlate sentence types with types of situation, and demonstrative conventions, which correlate token sentences with particular situations. His idea is that a token sentence is true just in case the particular situation with which it is correlated by the demonstrative conventions is the type of situation with which that sentence type is correlated by the descriptive conventions (see Austin 1970, p. 122). Thus, 'That dog is running' is, as a sentence type, correlated with situations in which a dog is running, and as a sentence token it is correlated with a particular situation. If the particular situation in question is one of the type in which a dog is running, then that sentence, as a token, is true. There are at least two problems with this approach, however. First, it is not clear what should be said about true sentences containing no demonstrative element, such as 'Horses are mammals'. Second, it seems that 'situations' are in no better shape,

ontologically, than 'facts'�though in recent times so-called 'situation semantics' has become rather fashionable in certain quarters, its leading defenders holding that they have an effective answer to the 'slingshot' argument (see Barwise & Perry 1981 and 1983, pp. 24-6).

Almost equally well known as the correspondence theory is the coherence theory, whose proponents are usually led to it by the perceived difficulties of the correspondence theory. Accepting that truth cannot consist in a relation between truth-bearers and items which are not themselves truth-bearers (such as 'facts'), these theorists propose instead that it consists

in a relation which truth-bearers have to one another�such as a relation of mutual support amongst the beliefs of an individual or a community. Opponents object that this leads to an unacceptable relativism about truth, since many different and mutually incompatible systems of belief could be internally consistent and self-supporting. They may also complain that advocates of the theory are guilty of treating a fairly plausible criterion of truth with a definition of truth. A criterion of truth is a rule of evidence for the evaluation of the truth or falsity of beliefs, whereas a definition of truth purports to state what the truth of a belief (or any other sort of truth-bearer) consists in.

In order to overcome the problem of relativism, some advocates of the coherence theory suggest that the notion of truth is a regulative ideal, which could only be realized in a unified and completed science far in advance of the partial belief-systems of any human community that actually exists or is ever likely to. In this guise, the theory overlaps with some versions of the so-called pragmatic theory of truth, associated with the American philosophers C. S.

Peirce, William James and John Dewey. The latter theory�particularly in the hands of

James�urges a connection between what is true and what is useful, pointing out, for instance, that a mark of a successful scientific theory is that it enables us, through associated developments in technology, to manipulate nature in ways hitherto unavailable to us.

Detractors protest that this (alleged) conflation of truth with utility is pernicious, because the ethics of belief require us to pursue the truth with honesty even if its consequences should prove detrimental to our material well-being.

All of the theories of truth so far mentioned may be called substantive as opposed to deflationary, in the sense that they all take truth to be a real and important property of

the items�whatever they are�that the theories take to be the primary bearers of truth. But in recent times deflationary theories of truth have become quite popular, the earliest example being the redundancy theory, first developed by F. P. Ramsey (1931, pp. 142-3). This

theory holds that the truth predicate, '�is true', only exists in order to effect economy of expression and that what is said with its aid can always in principle be said without it. What motivates this theory is the observation that if we take any sentence, such as, for example, 'Paris is the capital of France', then it seems that to say 'It is true that Paris is the capital of France' is logically equivalent to saying, quite simply, 'Paris is the capital of France'. The words 'it is true that' can be eliminated without loss of any substantive content in what is said. So why do we have a truth predicate at all? According to the redundancy theory, we do so, first and foremost, in order to avoid needless repetition. For example, consider the following valid argument: 'Paris is the capital of France; if Paris is the capital of France, then Paris is not the capital of the U.S.A.; therefore, Paris is not the capital of the U.S.A.' We can avoid needless repetition here by recasting this argument thus: 'Paris is the capital of France; if that is true, then Paris is not the capital of the U.S.A.; therefore, the latter is true'.

However, the redundancy theorist has a prima facie problem with occurences of the truth predicate in sentences such as 'Pythagoras's Theorem is true' and 'Something Jones said last night is true', for if we simply eliminate the words 'is true' from these sentences we do not

get sentences that are logically equivalent to them�indeed, we do not get sentences at all. Moreover, someone asserting these sentences may be quite unable to repeatPythagoras's Theorem or any sentence uttered by Jones last night. Thus, such a speaker cannot be assumed to be asserting 'Pythagoras's Theorem is true' simply as an abbreviated way of asserting 'In any right-angled triangle, the square on the hypoteneuse is equal to the sum of the squares on the opposite two sides', for he simply may not know what Pythagoras's Theorem is, even though he is sure that it is true (perhaps because a reliable mathematician has assured him of this). The redundancy theorist's answer to this problem is that what a speaker really means to assert by asserting 'Pythagoras's Theorem is true' is something like this:

(5) For any proposition P, if Pythagoras's Theorem is P, then it is true that P.

