Published in Grazer Philosophische Studien, Winter 2006, 73, pp. 113-131


Not Too Proud to Beg (the question):

Why Inferentialism Cannot Account for the A priori


            We believe that Modus Ponens (MPP) is valid.[1]  If this belief is justified it is justified either inferentially or non-inferentially.  The latter road is taken by a more or less traditional view of the a priori.  Fundamental logical principles, as well as mathematical, conceptual and even philosophical propositions, are thought to be justified on the basis of some non-empirical source of justification that goes by the name of “rational insight” (BonJour, 1998) or “intuition” (Bealer, 2000).  When it comes to certain sorts of proposition (MPP is valid being as good a candidate as any), cognizers can, upon understanding them, intellectually “see” that they are true.

Many philosophers have been deeply disappointed by the traditional view of the a priori.  The reason usually offered is that there is no good account of how an act of rational insight or intuition (whatever that is) could serve to justify belief.  It’s a big mystery.  This sort of worry leads some to the conclusion that there is no such thing as a priori knowledge or justification at all.[2]  But interest in the a priori has grown in recent years and now there are many alternatives to the traditional view.

One interesting alternative is inferentialism.  According to this sort of view, there is no need to appeal to any faculty of rational insight or intuition to explain how our a priori beliefs are justified because a priori justification is inferential.  Inferentialism attempts to account for all of our knowledge of things like logic and mathematics without postulating ‘inutition’ or ‘rational insight’ as a special non-empirical source of justification and to maintain that our knowledge in these areas is a priori. 

In this paper, I will argue that this project does not succeed.  The most pressing problem for inferentialism is that the justification it attempts to provide for fundamental logical beliefs involves a fallacy of begging the question.  I will begin by explaining what it is to beg the question and why it is a problem for inferentialism.  The inferentialist account of the a priori can be independentally motivated by criticisms of an alternative epistemological view.  In the second section, I will explain what this view is and how certain criticisms of it can be made to support the inferentialist account of the a priori.  Following that, I will explain why the sort of justification inferentialism offers for basic principles of logic needs to be restricted and how a plausible restriction can be grounded.  In section four, I will argue that the inferentialist's attempt to avoid the charge of begging the question fails.  In section five, I will argue that none of the reasons designed to motivate the sort of epistemological externalism required by the inferentialist account of the a priori are compelling and that, even with the above mentioned restriction, inferentialism still makes justifying rules of inference too easy.  The penultimate section discusses some modifications that have been made to inferentialism's underlying conceptual role semantics.  I argue that, while these modifications would help avoid some of the problems with inferentialism's semantics, they only serve to make its theory of the a priori much worse.  I conclude by pointing out some very surprising remarks from inferentialism's most prominent proponent. 


I.  Begging the Question

When we ask about the epistemic status of paradigmatically a priori, it is easy to see how the inferentialist runs into problems.  If my belief that MPP is valid is justified on the basis of an inference from other beliefs, this inference must be truth conducive.  But the inference is itself either an instance of MPP or not.  If it is not an instance of MPP, then the problem is merely postponed.  We can simply ask about the truth-conduciveness of this other inference.  If my belief that MPP is valid is arrived at using MPP, then we can see that the inference is (at least in some sense) circular.  The inference attempts to justify the very rule it employs.  This is known as "rule circularity". 

  Showing that rule circularity is at least sometimes epistemically unproblematic is one of the central obstacles for inferentialism.  Opponents of inferentialism will charge that a rule circular argument fails because it commits the fallacy of begging the question.  Before we can assess whether this charge is legitimate, we must ask exactly what it amounts to.

One might try to define a question begging argument as one in which the conclusion appears as a premise.  This definition, however, cannot even capture the textbook cases.  Consider the following:

1.     Everything in the Holy Text is true.

2.     The Holy Text says that God exists.

3.     Therefore, God exists.


In the typical case, although perhaps not in every case, this argument begs the question not because the conclusion appears as a premise (for that is not even true here) but because belief in a premise epistemically depends on belief in the conclusion.[3]  Most who believe (1) base this belief on a belief that God exists. [4]

            An argument is an ordered pair of a set of propositions (the premises) and a proposition (the conclusion).[5]  Arguments have their logical and semantic properties intrinsically but their epistemic properties are derivative of the epistemic states of the subjects who use them in reasoning or demonstration.  To say that an argument fails to justify its conclusion is to say that it is being used in a way such that a certain subject cannot be warranted in believing the conclusion based on his belief in the premises. 

In general, an argument serves to justify a subject in believing its conclusion only if the subject is already justified in believing the premises of that argument.  If a subject bases his belief in a premise on a prior belief in the conclusion then the subject is justified in believing that premise only if he is already justified in believing the conclusion.  Therefore, a question begging argument does no real work towards providing the subject with justified belief in the conclusion.  If he had that, he had it already.  The argument is, at best, a rhetorical exercise.

