A Priori Knowledge

7/18/2019 A Priori Knowledge

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© Michael Lacewing

priori knowledge

A PRIORI AND A POSTERIORI KNOWLEDGE

A priori knowledge is knowledge of propositions that do not require (sense) experienceto be known to be true. Propositions that can only be established through experience area posteriori. The a priori/a posteriori distinction is about how to check or establishknowledge. It is not a claim about how we acquire the concepts or words of theproposition. Babies are not born knowing that all bachelors are unmarried! Yet this is atruth that clearly doesn’t need testing against experience; we know it is true just byknowing what it means. Of course, we first have to learn what it means, but that is a

different issue from how we check if it is true.

This contrast between a priori and a posteriori knowledge should be distinguished fromanother contrast, between analytic and synthetic propositions. A proposition is analytic ifit is true or false just in virtue of the meanings of the words. Many analytic truths, such as‘all bachelors are unmarried’, are obvious, but some are not, e.g. ‘your mother’s brother’sfather’s niece’s sole female cousin is your mother’ (think about it!). A proposition issynthetic if it is not analytic, i.e. it is true or false not just in virtue of the meanings of the

words, but in virtue of the way the world is, e.g. ‘snow is white’. This is not, in fact, the way that Kant, who invented the distinction, describes it; but this is in part because ofcriticisms of Kant’s distinction made by people like Ayer, so we’ll discuss this below.

RATIONALISM AND EMPIRICISM ON A PRIORI KNOWLEDGE

Philosophers do not agree on precisely how to define rationalism and empiricism.Obviously, rationalism gives an important role to reason, and empiricism to experience,but the terms range across theories of knowledge, theories of concept acquisition,theories of justification, and historical schools of thought. Thinking of them just in termsof ‘reason’ versus ‘experience’ is much too simple – why should we think that we have tochoose? Most rationalists (the exception is Plato) do not deny that experience canprovide us with knowledge under certain circumstances; and empiricists clearly usereasoning, based on experience, to construct arguments about what we know.

Furthermore, we need to qualify just what is meant by ‘reason’ and ‘experience’.

Nevertheless, there is a way of contrasting rationalism and empiricism that makes themexclusive (no one is both a rationalist and an empiricist), and which goes to the heart ofthe historical debate. Stephen Law puts it like this: Rationalism claims that we can havesynthetic a priori knowledge of how things are outside the mind. Empiricism denies this.

In other words, rationalists argue that it is possible for us to know (some) syntheticpropositions about how the world outside our own minds, e.g. about mathematics,morality, or even the material world, is without relying on sense experience. Empiricistsargue that it is not. Notice that they don’t deny that all a priori knowledge – no empiricist

claims that you have to check whether all bachelors are unmarried to see if it is true! They simply claim that all a priori knowledge is of analytic propositions. If we don’t



know if a proposition is true or false just by the meaning of the words, we have to usesense experience to find out whether it is true or false.

(The clause ‘how things are outside the mind’ is necessary. Many propositions about mymental states are synthetic, e.g. ‘I feel sad’ or ‘I am thinking about unicorns’. But they

don’t require sense experience to be known; in fact, does knowing my own thoughtsinvolve experiencing them at all? We don’t need to worry about this. Rationalists andempiricists alike do not deny that we just do know that we have certain impressions andideas, thoughts and feelings. The argument is about knowledge of things other than ourown minds.)

EMPIRICISTS ON A PRIORI KNOWLEDGE

Empiricists deny that there is any substantive a priori knowledge of how things standoutside the mind. So for any area of knowledge, they have three options:

to deny that we have any knowledge in that area;to say that any knowledge we do have is based on experience; orto say that any knowledge we have is analytic.

Hume argues that we can have knowledge of just two sorts of thing: the relationsbetween ideas and matters of fact. His distinction was developed by later philosophers,and is now understood in terms of the two distinctions, mentioned above:analytic/synthetic and a priori/a posteriori. Hume argued that all a priori knowledgemust be analytic, while all knowledge of synthetic propositions is a posteriori. In other

words, anything we know that is not true by definition, every ‘matter of fact’, we mustlearn and test through our senses.