Then, it is suggested, just as 'it is true that' may be eliminated from 'It is true that Paris is the capital of France' without loss of any substantive content, likewise it may be eliminated from 'it is true that P' in (5), so that (5) is simply equivalent to the following, in which no truth predicate appears:

(6) For any proposition P, if Pythagoras's Theorem is P, then P.

However, the grammar of (6) looks decidedly odd at first sight, so much so that it is debatable whether (6) really makes sense at all. This is because the 'P' in (6) seems to

function as a pronoun�it functions effectively as an arbitrary name of whatever proposition

Pythagoras's Theorem is�and yet a noun or noun phrase cannot grammatically occupy the position which the third 'P' in (6) occupies. Only a whole sentence can occupy that position and a whole sentence has to contain a predicate. So it seems that eliminating the truth predicate from (5) has just left us with a piece of ungrammatical nonsense. Here, however, the so-called prosentential theory may be called to the rescue. According to this theory, we need to recognize the logico-grammatical category of 'prosentences', which are analogous to pronouns in their function, save that they stand in for whole sentences rather than for nouns or noun phrases. On this view, then, the third 'P' in (6) should be seen as functioning as prosentence, that is, as standing in for a whole sentence (for discussion, see Haack 1978, pp. 131-4).

Unfortunately, there is still what appears to be a fatal difficulty for any form of redundancy theory in handling this kind of example. This is that, even if the theory may and indeed must maintain that 'P' in its third occurrence in (6) functions as a 'prosentence', it nonethless seems clear that 'P' in its firstand second occurrences in (6) cannot be seen as functioning as

a prosentence, but only as a pronoun �- because, once again, it is effectively functioning there as an arbitrary name of whatever proposition Pythagoras's Theorem is. But then it transpires that the three occurrences of 'P' in (6) cannot be understood as having the same logico-grammatical function as one other, which means that they cannot have the same 'semantic value' and consequently that the use of the same letter 'P' three times in this sentence merely conceals a fatal ambiguity. Note, incidentally, that this difficulty also applies to (5), although in that case it can be overcome by replacing 'it is true that P' by 'P is true', for then 'P' is functioning as a pronoun in all three of its occurrences in (5). But then, of course,

(6) certainly cannot be derived from (5) by elimination of the truth predicate, '�- is true', because, as has just been pointed out, a pronoun cannot grammatically occupy the position of the third 'P' in (6).

Even if one does not believe, along with advocates of the redundancy theory of truth, that the truth predicate can always be eliminated without loss of expressive power, one may still be a 'minimalist' about truth. The minimalist holds that there is, as it were, nothing more to the concept of truth than is captured by such facts as that the sentence 'It is true that Paris is the capital of France' is logically equivalent to the sentence 'Paris is the capital of France'. On this view, the concept of truth is exhausted by this feature of the meaning of the truth predicate. However, it proves difficult to state what this supposed feature is in a perfectly general way. Obviously, we cannot state the logical equivalence in question for each sentence of a language individually, because any language contains a potential infinity of different sentences. On the other hand, we cannot state the logical equivalence in ageneralized form by saying

(7) For any sentence S, 'It is true that S' is logically equivalent to S

� firstly because there is a problem about how to understand a symbol, like 'S' here, which appears both outside and inside quotation marks; and secondly because the problem we met

in the case of (5) and (6) reappears with respect to the different occurrences of 'S' in (7)�'S' in its second occurrence is only replaceable by a whole sentence, whereas in its first and third occurrences it functions as an arbitrary name of a sentence. (For an interesting defence

of minimalism, see Horwich (1990); for an equally interesting critique, see Davidson (1996).)

Incidentally, the feature of the concept of truth which we are�unsuccessfully!�trying to capture here must be carefully distinguished from what is often called the 'disquotational' property of the truth predicate: the latter is illustrated by the fact that the sentence '"Paris is the capital of France" is true' is logically equivalent to the sentence 'Paris is the capital of France', obtained from the former by deleting both the quotation marks and the truth-

predicate, '�is true'.

