RPT Paper Draft Part 1

8/8/2019 RPT Paper Draft Part 1

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Jenkins Draft 2010 - 1

Rough Draft: Normativity of Logic

Possible Title: Changin' Views About the Role of Logic

Ralph Jenkins

12-14-2010


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There is something deep, something fundamental about studying logic. The feeling is that it's

something integral to a completed epistemology. A sense of logic's fundamental nature can be gotten

from the pivotal role that logic plays in the early twentieth century's foundational quest in

mathematics (Nagel and Newman 2001, Russel 1996), keeping in mind that maths are the most

pervasive and fundamental of the sciences. Alternatively, consider the role that formal logic plays in

developing rigorous metaphysical theories (Hofweber 2004).

There is something equally fundamental about the study of reasoning, though this

investigation is arguably the less well established of the two. A rigorous theory of correct ways to

think surely must be a part of a completed epistemology. Such a theory would provide principles for

understanding and, optimistically, improving human epistemic or inferential performance, and these

are essential goals of epistemology if anything is. It is natural to think that the two studies intertwine -

logic is the study of correct reasoning. On this view, logic has a clear role in epistemology.

There are good reasons to believe that this natural conclusion is either not true or must be

strongly qualifed. This controversy raises the question: what is the relation of logic to reasoning, to

the theory of reasoning, and, more broadly, to epistemology? Is logic a theory of reasoning? If S

performs a logical inference, is S performing a rational inference? Completely answering that

motivating question (and its tagalongs) is a daunting task. What will be put forward here is a

preliminary exploration. Hopefully, it will correctly indicate the shape that the complete answer must

have.

Plan of Exposition:

The received view is that logic is the study of correct reasoning (see, e.g., Jacquette 2002 for a


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self-aware expression of the view); hence, it imposes normative constraints on reasoning. Strong

ones. The connection is simple. Reasoning is composed of inferences, inferences are arguments,

arguments are systematically evaluated by logic. Reasoning is systematically evaluated by logic. (e.g.,

Klenk 1983, Salmon 1963; Harman 1986 cites this intuitively appealing view as grounding the

motivation behind nonmonotonic and relevant logics). Contrary to the received view, Gilbert

Harman presents arguments that effectively hollow out the space of possible descriptive and

normative constraints that logic could specify for reasoning. Room is left for logic to have importance

for the theory of reasoning but not the kind of special relevance that the received view sees for it.

The point of departure in this paper will be the various problems that Harman raises in his

(1973, 1986, 2002, and Harman and Kulkarni 2007) that distinguish logic from the theory of reasoning.

Part I will present and discuss the problems Harman raises. Part II contains discussion of two salient

responses to Harman's arguments, Field (2009) and MacFarlane (2004), that contribute interesting

and valuable analyses. It is concluded that they do not reject or refute Harman's arguments; they

construct bridge principles that, if correct, are potential explications of the non-specially relevant role

of logic in the theory of reasoning. These explications may help us understand the relation of logic to

reasoning, but in both cases, room is left for a full explanation of the relation.

Part I - The Problems:

The classic source of the following arguments is Harman (1986), but, showing remarkable

stability of views, Harman (1973), Harman (2002), Harman (2005), and Harman and Kulkarni (2007) all

reference, extend, or fill in the picture that (1986) paints. Here, in brief, are the arguments as I

reconstruct them:


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1. ~(Deduction Machines): Reasoning is defeasible, flexible, revisory; rules of inference

or proof and implication are not -> inference rules are not rules of inference; implication

cannot be a strong obligation for inference

2. Clutter Avoidance: It is not rational to infer infinite trivialities or arbitrary sentences

because, among other reasons, it is a waste of finite cognitive resources -> implication

cannot be a strong obligation for reasoning; logical closure is not a strong obligation for

reasoning

3. Unavoidable Inconsistency: In theories that are well established or powerful, there are

inconsistencies that are difficult to grasp and resolve; it's rational to retain these

theories even with their inconsistencies; it's rational to retain inconsistencies ->

maintaining logical consistency is not a strong obligation for reasoning

4. Recognition Problems: Human reasoners have computational imitations that prohibit

them from detecting some logical features of their beliefs -> only recognized implication

and inconsistency are plausible obligations for reasoning

I.1.) The Keys

Understanding the above reconstructions of Harman's arguments requires an assumption each

about logic and reasoning. Certain premises in the above arguments are supported by these

assumptions.

A. Strategic disambiguation:

There are varying conceptions and meta conceptions of logic in the field (See Shapiro 2006,


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Hofweber 2004, Beall and Restall 2000, van Benthem 1996, 2010 for some candidates), each

potentially encompassing distinct sets of logical systems and research programs. It is difficult to

proceed with the arguments here without assuming that there is a relatively solid idea of what logic is.

Harman presents a set of core objections that arguably do not equally apply to all of the conceptions

of logic available. This becomes clear below. For the sake of this exposition, logic is defined by A1:

A1: Logic is the theory of implication and is correctly codified in Classical Logic (CL).

That is, a Classical Logic is any formal language, with a syntax that determines well-formed formulae

and with a binary valued semantics, that picks out ordered pairs of sets of well-formed formulae of

the language under the implication relation. The implication relation is defined: A1-An imply P iff

there is no interpretation of the formulae that makes (A1-An) true and P false. An interpretation is a

uniform assignment of semantic values to each atom or constituent of a formula. Often, these

systems will contain rules of proof or inference that can be used to demonstrate implication, a formula

being implied by a set (possibly empty) of formulae if it can be derived or deduced, using the rules of

proof, from that set. Concepts like validity and inconsistency can be defined precisely in these

systems. A valid formula is one that is true in every interpretation. Two formulae are inconsistent

when there is no interpretation where they are both true. An inconsistent formula is one that is not

true in any interpretation - one can be formed by two formulae that are inconsistent.

These systems display interesting properties. For instance, valid formulae imply only other

valid formulae and inconsistent formulae imply anything (Quine 1982). There are properties of

classical logical systems that are crucial to some of Harman's arguments, e.g., the principle of

explosion or the implication of infinite trivialities by true formulae. But importantly, some of these


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properties are not possessed by Nonclassical logical systems, and some conceptions of logic or logical

consequence are not best codified in Classical systems. As MacFarlane points out, proponents of

different logical systems may be under indoctrination bias: A classicist will take it to be correct to infer

anything from a contradiction in formal argumentation, while a relevantist will not. If we do not limit

ourselves to a relatively restricted conception of logic, the discussion becomes more complicated than

it needs to be here. We may, for instance, have to figure out which logic (if any) is the correct logic for

this kind of project, and that might require performing a comprehensive survey of alternative

conceptions of logic, logical consequence, or logical systems. It is, of course, an extremely interesting

question whether alternative logical systems or conceptions of logic are impervious to the problems

Harman raises or not. MacFarlane (2004), Field (2009), and Shapiro (2001) actually do have a broader

conception of logic and their discussions reflect this. Even so, the main thesis of this paper, produced

from assuming A1, is unaffected. A complete theory will surely require an analysis of logicality or the

demarcation of logic, but our purposes here are too narrow to allow such a massive undertaking.

A.1 Another strategic disambiguation:

"Reasoning" can denote a number of things. For instance, there is the action-product

distinction (van Benthem 1996, 2008, 2010). Reasoning can be instantiated by a token of a mental

process or action targeted by a theory for possessing certain features (e.g., the process changes one's

beliefs or intentions). A token of inference, or belief revision, is thus an instance of reasoning. We will

call this A-reasoning. Reasoning can also be instantiated by a product of selected mental processes,

like an argument or a mathematical proof or a list of evidence. We will call this P-reasoning. When

we evaluate someone's reasoning, we may be looking at either sort of phenomenon. This distinction


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plays an important role in the discussion at hand. Classical Logic (hereafter referred to

interchangeably as logic, Classical Logic, or CL) uncontroversially codifies (classically) valid

argument. CL clearly has the power to separate (classically) valid arguments from invalid arguments.

Perhaps more controversially, Classical Logic codifies (classical) mathematical proof (Burgess 1992),

thereby having the power to separate good proofs from bad proofs. Moreover, CL provides various

deduction systems, rules, laws, and procedures for constructing proofs, valid arguments, or evaluating

for the validity of a given argument or the proofiness of a given proof.