Ayer follows Hume’s contention, doing so on the basis of meaning. Before we get to thequestion of what we can know, we must have a criterion for what is meaningful. There isno question that we cannot know what is meaningless; knowledge is of true propositions,and propositions are meaningful statements. Ayer argued for the ‘verification principle’as a criterion of meaning. The principle claims that that all true meaningful statementsare either analytic (true in virtue of the meanings of the terms used) or empirically

verifiable (can be shown by experience to be true or to be probably true). These are theonly two ways of establishing the truth (and hence the falsity) of a statement. Anystatement that cannot be shown to be true or false in these ways is meaningless; so theonly two classes of meaningful statements are analytic and a posteriori. So there can be

no a priori knowledge that is not analytic. But an area of knowledge that has provedproblematic for empiricists is mathematics , which I discuss below.

Morality and religionIt is difficult to argue that knowledge of God and knowledge of morality is gained justthrough experience, especially if this is limited to sensory experience. Hume and Ayerdeny that there is any moral knowledge at all, because moral judgements don’t expresspropositions that can be true or false. Ayer also argues that all talk of God is literallymeaningless.

John Locke, somewhat surprisingly, argues that truths of morality and the existence of

God can be established by reason because they are truths by definition. He uses a formof the cosmological argument to derive the idea of God and to prove that we can know



God exists. We need only the fact, from experience, that we exist, and some truths thatLocke claims are analytic: We know that we exist and that something cannot come fromnothing. So something must always have existed, and everything else which exists musthave come from this. As we have knowledge and intelligence, we may deduce that thisoriginal being is a knowing intelligence.

He argues that we can know moral truths in a similar way. From our knowledge of theexistence and nature of God, and of ourselves as creations of God, we can deduce whatour moral duties are. It is only because it is not obvious, and we don’t reason well, thatpeople have ever disagreed on such matters.

John Stuart Mill, by contrast, argues for moral knowledge on the basis of ‘observationand experience’. He argues that the only evidence we have for what is good is what wedesire. Everyone desires happiness, and so there is no better final aim for action thanhappiness. This argument doesn’t establish that we should desire and aim at each other’s happiness, since each person desires their own; but Mill assumes that morality is

concerned with all persons equally, and this is an analytic truth. So we know thateveryone’s happiness is what we should aim at.

KANT AND MATHEMATICS

Kant invented the analytic/synthetic distinction, and first defined analytic propositions asthose in which the predicate doesn’t add anything to the subject. Instead, the predicatebreaks the subject into its constitute concepts (hence ‘analysis’ – ‘analytic’). Kant talks ofthe predicate ‘being contained in’ the subject, and in developing this idea, argues that theconcept ‘12’ is not contained in the idea of ‘5 + 7’ – hence mathematics must besynthetic rather than analytic.

Most commentators now agree that Kant has misled himself here. He argues that youcan think of 5 + 7 without thinking of 12; but this is to do with how we (psychologically)understand subject and predicate (what Ayer refers to as their ‘subjective intension’, p.104). But because we are capable of understanding a concept without our mindsimmediately being led on to all its implications and components, it is a bad test of therelation between subject and predicate. His other test – can we deny the proposition

without contradicting ourselves? – is the better one. Hence Ayer argues that we shouldunderstand analytic propositions as those whose validity depends only on the symbolsthey contain; and synthetic ones as those whose validity is determined by facts ofexperience.

Locke, Hume, and Ayer argues that mathematical propositions are analytic. To show this, Ayer says, consider how we deal with potential counterexamples: if I count what I thinkare 5 pairs, and only arrive at 9, we don’t take this as evidence against the truth of 2 x 5 =10. We say either I was mistaken at some point or that the number of objects changed.

The same applies to the rules of formal logic. We don’t allow principles of logic ormathematics to be false. We can’t abandon them without contradicting ourselves, as theyare true in virtue of the meanings of the terms.

GeometryGeometry provides a serious challenge to Ayer’s claim that all mathematics is analytic.