This is a good place to mention Alfred Tarski's immensely important contribution to our understanding of truth, in the form of his so-called semantictheory of truth, though limitation of space prevents me from giving more than a brief outline (see further Tarski 1944). In developing this theory, Tarski was particularly concerned to overcome the semantic paradoxes to which talk of truth gives rise in natural languages, notably the Liar paradox. (In one well-known version, the Liar paradox is presented by any sentence which says of itself that it is not true, such as the sentence 'This sentence is not true': if that sentence is true, then it is not true, and if it is not true, then it is true.) Tarski held that truth could only be adequately defined for a language which is not 'semantically closed', that is, for one which does not contain either its own truth predicate or the means to refer to its own expressions. Calling such a language, L, the object language, Tarski undertook to provide a recursive definition of truth-in-L, the definition being formulated in an appropriate metalanguage. For such a definition to be satisfactory, Tarski maintained, it would have to enable one to prove all true equivalences of the form 'S is true-in-L if and only if P', where 'S' is a structural specification of a sentence of L (for instance, it might be that sentence itself, enclosed in quotation marks) and P constitutes the correct translation of that sentence into the metalanguage. This is his famous 'material adequacy' condition, and the schema 'S is true-in-L if and only if P' is known as the '(T) schema'. Clearly, the (T) schema is closely related both to the principle motivating minimalist theories of truth, discussed above, and to the 'disquotational' property of the truth predicate. This can be seen if we let S be some English sentence, such as 'Snow is white', and let P be the so-called homophonic translation of that sentence, whereupon we have as an instance of the (T) schema the following biconditional statement: 'Snow is white' is true-in-English if and only if snow is white. Tarski showed how the task of deriving all instances of the (T) schema from a definition of 'true-in-L' could indeed be carried out for certain artificial, formalized languages, but believed that the method could not be extended to provide a definition of truth for any natural language, such as English. (Lack of space prevents me from giving the form of Tarski's truth-definition, which involves a good deal of technical detail.) Because of this focus on formalized languages, Tarski's theory of truth has had more impact in formal logic (especially in the area of formal

semantics) than in philosophical logic�though Donald Davidson's appeal to Tarski's methods in working towards a theory of meaning for natural language has made Tarski's influence more widespread than it might otherwise have been (see Davidson 1984).

Whatever theory or theories of truth a philosophical logician favours, he or she will need at

some stage to address questions concerning the value of truth�for instance, why should we

aim at truth rather than falsehood?�and the paradoxes to which the notion of truth gives rise, such as the above-mentioned paradox of the Liar (see Martin (ed.) 1984). In the course of those inquiries, fundamental principles thought to govern the notion of truth will

inevitably come under scrutiny�such as the principle of bivalence (the principle that every assertoric sentence is either true or false). A rejection of that principle in some areas of

discourse is widely supposed to signify an 'anti-realist' conception of its subject matter (see Dummett 1991). Some theorists in the pragmatic tradition, such as Stephen Stich (1990),

now urge that truth as such has no cognitive value�that we literally should not care whether our beliefs are true or false, but rather whether they enable us to achieve more substantive goals such as happiness and well-being. However, Sophists were urging much the same in the

time of Plato and�fortunately!�it seems unlikely that philosophers will ever entirely give up asking 'What is truth?' and assuming that the answer is something of importance. Quite apart from anything else, giving up on the question of truth would deprive them of the endless enjoyment to be derived from attempting to solve the many paradoxes which the notion of truth throws up.

Problems of logical analysis

Propositions and sentences can be either simple or complex. A simple sentence may concatenate a single name with simple, one-place predicate, as in 'Mars is red'. Relational sentences involve more names, as in 'Mars is smaller than Venus', but a sentence like this is still regarded as simple. One way in which complex sentences can be

formed is by modifying or connecting simple ones�for instance, by negating 'Mars is red' to form 'Mars is not red', or by conjoining it with 'Venus is white' to form 'Mars is red and Venus is white'. Sentential operators and connectives, like 'not', 'and', 'or' and 'if', are extensively studied by philosophical logicians. In many cases, these operators and connectives can

plausibly be held to be truth-functional�meaning that the truth values of complex sentences formed with their aid are determined entirely by the truth values of the component sentences involved (as, for example, 'Mars is not red' is true just in case 'Mars is red' is not

true). But in other cases�and notably in the case of the conditional connective 'if'�a claim of truth-functionality may appear less compelling. The analysis of conditional sentences has accordingly become a major topic in philosophical logic, with some theorists seeing them as involving modal notions while others favour probabilistic analyses.