Of course, it seems like there are kinds of arguments other than valid ones. Some of them are

even good or important; inductive and abductive arguments being the traditional examples of good

non-deductive argument. So, we can say that valid arguments are a subset, and perhaps a proper

subset, of good arguments - valid arguments make up at least a part of the total body of good

arguments. Since proofs and arguments are products of mental processes, we can consider them

instances of P-reasoning. So, on the product view of reasoning, it follows that logic uncontroversially

provides at least a partial codification of good reasoning. To simplify:

1. CL codifies valid argument and proof.

1.1 P-reasoning = x is an instance of P-reasoning iff x is a product of mental processes

with features: ...

1.2 Valid argument and proof are products of mental processes with features: ...

1.3 There are other products of mental processes with features: ...

2. Valid argument and proof are (a proper subset of) instances of correct P-reasoning.


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C. CL codifies (a proper subset of) instances of correct P-reasoning.

So, there is a clear way in which logic demonstrates, in a uniquely reliable way, how to recognize good

P-reasoning, which is to say, there is a clear way in which logic is uniquely good for telling people that

use it or study it when P-reasoning is good or not-good. I take it that this is equivalent to saying that

there is a way in which logic is uniquely normative for P-reasoning. But, intuitively, logic is supposed

to be help us figure out what to believe. Logic cannot merely be the study of valid arguments and

proofs for its own sake we clearly assume much more of it than that considering its importance in

undergraduate education (not to mention the way it is written of in introductory texts). On this note,

the more interesting question is whether and how logic is integrated into A-reasoning. How does logic

contribute to our mental processes to help us get our beliefs in order? We have shown an obvious

way that logic constrains reasoning, but it leaves open the question of how argumentation and proof

contribute to the process of belief revision. No conclusion parallel to C follows from the action view of

reasoning (A-reasoning). For good measure:

A-reasoning = x is an instance of reasoning iff x is a mental process with features: ... (see

Harman (1973) for an interesting and plausible filling out of the ellipses).

Valid argument and proof do not appear to be instances of reasoning on this view, so it does not

follow that CL codifies any instances of reasoning. The conflation between P-reasoning and A-

reasoning may be essential to diagnosing the intuition that logic is a theory of reasoning. Given the

imprecision of English, there is a sense in which logic is the (partial) theory of (good) reasoning, but to

clearly understand these issues, we must sort out the two conceptions of reasoning and see how

exactly logic impacts them if it does.


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Harman (1986 et. al) raises problems that are aimed at distinguishing between logic and a

theory of A-reasoning. Reasoning, on Harman's view, is identified with the complicated process of

belief revision or "reasoned change/no change in view". That is, reasoning is the process of changing

one's beliefs. Reasoning is identical with this complicated process. Any process that goes on in

changing beliefs is on the list of processes that go on in reasoning, any process that goes on in

reasoning is included in the list of processes of belief revision. Note that belief revision includes

processes of addition and subtraction of beliefs. A theory of reasoning then, to the extent that it has

any normative aspect, will specify principles for correct revision. That is, a full list of principles of

reasoning will include principles for correctly adding and correctly subtracting beliefs.

Some of Harman's arguments pivot on noting that certain features of logic do not represent

reasoning processes or that potential bridge principles between logic and correct reasoning require

human reasoners to either revise their beliefs in ways that are not possible for them or that are

antecedently thought to be incorrect. To understand Harman's arguments, we must keep in mind

that:

A2. Reasoning is A-reasoning (i.e., belief revision/change in view/inference to the most

coherent view).

Unless explicitly or contextually indicated, reasoning, inference, belief revision, change in view

and cognate terms will denote A-reasoning in this discussion.

I.2.) A1, A2, and Explicating the Problems

~(Deduction Machines)


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In Classical Logic, there is an inference rule called Modus Ponens, it captures the fact that

whenever (schematic sentences) P and P->Q are both true in an interpretation, then Q is also true;

that is, P and P->Q together imply Q. If you are doing a proof or constructing a valid argument, and

you find that P takes up one line of the proof, and P->Q takes up another line of the proof, then Modus

Ponens says you must put down Q at another line of the proof. Modus Ponens is one among many

rules. Classical logic contains myriad rules for identifying implications. Every implication is treated in

the same way; when a formula Q is implied by previous formulae, you put down Q even if it results in

an inconsistency.

In the traditional view, P-reasoning and A-reasoning are confused, and reasoning is thought to

look the way an argument looks, where steps in the argument map to steps that the reasoning agent

takes. Since logic has rules for how arguments proceed, the most transparent way to connect logic to

reasoning is to translate the rules for arguments into rules for correct reasoning steps. So, where the

laws of logic say to write down Q in your proof whenever you find out that it is implied by previous

lines, the laws of logic also say to infer Q whenever you find out that you believe that Q is implied by

your previous beliefs. But this is transparently false.

Reasoning often does not look anything like an argument reasoners often move from a

conclusion to premises or from beliefs in the middle to assumptions and consequences (Harman and

Kulkarni 2007). In fact, reasoners are often right to do so. Suppose that S finds out that Q is implied

by her beliefs that P and P->Q. But she also believes ~Q for extremely strong reasons perhaps a long

list of her previous beliefs implies ~Q where only P and P->Q imply P. If she wants to maintain the

coherence of her view, she is better off rejecting her belief that P than she is accepting Q. The


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situation holds when Q is obviously false or self-refuting or otherwise absurd. It is simply not correct

epistemic behavior to accept a claim just because it is implied by your previous beliefs. There is more

to consider than the implication itself in reasoning. Not so in logic.

Moreover, consider the principle of Explosion. If S's view is inconsistent, then it (classically)

implies every proposition. Take the simple proof:

1. P ~P Assumption

2. P Simplification 1

3. P v Q Disjunction Introduction 2

4. ~P Simplification 1

5. Q Disjunctive Syllogism 3,4

6. (P ^ ~P) -> Q Conditional Proof 1-5

It is surely not acceptable to infer any arbitrary claim simply because one finds that one's inconsistent

view implies any arbitrary claim.

Clutter Avoidance

Since reasoning is a mental process, and human reasoners are finite in their cognitive

capacities, an absolute constraint on reasoning is that we cannot infer an infinite number of claims

we neither have the time or the memory to do so. However, there are two features of CL

that strain against this fact. First, an infinite number of trivialities is implied by any true claim. Using

the rule of Disjunction Addition, any formula P implies the compound formula P v Q, where Q can be


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replaced by any formula or compound of formulae. So P implies P v Q, P v Q v R, P v (P v (P v (Q v R))),

and so on. No rational agent ought to infer such things except in very strange situations (if there are

any situations where a rational agent ought to infer them). Second, there is the principle of Explosion

- inconsistent formulae imply any arbitrary formula. By a simple proof, P ~P always implies an

arbitrary formula Q, which can be replaced by any formula or compound of formulae. Clearly, if S

finds out she has an inconsistent set of beliefs, it is not correct for her to infer anything she likes or

dreams up afterward. Moreover, it is not rational for her to waste her finite resources on inferring an

infinite number of arbitrary claims based on inconsistent premises.

Unavoidable Inconsistency: Classical Logic is just as good for locating inconsistency as it is for

locating implication. It is natural to think that this logical property of sets of formulae translates

directly into a constraint on reasoning something to the effect that one ought to always make sure

one's beliefs are logically consistent. But this is false. Consider two paradoxes.

First, the Liar Paradox (Harman 1986, ch. 2). The biconditional truth schema - P is true iff P -

is the most intuitive, satisfying theory of truth around. However, using it, we can generate sentences

like L.):

L.) Sentence L.) is false.

L.) is true iff L.) is false. This means that if L.) is false, then L.) is true, and if L.) is true, then L.) is

false. These conditionals in turn mean that if L.) is false, then L.) is true, and if L.) is true, then L.)

is false. A heap of contradiction.

There are multiple assumptions contributing to this paradox. The biconditional truth schema


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and the assumption that true and false are the only two truth values are two of the assumptions. If

we are to eliminate all inconsistency, which do we reject? There is no uncontroversial solution to this

paradox.