Kant argued that geometry was a set of truths about physical space, yet it is clearly apriori (the truths of geometry, e.g. properties of triangles, is not arrived at by induction).



The fact that it takes at least three lines to enclose a space in two-dimensions seems to bea truth about the nature of space, rather than the concept of space. Yet it has mathematicalcertainty, and can be proved by mathematical geometry. How could such certainty comefrom sensory experience alone? Hence there can be a priori truths about the world. SinceKant’s time, as Ayer notes, different systems of geometry, known as non-Euclidean

geometries, with different initial axioms about lines and figures, have been developed bymathematicians, and in the process, the question arose as to which geometry bestdescribed physical space. This question, Ayer argues, is empirical. Geometries remainanalytic – they start with definitions (axioms) and derive theorems by deduction.

Mathematical discoveriesIf mathematics is all analytic, how are mathematical ‘discoveries’ possible? How can we‘discover’ something that is true by definition ? Ayer argues that analytic truths (in general,not just maths) can give us new knowledge in two ways. First, they draw attention tolinguistic usage that we may not have been aware of (e.g. the claim about colour); second,they can reveal unsuspected implications. Analytic knowledge doesn’t need to be

obvious; mathematical truths are very complex, so it takes work to establish that they aretrue. But that doesn’t mean they are not true by definition. The mathematician HenriPoincaré couldn’t believe that all the books of maths are just roundabout ways of saying

A=A. But Ayer comments that this is a result of the limitations of our reason. So theyare useful to us in both these ways. They are also useful in enabling us to make suresynthetic propositions form a self-consistent system, by rooting out contradictions in ouruse of words.

RATIONAL INTUITION?

Not all mathematicians and philosophers agree with Ayer’s argument. If we return to

Kant, setting aside his particular arguments regarding mathematics: his claim was thatstatements that are a priori yet synthetic define the structure of experience , as it is possible forus. This structure is manifest in our accepting certain judgments as non-logicallynecessary – unlike analytic judgments, they rest on something outside the circle ofconcepts, unlike a posteriori, not on experience itself.

Ayer argues that those statements in metaphysics that are not meaningless, such as‘Nothing can be coloured in different ways at the same time in the same part’, although itseems to be a statement about material objects, is not a synthetic truth at all. It is analytic,recording our determination to count the different colour as belonging to different partsof the object. The certainty of a priori knowledge derives from the fact that it can’t be

refuted (or confirmed) by any fact of experience, not from some guarantee provided byrational insight into the nature of things.

Kant’s response would be that our experience is ordered, but not, as Ayer would argue,by arbitrary linguistic rules, that we could change if we wish. If Kant is right, and thedebate is still live, then there is the possibility of synthetic a priori knowledge.

However, by what means, Ayer asks are we supposed to gain knowledge of metaphysicaltruths? Rationalists claim that reason (and what ‘reason’ is here is unclear) can discovernon-analytic truths independent of experience. From Plato onwards, there is a longtradition of arguing for rational ‘insight’, whether into the Forms, the structure of

possible experience (Kant), or moral values (Moore). (The alternative is that we knowcertain truths innately, as part of our rational nature.) Hume argued that many of the so-



called ‘truths’ previous philosophers claimed were known by ‘rational intuition’ wereactually just assumptions, propositions unjustifiably taken for granted; Kant sought torebut that charge.

So rationalists owe us an account of what intuition is and exactly how it can provide

knowledge. Knowledge needs to be secure, it needs justification, it needs to be reliable.Our senses are a reliable basis for beliefs because sense experiences are caused bymaterial objects. But what justifies the claim that rational intuition is reliable?

However, rationalism’s best form of defence may be attack. Empiricism has struggled toshow that all our knowledge is either analytic or comes from the senses. If there are goodarguments against empiricism, then rationalism can claim that, if we are not to fall intoscepticism, we must accept that we have rational intuition, even if we don’t know what itis or how it works. One way to display its continued relevance is to ask how we know

what ‘a reason’ – whether for a scientific or a value judgment – is.

A Priori Knowledge

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