It seems clear that if 'if' is a truth-functional connective, then it must be identified with so-called material implication. That is to say, 'If P, then Q' will be false just in case P is true and Q is false, but otherwise will be true. (Standardly, P is called the 'antecedent' and Q the 'consequent' of the conditional 'If P, then Q'.) However, this analysis is at first sight highly counterintuitive, because it implies that if we take any two false sentences at random and connect them by 'if', the result will be a true conditional: for instance, 'If snow is black, then grass is red' will have to be deemed to betrue. Certainly, this makes such an analysis untenable for counterfactual conditionals, which are asserted with a presumption that their antecedents are false, and yet are not on that account all deemed to be trivially true: for such conditionals a modal analysis framed in terms of 'possible worlds' is now the most popular option (see Lewis 1973). However, some philosophers, such as Paul Grice and Frank Jackson, believe that the material implication analysis of 'if' is, nonetheless, correct for so-called indicative conditionals and attempt to explain away the apparent counterexamples by appeal to pragmatic considerations (see Jackson (ed.) 1991). For instance, Grice (1975) points out that it is generally misleading for a speaker engaged in ordinary conversation to assert a proposition which he knows to be true if he knows some stronger proposition to be true. (One proposition is 'stronger' than another if it entails, but is not entailed by, that other proposition.) Thus, on Grice's analysis, it is generally inappropriate for a speaker to assert the indicative conditional 'If P, then Q' when he knows P to be false, since in that case it would be

more informative for him simply to assert 'Not P'. This, it seems, may explain why we are

instinctively reluctant to assert 'If snow is black, then grass is red'�not because it isfalse, but because to assert it would misleadingly suggest that we were unsure about the colour of snow.

Even so, many philosophical logicians remain unconvinced by this sort of explanation, insisting that the truth of an indicative conditional, 'If P, then Q', demands some sort of necessary connection between P and Q. The material implication analysis ignores any such connection, as can be seen from the fact that it deems 'If P, then Q' to be true

whenever P and Q are both true, no matter how 'unconnected' P and Q may be�as in the case of the conditional 'If snow is white, then grass is green'. Other philosophers, while agreeing that 'if' is used to express some sort of 'connection' between propositions stronger than anything acknowledged by the material implication analysis, see this connection as probabilistic rather than modal in nature. According to one influential account (see Edgington 1986, 1995), the (subjective) probability that a speaker assigns to the indicative conditional 'If P, then Q' equals that speaker's conditional probability of Q given P. (The conditional probability of Q given P in turn equals the probability of 'P and Q' divided by the probability of P, provided that the latter is not zero.) However, in the light of an important proof of David Lewis's (1976), an implication of this account is that indicative conditional statements do not have truth-values, and indeed do not express propositions. Whether that is a price worth paying remains to be seen.

There are other ways of forming complex sentences than by connecting simpler ones, the

most important being through the use ofquantifiers�expressions like 'something', 'nobody', 'every planet' and 'most dogs'. The analysis and interpretation of such expressions forms another major area of philosophical logic. An example of an important issue which arises under this heading is the question of how existential statements should be

understood�statements such as 'Mars exists' and 'Dogs exist'. Another issue connected with

the role of quantifiers is the question of howdefinite descriptions�expressions of the form

'the so-and-so'�should be interpreted, whether as referential (or namelike) devices or alternatively as implicitly quantificational in force, as Russell held. Let us look at these two issues in a little more detail, beginning with the problem of existential statements.

'Existence' is sometimes thought to denote the elusive characteristic which real things possess but merely fictional ones lack. But whether there really is any such characteristic is

debatable, because many philosophers would now agree with Frege and Russell that '�- exists' is not a first-level predicate. What this means is that 'exist' does not express a property of objects, in the way that verbs like 'shine' and 'fall' do. According to Frege and Russell, 'exist' is a second-level predicate, expressing a property of properties (see Frege 1892a). Thus, on this account, 'Mars exists' does not have the same logical form as 'Sirius shines', predicating a property of a particular object. Rather, it is equivalent to 'The property of being (identical with) Mars is instantiated', asserting that the property of being Mars has at least one instance, or that there is at least one thing possessing that property. On this view, then, the true logical form of 'Mars exists' is 'There is at least one object, x, such that x is identical with Mars'. (Of course, there cannot be morethan one!)

W. V. Quine's famous dictum, 'To be is to be the value of a variable', takes the Frege-Russell account of existence as its inspiration, and implies that the entities to whose existence a theory is committed are precisely those which need to be invoked to interpret the quantified sentences of that theory (see, e.g., Quine 1995, p. 33). However, this somewhat controversially assumes an 'objectual' rather than a 'substitutional' interpretation of the quantifiers (for discussion, see Haack 1978, pp. 43-50). According to the objectual interpretation, 'There is at least one thing which is F' is true just in case some object in the domain of discourse is F. (The domain of discourse may embrace the whole world or just some part of it, such as the contents of a certain room: context will usually make it clear what the intended domain is.) By contrast, according to the substitutional interpretation, 'There is at least one thing which is F' is true just in case there is some true sentence of the form 'a is F', where 'a' is a singular term. Thus, if 'Pegasus

is identical with Pegasus' is deemed true despite the non-existence of Pegasus�perhaps on

the grounds that any such identity statement is anecessary truth�then 'There is at least one thing which is identical with Pegasus' must likewise be deemed true, so that adherents of this account must evidently repudiate Quine's criterion of ontological commitment.