Second, the Paradox of the Preface (Field 2009, MacFarlane 2004). Suppose S is writing a

book. She has done meticulous research and, as far as she can tell, immaculate reasoning. Every

claim in the book is a product of her research and reasoning. So, S has strong reasons to believe every

individual claim in the book. But S also has strong reasons to believe that she is fallible (say, because S

is human, and humans are, invariably, fallible). So, S has strong reason to believe that there is some

mistake in the book at least one of the claims in the book is false. In short, S believes both that

there is no false claim in the book and that there is some false claim in the book. Both of these beliefs

are rational. S would be irrational to reject either the conjunction of all of the claims in her book

because each is, as far as she can tell, right. S would be irrational to reject her belief that she is fallible

and that her fallibility impacts this book given her very strong evidence.

In both of these cases, there is an inconsistency between powerful, well-supported claims and

there is no clear solution to the inconsistency. Given that human reasoners are finite, it may not be

rational to devote one's time to finding solutions. It may be better to simply accept the inconsistency

until a solution or an appropriate time for attempting solution presents itself. 1

Recognition Problems

Given that human reasoners have finite resources, it may be the case that there is an

inconsistency somewhere in the reasoning agent's beliefs that is impossible for a reasoner to resolve,

especially since it may require deriving a vast number of implications that the agent has no reason to


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derive. An injunction against inconsistency may run against the principle of Clutter Avoidance. Just so

for implications. It may take computational genius or infinite time to derive a particular implication

from one's beliefs, and human reasoners may not possess the capacity or the time.

In addition, recognizing logical implication and inconsistency, or logical features of any kind,

requires logical concepts or logical knowledge. Any constraint on reasoning that requires recognizing

logical features is impossible for an agent without logical concepts to respect.

Each of the above problems follows in a more or less straightforward fashion from the

assumptions A1 and A2. That is, we can see that they are at least antecedently plausible claims.

These antecedently plausible claims are severe problems for any attempt to construe logic as a theory

of reasoning.

I.3.) Burning Bridges

In order for logic to be a theory of reasoning, there must be a way to interpret the laws or

principles or parts of logic as laws or principles or parts of a theory of reasoning. What we want are

bridge principles from logic to reasoning. As a matter of course, we want this interpretation to be

systematic. Suppose we pick out a logical construction (a sequent or an argument...) P with a logical

feature F. If P represents a reasoning process R, and F represents feature G of R, then the

interpretation is unsystematic if there is a logical construction P' also with feature F that represents

process R', and R' isn't G.

One of the things that want from a theory of reasoning is recognition of when (e.g.) inference

is good. A logical theory is a foolproof, systematic way to recognize features of logical constructs. The


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utility of seeing a logical theory as a theory of reasoning is that it would give us foolproof, systematic

ways to recognize features of reasoning processes that are represented by logical constructions. If the

interpretation is unsystematic, there is nothing in the interpretation that allows us to tell when a

reasoning process is good based on recognizing features of its logical representation.

A bridge principle can give us a systematic interpretation by being of the schematic form:

Conditional Bridge Principle: If (statement about feature of logical construction), then

(statement about feature of reasoning).

A stronger systematic interpretation can be stated with:

Biconditional Bridge Principle: (Statement about feature of logical construction) iff

(statement about feature of reasoning).

In what follows, we may disregard Biconditional Bridge Principles, as we will show that the entailment

does not even run one way from logical features to reasoning features, so the biconditional versions

must be false.

A theory of reasoning may be descriptive, normative, or some combination of both. I do not

want to assume anything too strong about the distinction, if any, between normative and descriptive

principles. I merely want to note that there is an intuitive difference, and this intuitive difference can

help us sort out the ways that the above problems block bridge principles from logic to reasoning. So

we can refine the schematic bridge principle into a descriptive and normative version:

Descriptive Bridge Principle: If (statement about feature of logical construction), then

Descriptive(statement about feature of reasoning).


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Normative Bridge Principle: If (statement about feature of logical construction), then

Normative(statement about feature of reasoning).

It's not clear that, without a special relationship to some other domain (like reasoning), logic itself can

have any normative content, so I leave out the permutations that would capture the combinations of

options where logic is normative. Moreover, if logic were conceived of as normative, I can't see any

way that we could say what it was normative for without begging the question or returning to the

theory of P-reasoning.

Harman's arguments show that descriptive bridge principles would make for a pitiful theory of

reasoning and that normative bridge principles based on logic would not in any way be specially

relevant to reasoning, they would impose no indefeasible or uniquely high level constraints on

reasoning.

I.3.1.) Descriptive Bridge Principles:

Descriptive bridge principles can be ruled out right away by noting that human epistemic

behavior simply does not look anything like logical principles - neither inference rules that constrain

the behavior of theorem provers nor important logical properties like implication or inconsistency

actually seem to describe human behavior given the ~(Deduction Machines), Clutter Avoidance, and

Recognition Problems. The ~(Deduction Machines) concerns show that reasoning does not unfold the

way an argument does, from premises to intermediate and final conclusions. The considerations that

lead to the Clutter Avoidance Principles show that humans couldn't follow inference rules or

implication and inconsistency very far at all due to the limitations of mental powers. The Recognition

considerations also speak against descriptive bridge principles. Human reasoners simply do not have


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the powers to follow logic very closely in their inferences.

As discussed above, an obvious way to construct descriptive bridge principles from logic to

reasoning is to think of reasoning in terms of argument. Map parts of the reasoning process to the

parts of an argument. The premises of the argument are the beliefs S has at t1 and the conclusion is

the belief S adds at t2. Or we could take proof as the paradigm. Map steps in a proof to steps in

reasoning - at t1, P believes Premises 1-3, at t2, P infers intermediate conclusions from 1-3, at t3, P

infers final conclusion C. These seem intuitively pleasing, and it would enable a very direct proposal

for bridge principles from logic to reasoning. A theorist could simply take proof rules or "rules of

inference" from a logical system and translate them directly into rules that describe reasoning. A

standard natural deduction system contains rules Modus Ponens and Disjunctive Syllogism. Modus

Ponens translates into a rule saying that if you believe P and P->Q, then you believe Q. Disjunctive

Syllogism translates into an inference rule saying that if you believe that P v Q are the only options and

P is not true, then you believe Q. And so on. There are several reasons a proposal like this can't be

right.

First, an observation: inference rules belong to deduction systems, and deduction systems are

a dime a dozen. There are different styles of deduction system for Classical Logic. There are axiomatic

systems, natural deduction systems, sequent calculi, Quine's methods, etc. (Pollock 1990, Quine 1982,

Shapiro 2009). The inference rules can vary wildly across each of them (compare Lukasiewics axioms

to a natural deduction system), but they generate all of the same valid formulae (if they are complete

and consistent and have the same truth values). This means that there must either be one correct set

of inference rules - and an explanation for why it's the right set - or there must be many different


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right sets of principles of reasoning, each corresponding to a different deduction system. Neither of

these options is clearly unworkable, but the theoreticl difficulty is the burden of the proponent.

Second, the ~(MP Machines) argument. It is not at all clear how a reasoning process could

resemble an instance of an inference rule. Should we think, as above, of an agent S believing P and P-

>Q at time t1, and then at t2 taking on the belief Q? That's clearly a false way to characterize many

sequences of mental actions that are intuitively instances of reasoning. Sometimes an agent starts

with Q at t1 and then infers P and P->Q at t2 to justify it. There is no correct inference rule going from

Q to P and P->Q. Just so for Disjunctive Syllogism or any other inference rule. Sometimes an agent

starts with a belief Q and then realizes that, on that topic, either P or Q is true and that P is patently

false, thereby affirming the belief that Q. So this inference goes unrepresented in logic as well. As

Harman pointed out, inference often moves from a conclusion to reasons for the conclusion or from

somewhere in the middle outward to both assumptions and conclusions. Logic doesn't have any

inference rules that describe these moves. It seems that processes of inference generally do not

match inference rules.

It has not been shown that no reasoning unfolds the way that proofs or arguments unfold, but

it has been claimed that, as is antecedently plausible, there are normal instances of reasoning that do

not follow this format. If logic's only real resource for understanding reasoning is that it has rules that

mirror a small number of unusually orderly sequences of inferences (intermediate and final

conclusions), it is at best, a highly fragmentary theory of reasoning. It is an empirical question whether

most human reasoning follows the format of logical argument, and the evidence suggests that it does

not (as summarized by Hanna 2005.). A view that holds that logic descriptively captures reasoning


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fails to countenance a clear, unambiguous fact: what theorem provers do is not what reasoning agents

do. Reasoning is not theorem proving. And rules for the latter are not rules for the former.