The thought that fictional entities like Pegasus have some sort of reality despite lacking full-blooded existence is a tempting one, often associated with the views of Alexius Meinong. But according to David Lewis's more recent doctrine of modal realism, Pegasus and other possible but non-actual objects do have full-blooded existence, and differ from actual objects only in residing in other possible worlds (see Lewis 1986). This doctrine requires one to distinguish sharply between existence and actuality, treating the latter as an indexical notion akin to those expressed by the words 'here' and 'now'. On Lewis's view, Pegasus is just as 'actual' in the worlds in which it exists as Julius Caesar is in this world, and the objects existing in a world are all actual to its inhabitants in just the way that all moments of time are present or 'now' to those experiencing them. Whether modal realism of this sort is, as Lewis believes, necessary for the proper elucidation of modal truths, is debatable, but on the face of it it seems to commit us to a grossly over-inflated ontology. We shall return to such matters in the next section.

The problem of non-being, which has just been illustrated by the case of Pegasus�how can we speak meaningfully of something which does not exist, even to say that it does not

exist?�was a strongly motivating factor in Russell's development of his so-called theory of descriptions (see Russell 1919). Definite descriptions, which we met earlier when discussing

theories of reference, are noun phrases of the form 'the such-and-such'�for example, 'the winged horse of Bellerophon'. Russell's aim is to provide an analysis of sentences such as 'The winged horse of Bellerophon was white' which will always enable us to assign such a sentence a truth value, even though no existing object may answer to the description which forms its grammatical subject. According to Russell's theory, a sentence of the form 'The F is G' is not really of subject-predicate form at all, but is equivalent rather to an existentially quantified sentence of the form 'There is one and only one F and it is G'. Thus, for Russell, 'the F' is never a referring expression, having as its reference a particular object; indeed, he describes such an expression as an 'incomplete symbol', which disappears upon analysis and consequently has no fixed meaning on its own. It turns out, on Russell's analysis, that most sentences containing the definite desecription 'the winged horse of Bellerophon'

are false�though, very importantly, the following one turns out to be true: 'The winged horse of Bellerophon did not exist'.

In an important paper, Peter Strawson (1950) complains that Russell fails to distinguish between sentences and the statements made by speakers in uttering them, arguing that whenever a speaker makes a statement by uttering a sentence of the form 'The F is G', he uses 'the F' with the intention of making reference to a specific object which has the property of being F. That there is such an object is, according to Strawson, a presupposition of the speaker's statement rather than, as Russell implied, part of what is being stated. Thus, Strawson would say that someone who sincerely asserted that the winged horse of Bellerophon was white would not be making a false statement, but rather one which altogether lacked a truth value because it rested upon a mistaken presupposition. This position is rather similar to Frege's, who likwise regarded definite descriptions as referring

expressions�indeed, as names�and held a statement to be neither true nor false if it contained an empty name (that is, one lacking a reference).

More recently, a position embracing features of both Russell's and Strawson's views has been developed by Keith Donnellan (1966), who maintains that definite descriptions have two

distinct kinds of use�a 'referential' use and an 'attributive' use�the former somewhat akin to Strawson's understanding of their use and the latter akin to Russell's. Other philosophers now maintain that, without needing to make Donnellan's distinction, Russell's account can be effectively defended against Strawson's main criticisms by invoking pragmatic considerations concerning the domain of discourse intended by the speaker (for discussion, see Neale 1990). For instance, if it is complained that, by Russell's account, someone asserting 'The door is shut' says something false, because for Russell this is equivalent to 'There is one and only one door and it is shut', it may be replied that the context of the assertion makes it clear that the domain of discourse is restricted to objects in a certain room, which may indeed contain only one door. In the same way, a teacher speaking to a class of children may say 'Open all your books', and the context makes it clear that books which the children may have at home are not included.

Problems of modality

We move on now to issues in philosophical logic which focus on the notions of necessity, possibility and contingency. We may begin with the problem of distinguishing between 'analytic' and 'synthetic' statements, first addressed by Kant. According to Kant, an analytic statement (or judgement) is one in which the concept of the predicate is already contained (or thought) in the concept of the subject: an example would be the statement that a vixen is a female fox. In contrast, a synthetic statement, for Kant, is one in which the concept of the predicate is not already contained in the concept of the subject, such as the statement that foxes are carnivorous. The logical positivists, giving this doctrine a linguistic cast, held that an analytic statement is one which is true or false purely in virtue of the meanings of the words used to make it and the grammatical rules governing their combination (see Ayer 1936). This definition has the advantages that it does not only have application to statements of subject-predicate form and avoids reliance on the obscure notion of 'containment' or appeal to merely psychological considerations. Both Kant and the logical positivists assumed that true analytic statements must express necessary truths knowable a priori, though Kant also held that some synthetic statements express such truths,

including mathematical statements such as '7 plus 5 equals 12' and metaphysical statements such as 'Every event has a cause'. The logical positivists, by contrast, held mathematical truths to be analytic and metaphysical statements to be nonsensical or meaningless.