It seems clear that inference rules do not describe actual human reasoning. Moreover,

important properties that logic codifies like implication and inconsistency are no guide to human

reasoning practice. We might propose a principle of reasoning that says that if agent S finds that P

entails Q, S will infer Q. The considerations of Clutter Avoidance and Recognition show that any

principle like this is false. Implications and inconsistencies may not only go unnoticed by human

reasoners, they sometimes are impossible to recognize given human computational and storage

limitations. Even if one invokes the distinction between implicit and explicit beliefs, it is not possible

for reasoners to infer every implication of their beliefs because it may take some inhumanly intricate

proof to recognize the implication.

Of course, the space of actual practice may not be what logic is supposed to model. The

natural response to these considerations is that logic is designed to model correct reasoning. In fact,

historically, logic was developed to model the reasoning involved in successful mathematical proof

(Burgess 1992). If anything could be said to mimic the steps of proof that logic specifies, it would be

the thoughts of mathematicians. But here there is conflation between A-reasoning and P-reasoning.

The word "reasoning" can denote mental actions or processes and it can denote products of mental

processes. These are very different categories. It seems clear that logic can represent and explain

why the mathematical proof that there is no prime number is a proof or why such an argument is

valid. But that does not mean that its discovery was produced by a process that looks anything like

the proof itself. It does not follow that the inference to the conclusion that there is no prime number


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looks at all like something that a logical system can generate. Even the inferences of mathematicians

do not follow the pattern of proof. Consider Burgess' (1992) discussion of mathematics' contexts of

discovery and justification:

[I]t must be acknowledged that the requirements of rigor pertain to the context of

justification, publication for collective evaluation by a community of colleagues, and not

to the context of discovery, private mental processes of individual researchers. No one

discovers a theorem by first discovering the first step of the proof, second discovering

the second step of the proof, and so on. The role of inductive, analogical, heuristic,

intuitive, and even unconscious, thought in the context of discovery has been

emphasized by all mathematicians discussing mathematics[...]

Logic is, as has already been discussed, a good theory of the product of a mathematician's reasoning,

her arguments and proofs. Not so a theory of the actual process by which she constructed these

products. Of course, that is not the issue at hand. Logic may be the science of valid argument or

proof, but then the task of clarifying the role of valid argument or proof in A-reasoning remains.

More to the point, the moment we inject the concept of correct reasoning into the discussion,

we have crossed over into thinking about normativity.

I.3.2.) Normative bridge principles:

The received view is that the process of reasoning is a lot like the way an argument proceeds.

An agent begins with previously held beliefs and in a stepwise fashion derives intermediate and final

conclusions. Since logic is so well developed and so clearly codifies arguments, it's natural to think


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that we can translate features of logic directly into principles for reasoning. We have seen why this is

likely to be false descriptively, but perhaps it may be true normatively. That is, we may propose that

logic models correct reasoning. It doesn't matter whether most actual reasoning is described by

principles of logic, the point is that it ought to because correct reasoning resembles argument or

proof. However, we shall see that actual agents are often right when they do not do as logic would

advise them to.

Since we are talking about normative bridge principles, perhaps we can find a way to translate

proof rules into correct reasoning, even though they cannot correctly describe a great deal of

reasoning practice. A theorist could take proof rules or "rules of inference" from a logical system and

translate them directly into rules that describe what an epistemic agent does when reasoning right.

Suppose a standard natural deduction system agan. Modus Ponens could translate into a rule saying

that

Modus Rulus.) if you believe P and P->Q, then you (deontic operator) 2 to believe Q.

Disjunctive Syllogism or other inference rules could translate similarly. There are several

reasons a proposal like this can't be right.

First, remember that inference rules belong to deduction systems, and deduction systems are

legion. This means that there must either be one normatively correct set of inference rules - and an

explanation for why it's the right set - or there must be many different right sets of principles of

reasoning, each corresponding to a different deduction system. This is not a knockdown objection,

but it makes the bridge principle theorist's job complicated.


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Second and stronger, human reasoners are not normative Modus Ponens machines either.

There are cases where, rather than being obligated to infer Q from her beliefs P and P->Q, S is right to

infer ~P or ~(P->Q). Just so for every other inference rule. The proof of this is simple. Suppose that i.)

the overall goal of reasoning is to try to believe in accord with any epistemic desideratum coherence,

truth tracking, etc. and ii.) that reasoners are fallible - a reasoner's premises can be incoherent, false,

etc.. Now, suppose S believes P and P->Q and S also believes ~Q. In our hypothetical scenario,

suppose also that P is false (or incoherent with S's other commitments, or...). In this case, S's beliefs

are obviously brought in line with the truth (or made more coherent) by rejecting her belief that P

rather than inferring Q (or revising her belief that ~Q). 3 We don't have to accept i.) strongly, either.

We merely need to assume that the goal of believing true things (coherent things) imposes some

constraint on S's reasoning. S then has reason to reject P even though Modus Ponens says that she

should infer Q. Clearly, in some scenarios, conforming to inference rules goes against our best

epistemic interests.

Third, there are instances of incorrect reasoning that look like valid arguments. Suppose that S

believes P and P->Q and S believes ~Q. Should S still infer Q? If she did, her inference would look like

an instance of Modus Ponens. She ends up with a contradiction if she does. It may not be

indefeasibly wrong to believe inconsistencies, but it surely it indicates that something is not as it

should be in S's beliefs.

Fourth, extending ~(Deduction Machines), it is at least prima facie false to say that agents that

do not infer in the same order of steps as a proof are breaking a law or rule of reasoning. There is a

lot of good reasoning that does not unfold according to inference or proof rules. Any instance of


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induction is an example. If we are committed to translating proof rules into principles of reasoning,

then logic provides at best a fragmentary theory of reasoning, one that does not really give us the

ability to tell whether an instance of reasoning is right or wrong. Logic is not specially normative for

reasoning, then. It is just like any partial theory of a complex phenomenon.

Another proposal for bridge principles presents itself immediately. Proof rules are not rules for

inference (qua reasoned change in view), but they are rules for recognizing implication and

inconsistency. A feature of logical systems is that successfully constructing a valid argument or proof

with the proof rules of a system demonstrates that the conclusion is implied by the premises. The

emphasis in logic of implication can be shown by the fact that so much interest has been placed on

completeness and inconsistency proofs logicians want to know whether proof rules generate all of

the same validities and implications as semantic analysis does. Any implication or inconsistency can,

in principle, be verified by checking its truth table. So it is plausible that bridge principles should focus

on properties of implication or inconsistency rather than inference rules.

Implication Principle I.) If P is logically implied by S's view, then S has a reason to believe

P.

There is preliminary discussion to get to before we note Harman's dismantling of this proposed

principle. Suppose S believes P and P->Q. S's view classically implies Q. By the letter of the principle

I.), S has a reason to believe Q. But human reasoners are not Modus Ponens machines; sometimes S

should not infer Q, but should rather infer ~P or maybe ~(P->Q). Notice that the shift of locution

from "S has a reason to believe ..." to "S should infer ..." is not negligible. A rule describing what one

has a reason to believe is not equivalent to a rule describing what one should infer. We can see this


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clearly if we read should as should ultimately or should, on final assessment. At least, that

equivalence does not follow without the further assumption that one should infer anything that one

has the slightest reason to believe. Since we are without that assumption here, it looks like the

counterinstances provided by ~(Deduction Machines) are really perfectly compatible with principle I.).

In all of the cases Harman presents, it may turn out that S should infer something that implication

gives her a reason not to infer or vice versa.

Here, I want to digress to a textual consideration. In Harman (1973), (1986), (2002), (2005),

(2009) and Harman and Kulkarni (2007), the project is to show that logic is not specially relevant to

reasoning. This is important. Harman is often at pains to point out that he does not think that logic

has no relation to reasoning. Logic has the role in reasoning of any good science, we want to believe

the right things about it and not use the things we believe about it to infer falsehoods. Harman (1973

Ch. 3, 10; 1986 Ch. 7; 2002; Harman and Kulkarni 2007, Ch. 1) argues that argument, deduction, and

implication do have interesting roles in reasoning. These roles may even turn out to be robust. The

major point is that the role is not that of a highest level norm or constraint on reasoning practice. You

are not irrational if your belief revision moves do not match a proof. You may be irrational if the only

considerations you have no support for your view and you know of many valid arguments and proofs

from things you believe to something other than your view.