Some contemporary philosophers are very wary of appearing to endorse the analytic/synthetic distinction, following W. V. Quine's devastating onslaught upon it, notwithstanding Grice and Strawson's vigorous rearguard defence of its validity (see Grice & Strawson 1956). Quine (1951) argues that the supposed distinction cannot be defined save circularly, in terms which already presuppose it and that, in any case, it depends upon an untenable view of meaning. The positivists had adopted a verificationist theory of meaning according to which there is a sharp distinction to be drawn amongst meaningful statements between those which can only be known to be true on the evidence of experience (synthetic statements) and those which are verifiable independently of any possible experience and which are therefore immune to empirical falsification (analytic statements). Quine, however, contends that no such sharp distinction can in principle be drawn, because our statements are not answerable to the court of experienceindividually, but

only collectively�and any statement, even a supposed 'law' of logic, is potentially revisable in the light of experience, though some revisions will have more far-reaching implications than others for the rest of our presumed knowledge.

One modal distinction that is still very commonly drawn is that between de re and de dicto necessity and possibility, the former concerning objects and their properties and the latter concerning propositions or sentences. Thus, a supposedly analytic truth such as 'All bachelors are unmarried' is widely regarded as constituting a de dicto necessity, in that, given its meaning, what it says could not be false. But notice that this does not imply that any man

who happens to be a bachelor is incapable of being married�though should he become so, it will, of course, no longer be correct todescribe him as a 'bachelor'. Thus there is no de re necessity for any man to be unmarried, even if he should happen to be a bachelor. By contrast, there arguably is a de re necessity for any man to have a body consisting of flesh and bones, since the property of having such a body is apparently essential to being human.

As for the question of how, if at all, we can analyse modal propositions, opinions vary between those who regard modal notions as fundamental and irreducible and those who

regard them as being explicable in other terms�notably, in terms of possible worlds, conceived as 'ways the world might have been'. For example, the claim that every man necessarily has a body made of flesh and bones may be construed as being equivalent to saying, of each man, that he has a body made of flesh and bones in every possible world in which he exists. But what exactly is a 'possible world'? In the previous section we encountered David Lewis's (1986) doctrine of 'modal realism', which treats other possible worlds as concrete entities enjoying a full-blooded existence quite on a par with that of 'our' world. He admits that this doctrine is likely to be greeted with incredulity, but maintains that nothing less will do justice to the analysis of modal truths. Other philosophers are 'actualists', maintaining that the only entities that exist at all are entities that actually exist. These philosophers accordingly hold that other 'possible worlds' can only exist if they are included amongst the abstract entities actually existing in our world. One popular view along these

lines is that other possible worlds are 'maximal consistent sets of propositions'�a view which Lewis rather contemptuously dismisses as 'ersatz realism'. However, further discussion of these matters would take us too far into the realms of metaphysics.

We should always be on guard against ambiguity when talking of necessity, because it comes

in many different varieties�logical necessity, metaphysical necessity, epistemic necessity and physical necessity being just four. Of these, the first two are of most interest to philosophical logicians, so something more should be said about them here. In the narrowest sense, what is logically necessary is what follows from the laws of logic alone (though there is some debate as to what those laws are). Thus, a statement like 'Either it will rain or it will not rain' expresses a logically necessary truth, because it is an instance of the law of excluded middle. A sentence expressing a logically necessary truth, in this narrow sense, is true solely in virtue of its logical form. Thus 'Either it will rain or it will not rain' expresses a logically necessary truth because it has the logical form 'Either P or notP'. However, in a wider sense a sentence may be said to express a logically necessity if, although not itself a sentence true solely in virtue of its logical form, it may be transformed into such a sentence by replacing certain terms in it by other, definitionally equivalent terms. For example, 'All bachelors are unmarried' does, in this wider sense, express a logically necessary truth, because 'bachelor' may be defined as 'unmarried man', and 'All unmarried men are unmarried' is true solely in virtue of its logical form. In this wider sense, logically necessary truths are often identified with analytic truths (see above).