Without wandering into a conceptual analysis of specially relevant, I want to propose this

reading: If it turns out that logical principles are connected to reasoning by bridge principles that

impose defeasible and not generally overwhelmingly strong epistemic constraints, then logic isn't

specially relevant to reasoning. It is a discipline that presents one among many epistemic constraints


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on reasoning. Here, it might help to distinguish some grades of obligation potentially imposed by a

principle of reasoning.

Rules of correct reasoning impose some degree of epistemic obligation or permission on a

cognizing agent. Since we are assuming that reasoning is essentially the process of inference or

revision of beliefs, rules of correct reasoning will state what a reasoning agent is to infer given what

she already believes. Here are four informal examples of the degree of obligation that a rule of

correct reasoning might impose:

i.) If you believe P and P->Q, you must infer Q (if you don't, you are irrational).

ii.) If you believe P and P->Q, you are (especially) strongly obligated to believe Q (but

especially strong counterevidence can make it rational not to).

iii.) If you believe P and P->Q, you have a reason to believe Q (a reason that can be more

or less easily counterbalanced to make ~Q perfectly rational).

iv.) If you believe P and P->Q, you are permitted to believe Q (but feel free not to).

The thesis under investigation is that logic provides no indefeasible or overwhelmingly strong laws for

reasoning. i.) captures an indefeasible requirement for rationality. ii.) is a strong obligation. If logic

provides principles of strength i.) or ii.), that counts as satisfying the special relationship clause. The

grades of iii.) and iv.) are not sufficient to satisfy the condition of special relevance. That is, if we find

bridge principles from logic to reasoning of grades iii.) or iv.), we have found bridge principles that are

perfectly compatible with Harman's thesis. In such a case, logic provides only principles that are

defeasible, that may be overridden by other considerations in reasoning that are not especially


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powerful. If all of the bridge principles we discover impose low grades of obligation, logic is not

specially relevant to reasoning.

So, on the initial proposal I.), S can have a reason to come to infer Q while also being strongly

or most strongly obligated to infer ~P or ~(P->Q). Here, I'm assuming that "S is strongly or most

strongly or just more strongly obligated to infer ..." is something pretty close to "S should infer ...". On

the final tally of reasons that S has, the implication of Q by S's view may be outweighed by other

considerations - stronger epistemic obligations to believe ~Q, a greater number of parts of S's view

implying ~P, etc. I.) does not amount to a special relevance of implication to reasoning. A parallel

argument can be made for a similarly structured inconsistency principle. We are obligated to some

degree to not retain inconsistencies, but sometimes other considerations just overpower that

obligation. Even if the obligation imposed by an implication or inconsistency principle is very high, it is

still possible that it is outweighed by either other epistemic obligations or constraints on reasoning

ability. (This is the insight of MacFarlane's view, in my estimation).

It should be at least prima facie clear that indefeasible implication principles are falsified by

Harman's ~(MP Machines), Clutter Avoidance, and (arguably) Recognition Problems. It is in fact

rational for S to not infer P sometimes even if P is implied by S's view due to the actual or potential

existence of other epistemic constraints, storage limitations, and computational limitations. If I.) and

an indefeasible principle were the only options, since an indefeasible principle is clearly false on

Harman's considerations, logical implication would clearly not have a special relevance to reasoning; it

would merely put one among many obligations on our reasoning practice.

But maybe we are aiming slightly too high. Indefeasibility is not the place to look. It could be


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that logical implication imposes the single strongest obligation on inference while still being a

defeasible obligation. Maybe something like I+.) is right...

I+.) If P is logically implied by S's view, then S has a degree of obligation x to infer P -

where x is greater than y, and y is the next strongest degree of epistemic obligation

imposed by any other single reasoning principle.

A parallel principle would take care of inconsistency - we have the strongest of obligations to eliminate

inconsistencies, but I+.) is defeasible. I+.) is consistent with the fact that sometimes we should not act

like Modus Ponens machines. While I+.) can get past ~(Deduction Machines), Harman's

counterexamples form a coherent net that screens off potential principles of logic cum reasoning.

Remember the principle of Explosion. If S believes P and ~P, then S can deduce any Q. But if that's

allowed, on principle I+.), S has the highest degree of obligation to infer an arbitrary Q. In fact, S is

obligated to infer infinitely many arbitrary propositions. That obviously cannot be right; remember

Clutter Avoidance.

It would be a potentially egregious mistake to infer an infinite number of sentences from what

you believe (inconsistent or not). But the wrongness of I+.) is not merely a matter of S having

competing epistemic obligations or cognitive limitations that outweigh the obligation imposed by I+.).

Intuitively, S has no real obligation to infer arbitrary propositions at all. Inconsistent beliefs don't

license you to infer that anything goes. Everything obviously does not go. More precisely, we are at

least interested in roughly keeping track of truth with our beliefs, and it is clearly not true, on cursory

observation of even local parts of the world, that every arbitrary sentence you could possibly conjure

up is true. (Try it! Find an inconsistency in your beliefs, observe some fact Q, then prove that that fact


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is false. Do you sense that you are justified in your belief Q?)

We might save I+.) by proposing an inconsistency principle that prohibits us from maintaining

an inconsistency in our beliefs, so we need not ever worry about having to infer arbitrary nonsense.

There are two problems with such a proposal. First, it means that the inconsistency principle takes

priority over the implication principle; we should make sure the inconsistency principle is respected

before applying I+.). Of course, this means that the clause explaining the value of x in I+.) is false.

Second, unless the inconsistency principle is indefeasible, there is always the possibility that an

agent will rightly retain an inconsistency (Unavoidable Inconsistency), in which case I+.) comes into

play and we are very strongly obligated to fill up our minds with nonsense.

Concerning the first problem, we could always switch the values of x and y so that the

inconsistency principle imposes the strongest epistemic obligation and the implication principle

imposes a weaker but still very strong obligation. That's all well and good, but the second problem

remains as strong as ever. The consideration of Unavoidable Inconsistency shows that any proposed

indefeasible inconsistency principle is false.

These objections rule out an indefeasible inconsistency principle. But that means that

accepting I+.) forces us to accept the possibility that we can be obligated to infer everything we can

imagine willy nilly (that is, willy nilly modulo other epistemic principles). There are two options:

accept that I+.) is false or suggest that our mysterious other epistemic principles come online when we

retain inconsistent beliefs to prevent us from being obligated to clutter our minds by I+.). Accepting

that I+.) is false is accepting that logical implication is not specially relevant to reasoning - it gives us

(potentially very high grade but defeasible) reasons to believe and nothing more. Relying on some as


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yet unspecified other reasoning principles is doing exactly what Harman wants us to do - develop

principles of reasoning that override logical principles and are not logical principles or transparently

derived from logical principles. I+.) may technically be the single strongest constraint on reasoning,

and so may technically be specially relevant at least in normal situations where other reasoning

principles don't gang up to take it down. This technical victory seems slim enough that we might be

suspicious of our previous decisions about the satisfaction of the predicate is specially relevant for

reasoning.

So inconsistency and implication are not the logical principles to focus on for discovering a

bridge principle from logic to reasoning because they strain against each other too much. There is a

logical feature of sets of sentences that balances them. Logical closure. Maybe this is right:

C.) S (is indefeasibly obligated or is strongly obligated) to infer or reject whatever S

needs to infer or reject in order to make sure S's beliefs are closed under logical

implication.

This cannot be right. In fact, it fares worse than the implication principle. I leave the deontic strength

of the rule open because the indefeasible and strong versions of it must fail. A closure principles

treats beliefs like a set of sentences. A set T of sentences is closed under logical implication iff every

sentence that is in T and every sentence implied by a sentence in T is in T and there are no

inconsistencies. Closure requires that everything implied by something you believe is in your beliefs

as long as there are no inconsistencies. This principle offers enough flexibility to avoid the fact that

people are not Modus Ponens machines, as sometimes agents ought to retract belief that P or that P-

>Q.


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However, infinite trivialities are classically implied by any single belief. A principle like C.) is

clearly absurd if we are indefeasibly required to infer infinite trivialities; remember Clutter avoidance.

In order to avoid inferring infinite trivialities, we would have to drop every belief out of set T. Such a

principle is only slightly less absurd if we are only strongly obligated to infer infinite trivialities. Here, I

appeal to intuition. We are not strongly obligated to infer infinite trivialities. We shouldn't need to

marshal ampliative reasons (say, about computational or memory limitations) to justify not inferring

an infinite number of trivialities. A skeptic on this point is encouraged to provide an argument. Until

then, the only plausible level of obligation for such a principle is at the level of "S has a reason to

believe..." (or weaker, "S has permission to believe...") and that is clearly the level that Harman would

have us accept is appropriate for the normativity of logic. Logic is not special!

Part II: Enter Field and MacFarlane

Hartry Field (2009) and John MacFarlane (2004) offer fascinating and informed takes on

Harman's arguments. Unfortunately, I think that, insofar as they take themselves to be refuting

Harman's arguments, they fail.

II.1.) Field Day

Field (2009) attempts to reject Harman's arguments against the view that logic is a theory of

reasoning by a.) supplying a bridge principle between logical implication and reasoning that invokes

degrees of belief and b.) offering an argument from solutions to semantic paradoxes against Harman's

view of logic. I will not take up b.) in this paper, as Harman (2009) notes that the view of logic that

Field argues against is not the view that Harman himself accepts.


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Concerning a.), I will argue that Field's bridge principle does not provide logic a special

relevance to reasoning. Field's considered view of the normative impact of logic on reasoning is:

E.) Employing a logic L involves it being one's practice that when simple inferences of the

form A1, ..., An|-B licensed by the logic are brought to one's attention, one will normally

impose the constraint that P(B) is to be at least P(A1)+...+P(An) - (n - 1).

Harman (2009) points out that that insofar as Field appeals to employing a logic or a logic's licensing

inference, he might be begging the question against Harman (1986). For Harman explicitly argues

against the idea that an agent might employ a logic as a set of normative constraints on belief. Field's

view is not clearly circular to me, as I take him to be offering an explication of the idea of employing a

logic in order to aid in addressing the question of whether or not agents actually employ logics. In any

case, Harman (1986) argues at length against the idea that probabilities play the role in belief that

Field's response requires of them, so Field's arguments against Harman (1986) are at best incomplete.

These criticisms aside, it should be noted that Field's purported rejection of Harman's view is

not a rejection at all. Let us grant that one might employ a logic to constrain one's degrees of belief.

Field's final view leans on an important qualification: that one employs a logic if if that logic licenses

an inference, it is normally one's practice to constrain one's beliefs in the appropriate way. Since the

most appropriate way to read Harman in (1986) and elsewhere is as presenting arguments that logic is

not specially relevant to reasoning, Field's view shows us nothing that is not ultimately compatible

with Harman's view. 4

First, some some semi-formal definitions of notions that I will take for granted:


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Epistemic agent.) S is an epistemic agent iff - i.) S has a set of beliefs B, ii.) S has powers

of revision over the set B such that S can add and subtract members of B, iii.) S's

application of revisionary powers is subject in all situations to possibly conflicting

epistemic constraints, and iv.) the epistemic constraints that S is subject to may vary

from one situation to the next

Epistemic Constraints.) an epistemic agent S is under an epistemic constraint M iff v.) if

conditions x,y,z are met, then epistemic agent S is under n-degree of obligation to add or

subtract a belief P and vi.) a rule M expresses v.)

Essentially, I think the notions of epistemic agents and epistemic constraints are obvious. Epistemic

agents have representational views or theories of the world or conceptual systems and they revise

them. But they do so under constant pressure from multiple and possibly competing epistemic

constraints, for they don't want to be wasting their epistemic resources. Clause iv.) is just a matter of

respecting the plausibility of epistemic contextualism.

One's practice of normally constraining one's beliefs in a certain way does not amount to a

special normative constraint on reasoning. One only constrains one's degrees of belief in the way

stated in E.) when there are no factors that make it better not to constrain one's beliefs in that way.

Consider a toy situation: S is an epistemic agent. It is brought to S's attention that A1,...,An|-B in her

logic. E.) says that, given the licensing of A1,...,An|-B, S normally constrains S's beliefs so that P(B) is at

least P(A1)+...+P(An) - (n-1). Cashing "normally" as "in most situations", we can see that an epistemic

agent S, always under a set of epistemic constraints, will respect E.) in most situations. That is,

constraining her beliefs in the way of E.) is S's default rule. If there are conflicting epistemic


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constraints in most situations, they are overridden by E.). Its normally being the case that one

constrains one's belief in the manner of E.) when a simple licensed inference A1,...,An|-B is brought to

one's attention means that finding out about a licensed inference imposes a stronger obligation than

the other epistemic constraints on an epistemic agent in most situations.

So what? The obligation imposed by E.) is still highly defeasible. There are still any number of

situations (below the threshold, whatever it is, of most situations) where E.) is either not the

strongest constraint on S's reasoning or it is overruled by a combination of other constraints. The

normal case need not represent even the most frequent case it merely must be the case matching

S's default assumptions. In what sense is logic specially relevant to the theory of reasoning, then?

Noticing a simple, licensed inference imposes a ceteris paribus epistemic constraint on S, and that is

exactly what Harman and Kulkarni say that logic imposes on reasoning:

Deductive logic is a theory of what follows from what, not a theory of reasoning. It is a

theory of deductive consequence. Deductive rules like (R) are absolutely universal rules,

not default rules; they apply to any subject matter at all, and are not specifically

principles about a certain process or activity. Principles of reasoning are specifically

principles about a particular process, namely a process of reasoning. If there is a

principle of reasoning that correspondes to (R), it holds only as a default princple, that is,

other things being equal. (2007)

These considerations do not show that Field's view is false, merely that if he takes himself to refute

Harman's points about logic, he is wrong. In fact, the bridge principle that Field proposes may be

right. There are resources in Harman's overall philosophical views that conflict with it (e.g., over


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degrees of belief (see Harman 1986) and conception of logic (see Harman 2009)), but that alone does

not show the bridge principle false. Field may be exactly right about this bridge principle, and right

about degrees of belief, and right about the nature of logic, while being wrong about the bridge

principle's import for Harman's views about the relation between logic and reasoning. Perhaps E.) is

the relation between logic and reasoning.

II.2.) Conflicting Norms and Logic

MacFarlane's (2004) is a very subtle, systematic, and deeply satisfying paper to read. That

being said, I will gloss over the main part of it and discuss only the major conclusions. MacFarlane

supports two potential bridge principles between logic and reasoning in tandem:

If A, B |= C, then

Wo-: you ought to see to it that if you believe A and you believe B, you do not disbelieve

C

Wr+ you have reason to see to it that if you believe A and you believe B, you believe C

The principles focus on implication. Where the W means that the deontic operator has wide scope

or scope over the entire conditional. The o means that the deontic operator is at the grade of S

ought to.... The r means that the deontic operator is at the grade of S has a reason to.... The +

and - indicate belief and disbelief. The two bridge principles are complementary. To see this, we

must rewind and visit a part of Harman's and Field's discussions that we have so far ignored.

In Harman (1986) and Field (2009) bridge principles are proposed that connect logic to

reasoning by way of recognized or obvious logical implication in order to deal with the Recognition


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Problem. When one realizes that there is a logical implication, then it has an impact on what one

should do in reasoning. That is, recall Field's E.)

E.) Employing a logic L involves it being one's practice that when simple inferences of

the form A1, ..., An|-B licensed by the logic are brought to one's attention , one will

normally impose the constraint that P(B) is to be at least P(A1)+...+P(An) - (n - 1).

If the logical implication is comprehended by an agent, then the agent is under a constraint. Harman

deals with this kind of principle by noting that it is not at all clear that such a recognized or immediate

implication based principle will set logical implications apart from any other kinds of immediate or

obvious implication. Consider whether X is Y's brother immediately implies X is male or whether

Today is Thursday immediately implies that Tomorrow is Friday. These are not logical implications

(at least, not without assuming some set of axioms that define brotherhood or the relation between

days of the week).