In a still broader sense, a logical necessity may be characterized as a proposition which is true

in every possible world, without restriction�that is to say, in every logically possible world, the assumption being that every such world is at least a world in which the laws of logic hold. This is sometimes called 'broadly' logical necessity and is assumed to conform to the principles of a system of modal logic known as S5, first formulated by C. I. Lewis (see Hughes & Cresswell 1996). The characteristic feature of that system, not present in certain weaker systems of modal logic, is that 'It is possible that it is necessary that P' entails 'It is necessary that P'. If the Ontological Argument is sound, then 'God exists' expresses a logically necessary truth in this broad sense, because the argument can be construed as concluding that that sentence is true in every possible world. (However, it is generally agreed that the Ontological

Argument is not sound, often on the grounds that the Frege-Russell analysis of '�- exists' as being a second-level predicate is correct: see the previous section.)

The notion of broadly logical necessity is closely related to that of metaphysical necessity. The notion that there is a kind of objective necessity which is at once stronger than physical necessity and yet not simply identifiable with logical necessity in either of its narrower senses owes much to the work of Saul Kripke (1980). Logically necessary truths in these narrower senses are, it seems, knowable a priori, but Kripke argues that metaphysical necessity is,

typically, only discoverable a posteriori�that is, on the basis of empirical evidence. For instance, Kripke holds that if an identity statement such as 'Water is H2O' is true, then it

is necessarily true�in the sense that it is true in every possible world in which water exists. However, plainly, we can only know that water is H2O on empirical grounds, through

scientific investigation�and we might be mistaken about this. Just as Kripke�unlike both

Kant and the logical positivists�allows there to be a posteriori necessary truths, so too he allows there to be contingent a priori truths, an example being the proposition that the standard metre rod in Paris is one metre long.

Modal expressions give rise to special problems insofar as they often appear to create

contexts which are non-extensional or 'opaque'�such a context being one in which one term cannot always be substituted for another having the same reference without affecting the

truth value of the sentence as a whole in which the term appears. For example, substituting 'the number of the planets' for 'nine' in the sentence 'Necessarily, nine is greater than seven', appears to change its truth value from truth to falsehood, even though those terms appear to have the same reference (see Quine 1953, pp. 143-4). (No such change occurs if the modal expression 'necessarily' is dropped from the sentence.) How to handle such

phenomena�which also arise in connection with the so-called propositional attitudes, such

as belief�is another widely studied area of philosophical logic. In the case of the example just cited, one solution is to follow Russell by denying that the definite description 'the number of the planets' is a referring term at all. Then it can be held that 'Necessarily, the number of the planets is greater than seven' is ambiguous, having both a true and a false interpretation, on the second of which it is not entailed by the premises 'Necessarily, nine is greater than seven' and 'The number of the planets is nine'. On this false interpretation, the sentence in question means 'Necessarily, there is one and only one number which numbers the planets and it is greater than seven'. On the true interpretation, it means 'There is one and only one number which numbers the planets and it is necessarily greater than seven'. The distinction between these two interpretations is called by logicians a scope distinction; overlooking such distinctions is a frequent source of fallacies in reasoning, both in philosophy and in everyday life. Note, incidentally, that the false interpretation involves de dicto necessity whereas the true interpretation involves de re necessity. (Consequently,

Quine�who repudiates the notion of de re necessity as importing an unacceptable

essentialism�would not agree with my description of that interpretation as being a 'true' one.)

An example of the phenomenon of non-extensionality involving belief rather than necessity would be this: despite the fact that George Eliot is the very same person as Mary Ann Evans, if 'Mary Ann Evans' is substituted for 'George Eliot' in the sentence 'Smith believes that George Eliot wroteMiddlemarch', which we may suppose to be true, the result is a sentence which may well be false, namely, 'Smith believes that Mary Ann Evans wrote Middlemarch'. This may be false because, of course, Smith may be unaware that George Eliot and Mary Ann Evans are one and the same person. Clearly, then, this example is related to Frege's puzzle about informative identity statements, discussed earlier. Frege's explanation in this case is that when a name, such as 'George Eliot' or 'Mary Ann Evans', appears within the scope of a propositional attitude verb, such as 'believes', it ceases to have its customary reference (in this case, a certain person) and refers instead to its customary sense (see Frege 1892b). Hence, on this account, 'George Eliot' and 'Mary Ann Evans' do not in fact have the same reference as they appear in the sentences 'Smith believes that George Eliot wroteMiddlemarch' and 'Smith believes that Mary Ann Evans wrote Middlemarch', because in those two sentences they refer, respectively, to the customary sense of the name 'George Eliot' and the customary sense of the name 'Mary Ann Evans', and these two senses are different. (That these senses are different was, it will be recalled, the basis of Frege's solution to the puzzle as to how the identity statement 'George Eliot is Mary Ann Evans' could be informative.) Evidently, though, this kind of explanation is not available to someone who favours the so-called 'direct' theory of reference, according to which names do not possess descriptive 'senses'. Understandably, then, the phenomenon of non-extensionality is extensively discussed in connection with rival theories of how proper names refer.