A deeper problem with this view is due to MacFarlane. If we relativize the normative

restrictions that logic imposes on an agent to an agent's logical abilities or knowledge, then we are

essentially promoting logical ignorance. If S is under an obligation to not believe C only if S is aware

that her view logically implies that C is false, then the less S knows about logic, the greater her liberty

to believe C. If S does not know that her view implies that C is false, she does not have an obligation

to not believe it. In Field's terms, if it cannot be brought to her attention, she does not need to

normally constrain her beliefs so that the P(B)... To parody the point: suppose that C is a patently

absurd claim and S is irrational to believe C given her logical knowledge. Suppose that there is a

surgery S can undergo that removes her logical knowledge. If we only hold that she is obligated to not


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believe C if she knows about logical implication, her continuing belief in C can be made more rational

by surgically removing her logical knowledge center. This can't be right. In MacFarlane's words:

The more ignorant we are of what follows logically from what, the freer we are to

believe whatever we pleasehowever logically incoherent it is. But this looks

backwards. We seek logical knowledge so that we will know how we ought to revise our

beliefs: not just how we will be obligated to revise them when we acquire this logical

knowledge, but how we are obligated to revise them even now, in our state of ignorance.

To spin it in an intuitive way, logical norms should tell us what we are learning logic for. And

MacFarlane's principles seem to codify that intuition. Wr+ and Wo- complement each other in that,

where an agent operating under Wo- is only obligated to not disbelieve Q (where disbelief roughly

plays the role of believing the negation), she can get away with simply not inferring Q. But with Wr+

in action, she does have reason to believe Q. That seems to be the right assessment of the situation.

Even if S is ignorant of the relevant implication, she has some defeasible, possibly default reason to

figure it out.

Although this seems like the right solution to the problem of logical ignorance, there is no

reason to reject Harman's view that logic is not specially relevant to reasoning. Indeed, it is not

MacFarlane's goal to reject Harman's views, but to explain how logic relates to norms of belief revision

given that there are difficulties like the ones that Harman raises for understanding the relation

(MacFarlane 2004, pg. 5). MacFarlane's key insight is that epistemic agents operate under multiple,

possibly competing obligations and these can override the obligations that logic imposes on them.

MacFarlane even goes so far as to propose multiple, occasionally competing logical obligations. One


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logical obligation may overwhelm or even completely block another under the right conditions.

Discussing the preface paradox:

From the fact that it is more rational for our writer to keep her logically incoherent

pattern of belief and disbelief than to revise it in the ways now open to her , it does not

follow that she is not obligated to revise her beliefs and disbeliefs in a way that restores

logical coherence. For it may be that making her beliefs coherent in any of the ways now

open to her is also forbidden. She cannot give up all of her individual beliefs about sea

turtles, because in each case she is under an obligation to believe that for

which she has compelling evidence. But she cannot give up her general inductive

disbelief in her own infallibility, either, because it too is well grounded in evidence. Thus

she is under conflicting obligations. Whatever she does, she will not be entirely as she

ought to be.

If there is a critical blindspot in Harman's view, it is that there may be situations where epistemic

constraints cause a glut. Perhaps we ought to try to bring them into coherence or perhaps we ought

to retain the problematic principles until a solution is available.

The bridge principles Wo- and Wr+ do not show that logic has a special relevance to reasoning,

they impose two among many constraints on belief revision. Wo- allows S to refuse to infer C if it is

implied by her beliefs but obligates S to not disbelieve it so long as she doesn't reject the beliefs that

imply it. This is compatible with the four problems we have been studying. If she believes P and P->Q,

then Wo- says that she must not believe ~Q while retaining P and P->Q. The ~(Deduction Machines),

Clutter Avoidance problems are consistent with this. Where Wo- is troubled by Unavoidable


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Inconsistency (sometimes S ought to believe Q and ~Q even if she believes P and P->Q), MacFarlane's

view allows that Wo- conflicts with other epistemic norms. It's fine that Wo- is troubled. That's just

going to happen and hopefully S can fix it eventually. Wo- is a deontically strong constraint on

reasoning, but not The Mother of All Constraints. It is not specially relevant. Wr+ says that S has

reason to believe what is implied by her beliefs, but as we mentioned before, having reason to believe

something does not amount to a special relevance for reasoning.

The duo of logical bridge principles, Wo- and Wr+, places constraints on reasoning, but not

uniquely strong constraints. As the discussion earlier concluded, if we explain logic's connection to

reasoning without finding an especially strong or unique role for it, we are just unpacking the idea that

logic has no special relevance to reasoning. That being said, MacFarlane proposes an immensely

appealing theory for doing just that.

Conclusion and Recapitulation

The discussion so far can be summarized as the following argument:

A1. Logic is the science of implication/consequence and is correctly codified in ClassicalLogic.

A2. Reasoning is A-reasoning (process, activities; belief revision/change inview/inference to most coherent view.)

1. If Problems 1-4 defeat all strong or specially relevant bridge principles, then logic isnot a theory of A-reasoning and logic imposes no specially relevant constraints on A-reasoning.

1.1. Problems 1-4 show that logic may only describe or model a tiny fragment of A-reasoning.

1.2. Problems 1-4 show that logic imposes no specially strong normative constraints onA-reasoning.


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1.3 Neither Field's nor MacFarlane's bridge principles are strong or specially relevantenough to show logic is specially relevant to A-reasoning.

2. Problems 1-4 defeat all available strong or specially relevant bridge principles.

C:. Logic is not specially relevant to A-reasoning - it is not a theory of A-reasoning andlogic imposes no specially relevant constraints on A-reasoning.

It does not follow that logic does not have an important and oft-employed relevance to

reasoning (e.g. in philosophical reasoning and other discursive disciplines) and to the theory of

reasoning (e.g., as a theory of P-reasoning that translates into some complexly interrelated, defeasible

constraints on A-reasoning). Though the most attention has been paid to Harman's negative

considerations concerning the bridge between logic and reasoning, the negative case should not be

overstated. It's important to recall his positive suggestions about the relation. Rationality may require

sensitivity to logical implication and inconsistency (1986, ch. 2). Deductive arguments, proofs, and the

logical laws and consequence relations that go along with them may often be a part of reasoning, and

explanation often relies on valid argument and logical implications (1973, 1986, w/Kulkarni 2007).

There is, on Harman's view, a role for logic in reasoning, but not as a theory of reasoning or as a set of

(uniquely powerful or informative) norms for inference. Harman explicitly calls for the spelling out of

this role :

It is true that deductions, proofs, and arguments do seem relevant to reasoning. [...] It is

an interesting and nontrivial problem to say just how deductions are relevant to

reasoning, a problem that is hidden from view by talk of deductive and inductive

reasoning, as if it were obvious that some reasoning follows deductive principles. It must

be useful to construct deductions in some reasoning about ordinary matters, and not


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just when one is explicitly reasoning about deductions or proofs. But why should it be

useful to construct deductions? What role do they play in reasoning? Sometimes one

accepts a conclusion because one has constructed a proof of that conclusion from other

things one accepts. But there are other cases in which one constructs a proof of

something one already accepts in order to see what assumptions might account for it. In

such a case, the conclusion that one accepts might be a premise of the proof. The

connection between proofs and reasoning is therefore complex. (2002)

Given the argument above, it seems that a full answer to the motivating question from our

introduction will have to have certain properties. Theories that do not reject the above argument will

be committed to constructing a theory of defeasible logical constraints on A-reasoning that interact

with other constraints on A-reasoning. Field and MacFarlane provide two distinct inroads. Deciding

between these two candidate bridges, or a structurally different third candidate (Christensen 2004,

Brandom 2006), or even some as-yet unformulated new proposal is a complicated task that demands

further attention.

Theories that insist that logic bears a special relevance to reasoning must take the form of a

theory that: i.) finds an alternative conception of logic that is impervious to Problems 1-4 (Reject A1),

ii.) finds an (empirically, normatively) adequate alternative conception of reasoning to which 1-4 do

not apply (Reject A2), iii.) proposes a new bridge principle that is is somehow immune to Problems 1-4

(Reject 2), or iv.) cleverly shows that Problems 1-4 do not defeat the available bridge principles

(*Reject 2), or v.) combines the foregoing tactics.

For instance, Johan van Benthem seems to implement i.), Reject A1. His Logical Dynamics


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program (1996) takes A-reasoning to be a part of the entire suite of tasks, abilities, and procedures

that agents employ to represent and transform information. Logic is the unified project of

understanding this suite, using logical systems as the tools (2010). On this broadened view of logic,

very few divergences between logical models and actual practices come up, and they matter little as

one of the guiding facts that logical dynamics must countenance that epistemic agents insert formally

designed divergences from natural inferential or cognitive practice into natural practice. The balance

between modelling actual informational tasks and correct informational tasks is a delicate one (van

Benthem 2008). Other views that emphasize the delicate relation between modelling actual practice

and specifying correct practice in logic and reasoning: Shapiro (2001) and Burgess (1992).