Problems of rational argument

Finally, we pass, very briefly, to questions concerning relations between propositions or

sentences�relations such as those of entailment, presupposition and confirmation (or probabilistic support). Such relations are the subject matter of the general theory of rational argument or inference, whether deductive or inductive. Some theorists regard entailment as

being analysable in terms of the modal notion of logical necessity�holding that a proposition P entails a proposition Q just in case the conjunction of P and the negation of Q is logically impossible. This view, however, has the queer consequence that a contradiction entails any proposition whatever, whence it is rejected by philosophers who insist that there must be a 'relevant connection' between a proposition and any proposition which it can be said to entail (for discussion, see Haack 1978, pp. 197-203). The notion of presupposition, though widely appealed to by philosophers, is difficult to distinguish precisely from that of entailment, but according to one line of thought a statement S presupposes a statement T just in case S fails to be either true or false unless T is true. For instance, the statement that the present king of France is bald may be said to presuppose, in this sense, that France currently has a male monarch. (Recall our earlier discussion of Strawson's account of definite descriptions.) Such an approach obviously requires some restriction to be placed on the principle of bivalence. As for the notion of confirmation, understood as a relation between propositions licencing some form of non-demonstrative inference (such as an inference to the truth of an empirical generalization from the truth of observation statements in agreement with it), this is widely supposed to be explicable in terms of the

theory of probability�though precisely how the notion of probability should itself be interpreted is still a matter of widespread controversy.

No general theory of argument or inference would be complete without an account of the various fallacies and paradoxes which beset our attempts to reason from premise to conclusion. A 'good' argument should at least be truth-preserving, that is, should not carry us from true premises to a false conclusion. A fallacy is an argument, or form of argument, which is capable of failing in this respect, such as the argument from 'If Jones is poor, he is honest' and 'Jones is honest' to 'Jones is poor' (the fallacy of affirming the consequent), since these premises could be true and yet the conclusion false. (Strictly, this only serves to characterize a fallacy of deductive reasoning.) A paradox arises when apparently true premises appear to lead, by what seems to be a good argument, to a conclusion which is

manifestly false�a situation which requires us either to reject some of the premises or to find fault with the method of inference employed. One example would be the paradox of the Liar, discussed earlier. Another would be the paradox of the heap (the Sorites paradox): one stone does not make a heap, nor does adding one stone to a number of stones which do not

make a heap turn them into a heap�from which it appears to follow that no number of stones, however large, can make a heap. This paradox is typical of those which are connected with the vagueness of many of our concepts and expressions, a topic which has itself received much attention from philosophical logicians in recent years (see Williamson 1994). This is again an area in which the principle of bivalence has come under some pressure.

Although philosophical logic should not be confused with the philosophy of logic, the latter must ultimately be responsive to considerations addressed by the former. In assessing the adequacy and applicability of any system of formal logic, one must ask whether the axioms or rules it employs can, when suitably interpreted, properly serve to articulate the structure of

rational thought concerning some chosen domain�and this implies that what constitutes 'rationality' cannot be laid down by logicians, but is rather something which the formulators of logical systems must endeavour to reflect in the principles of inference which they enunciate.

What is Syllogism?

It is one form of deductive reasoning. It as the standard expression of argument in Aristotelian logic , it is a basic form of argument wherein It is arranged orderly so as to show the structure or form of the argument and important terms and propositions to facilitate logical analysis.

It is a set of three propositions, the first two being the premises and the last is the conclusion. The conclusion must always follow and must be derived from the premises.

Eg.) Computers are electronic machines.

Some computer students are good in Math and Logic.

Some computer students are good in electronics.

2 Basic Elements of Syllogism: Matter and Form

Matter – consists of the various ideas/terms and judgments propositions of the argument or syllogism.

Substance – it is what the syllogism is about.

Kinds of Syllogism

Categorical Syllogism – composed of categorical propositions. First two are the premises and the third is the conclusion. It contains three terms: major, minor and middle terms.

Eg.) All inventors are scientists. Some inventors are well-known worldwide. Hence, some people who are well-known worldwide are scientists.

Hypothetical Syllogism – composed of hypothetical propositions. They are not identified as major, minor and middle.

Eg.) If the suspect is found guilty he will serve time in prison. But he will not serve time in prison. Ergo, he was found guilty.