Remarks in Harman and Kulkarni (2007) suggest that Harman would not actually oppose the

construction of a formal theory of reasoning along these lines (or, for instance, AGM Theory

(Alchourron, Gardenfors, and Makinson 1985, Ove Hansson 2006) or perhaps Dynamic Epistemic Logic

(Van Ditmarsch 2008)). It is rather suggested that he would tend to see these programs as not actually

being logics but the theory of reasoning calling itself logic. Deciding whether this is merely a

terminological dispute is worth investigation. My own prefered solutions, to the questions lately

raised and to the motivating quest, are merely distant sketches at the moment.


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1. There are other problems of this form. The Copenhagen interpretation of quantum mechanics

looks inconsistent with the laws of Classical Logic, and the Copenhagen interpretation has

good support. Which do we toss out? Which would we be better off retaining? For doing

work in just about any field, we do well to retain both.

2. Replace deontic operator with a deontic operator phrase like ...are obligated..., ...are

permitted..., ...have a reason....

3. Note that this does not mean that logic had nothing to do with her making the right move. It

just means that a bridge principle translating rules of inference into rules for reasoning moves

won't do the job of explaining how logic helps her make the right move.

4. This does not mean that Field does not show us anything incredibly informative his

consideration of alternative logics in designing a bridge principle may require a further paper


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Bibliography

Alchourrn, C.E., P. Grdenfors, and D. Makinson. (1985) On the Logic of Theory Change: Partial Meet

Contraction and Revision Functions." Journal of Symbolic Logic. 50: 510-530.

Beall, J.C. and Restall, Greg. (2000) "Logical Pluralism." To appear, Special Logic issue of the

Australasian Journal of Philosophy. Accessed Online:

http://citeseer.ist.psu.edu/viewdoc/download ? doi=10.1.1.100.5715&rep=rep1&type=pdf

van Benthem, Johan. (1996) Exploring Logical Dynamics . Stanford; CSLI Publications

van Benthem, Johan. (2008) "Logic and Reasoning: Do the Facts Matter?" STUDIA LOGICA. V olume

88, Number 1, 67-8

van Benthem, Johan. (2010) Logical Dynamics of Information and Interaction . New York; Cambridge

University Press. Accessed online:

www.stanford.edu/class/cs222/Dynamic2010.BOOK.89new.pd

Brandom, Robert. (2006) Elaborating Abilities: The Expressive Role of Logic. John Locke Lectures

2005-2006 - Between Saying and Doing: Towards and Analytical Pragmatism . Accessed Online:

http://www.pitt.edu/~brandom/locke/index.html

Burgess, John P. (1992) "Proofs About Proofs: A Defense of Classical Logic." Proof, Logic, and

Formalization . Ed. Michael Detlefsen. London: Routledge.

Christensen, David. (2004) Putting Logic in Its Place: Formal Constraints on Rational Belief. Oxford;

Clarendon Press
http://citeseer.ist.psu.edu/viewdoc/downloadhttp://citeseer.ist.psu.edu/viewdoc/download?doi=10.1.1.100.5715&rep=rep1&type=pdfhttp://www.stanford.edu/class/cs222/Dynamic2010.BOOK.89new.pdhttp://www.pitt.edu/~brandom/locke/index.htmlhttp://www.pitt.edu/~brandom/locke/index.htmlhttp://citeseer.ist.psu.edu/viewdoc/download?doi=10.1.1.100.5715&rep=rep1&type=pdfhttp://www.pitt.edu/~brandom/locke/index.htmlhttp://www.stanford.edu/class/cs222/Dynamic2010.BOOK.89new.pdhttp://citeseer.ist.psu.edu/viewdoc/download


44/45


van Ditmarsch, Hans. (2008) Dynamic Epistemic Logic . Synthese Library 337. Dordrecht; Springer.

Field, Hartry. (2009) "What is The Normative Role of Logic." Aristotelian Society Supplementary

Volume 83 (1):251-26

Hanna, Robert. (2005) Rationality and Logic . Cambridge; MIT Press.

Hansson, Sven Ove. (2006) "Logic of Belief Revision." Stanford Encyclopedia of Philosophy . Accessed

Online: http://plato.stanford.edu/entries/logic-belief-revision/

Harman, Gilbert. (1986) Change in View . Cambridge; MIT Press.

Harman, Gilbert. (1973) Thought . Princeton; Princeton University Press.

Harman, Gilbert. (2002) "Internal Critique: A Logic is not a Theory of Reasoning and a Theory of

Reasoning is not a Logic," in D.M. Gabbay, R.H. Johnson, H.J. Ohlbach, and J. Woods, eds.

Handbook of the Logic of Argument and Inference: The Turn Towards the Practical. Volume 1 in

Studies in Logic and Practical Reasoning. Amsterdam: Elsevier Science B.V., pp. 171-86.

Harman, Gilbert (2005) "Epistemology as Methodology." Ed. Jonahan Dancy, Ernest Sosa, and

Matthias Steup. A Companion to Epistemology . Malden, MA: Wiley-Blackwell. 2010. pp.\ 152-

156. Accessed online: http://www.princeton.edu/~harman/Papers/Profile.pdf

Harman, Gilbert (2009) "Field on the Normative Role of Logic." Proceedings of the Aristotelian

Society . Accessed online: http://www.princeton.edu/~harman/Papers/Harman_on_Field.pdf

Harman, Gilbert and Kulkarni, Sanjeev. (2007) Reliable Reasoning . Cambridge; MIT Press.

Hofweber, Thomas. (2004) "Logic and Ontology." Stanford Encyclopedia of Philosophy . Accessed
http://plato.stanford.edu/entries/logic-belief-revision/http://www.princeton.edu/~harman/Papers/Profile.pdfhttp://www.princeton.edu/~harman/Papers/Harman_on_Field.pdfhttp://plato.stanford.edu/entries/logic-belief-revision/http://www.princeton.edu/~harman/Papers/Profile.pdfhttp://www.princeton.edu/~harman/Papers/Harman_on_Field.pdf


45/45


online: http://plato.stanford.edu/entries/logic-ontology/#2

Jacquette, Dale. (2002). Introduction. Companion to Philosophical Logic . Ed. Dale Jacquette.

Oxford: Blackwell Publishing.

Klenk, Virginia. (1983) Understanding Symbolic Logic . Englewood Cliffs; Prentice-Hall.

MacFarlane, John. (2004) "In What Sense, If Anything, is Logic Normative for Thought?"

Unpublished. Accessed from personal site: www.johnmacfarlane.net/normativity_of_logic.pdf

Nagel, Ernst and Newman, James. (2001) Godel's Proof . New York; New York University Press.

Pollock, John. (1990) Technical Methods in Philosophy . San Francisco; Westview Press.

Quine, W.V. (1950) "On Natural Deduction." Journal of Symbolic Logic . Volume 15 (2): 93-102.

Quine, W.V. (1982) Methods of Logic . Cambridge; Harvard University Press.

Russell, Bertrand. (1996) Principles of Mathematics . New York; Norton & Company.

Salmon, Wesley C. (1963) Logic. Englewood Cliffs; Prentice-Hall.

Shapiro, Stewart. (2001) "Modeling and Normativity." Agora . Volume 20 (1): 159-173

Shapiro, Stewart. (2002) "Necessity, Meaning, and Rationality." Companion to Philosophical Logic . Ed.

Dale Jacquette. Oxford: Blackwell Publishing.

Shapiro, Stewart. (2009) "Classical Logic." Stanford Encyclopedia of Philosophy . Accessed Online:

http://plato stanford edu/entries/logic-classical/#3
http://plato.stanford.edu/entries/logic-ontology/#2http://plato.stanford.edu/entries/logic-ontology/#2http://www.johnmacfarlane.net/normativity_of_logic.pdfhttp://plato.stanford.edu/entries/logic-classical/#3http://plato.stanford.edu/entries/logic-ontology/#2http://www.johnmacfarlane.net/normativity_of_logic.pdfhttp://plato.stanford.edu/entries/logic-classical/#3

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