The use of an argument begs the question (and thus we can loosely say that the argument begs the question) when belief in a premise is epistemically based on belief in the conclusion.[6]  The success of inferentialism as an account of the epistemology of basic logical beliefs turns on whether there are rule circular arguments that are not question begging in this sense.  The distinction between rule circular arguments and question begging arguments is drawn by appeal to two general philosophical ideas: (a) a limited sort of epistemological externalism and (b) conceptual role semantics. These two ideas and how they fit into the inferentialist account of the a priori will be discussed in the next two sections. 


II.  The Internalist Challenge

One theory about the nature of inferential justification, “Simple Inferential Internalism” (SII), would pose serious problems for any attempt to rule circularly justify basic principles of inference.  SII is the view that for S to be justified in believing that p on the basis of an inference from some other set of propositions, S must be able to know “by reflection alone” that these other propositions provide good reasons for believing that p.[7]  In this case, if S is to know that MPP is valid on the basis of a modus ponens inference from other propositions, S must know (or at least be in a position to know) in advance that MPP is valid.  Therefore, if SII is true, then a rule circular argument can contribute nothing to the justification we have for believing that the rule in question is valid.  The legitimacy of the argument would require that we already have warrant for belief in the conclusion.  This is not the same thing as saying that SII entails that all rule circular arguments are question begging.  But it is to say that if SII is true, then all rule circular arguments fail to provide anything new in the way of warrant for belief in their conclusions.  This would mean that rule circular arguments are epistemically uninteresting for the same reason that question begging arguments are.  Since the inferentialist account of the a priori requires that rule circular arguments provide substantive epistemic justification, proponents of inferentialism must find reason to reject SII.      

There are two major criticisms of SII.  The first is that ordinary folk, on this view, can have no inferentially justified beliefs.  SII entails skepticism.  Granny wonders what’s on TV tonight.  So she opens the TV guide and reads that Matlock starts at 8.  She then forms the belief that Matlock will begin at 8.  We can model Granny’s reasoning this way:


4.     If the TV guide says Matlock starts at 8, then Matlock starts at 8.

5.     The TV guide says Matlock starts at 8

6.     Therefore, Matlock starts at 8.


We assume that Granny has good inductive support for 4 and good observational evidence for 5.  This, we hope, allows Granny to be justified in believing 6.  Is Granny able to know “by reflection alone” that (4) and (5) constitute good reasons for believing (6)?  Where deductive inferences are concerned, it is fair to assume that the standard the inference must meet to be a good one is deductive validity.  And to say that an argument is valid is to say that it has a logical form to which there is no counterexample.  Just being able to identify the logical form of an argument requires some pretty hefty theoretical knowledge which Granny doesn’t have right now, and it is not clear that she could obtain it if she just sat down and thought about it.  Philosophers such as BonJour (2001), however, have contended that naēve subjects can very easily know that inferences such as the one above are good ones.  This has the surprising consequence that one can know that his deductive inferences are good ones without knowing that they are valid. 

There is another problem for the view that seems even more devastating.   Some argue that no one could ever in principle know that all of his inferences are good ones prior to making them.[8]  The argument for this claim borrows from Lewis Carroll’s (1895) famous note ‘What the Tortoise Said to Achilles’.  SII requires that Granny know that (4) and (5) constitute good reasons for (6).  Granny’s requisite knowledge therefore must consist in knowledge of something like the following:


7. Necessarily: p ą ((p ąq) ą q)



Suppose Granny knows that (7) is true.  Does this suffice for Granny to know that (4) and (5) constitute good reasons for (6)?  Boghossian, the most prominent proponent of the inferentialist view of the a priori, says that if we demand that Granny’s warrant for (6) is dependent on her knowing something like (7) then “we commit ourselves to an unstoppable regress.”  (Boghossian, 2001, 639)  If (7) is part of Granny’s justification, her reasoning is not merely an inference from (4) and (5) to (6).  Rather, it takes the following logical form:


8.     p ą ((p ą q) ą q)

9.     p

10.  (p ą q) ą q

11.  p ą q

12.  Therefore q


But again, if this is actually Granny’s argument, we must ask whether Granny knows that the inferences in this argument are good ones.  And again, we can grant Granny some further logical knowledge and reconstruct Granny’s reasoning with a third argument.  But this will only raise the same question all over again.  The regress is up and running. 

The conclusion is that SII requires too much, not just of Granny, but of anyone; even the logically sophisticated.  Our warrant for belief in the conclusions of our inferences cannot depend on an antecedently justified belief in the truth-conduciveness of those inferences.  “At some point is must be possible simply to move between thoughts in a way that generates justified belief.”  (Boghossian, 2001, 639)

            This Carrollian argument, if sound, does three things.  First, it demonstrates the falsity of SII.  It also undermines the first paragraph of this section's criticism of rule circular justifications for basic logical beliefs because that criticism presupposed a commitment to SII.  In addition, the Carrollian regress argument independently motivates us to accept a certain sort of epistemologistical externalism.  Subjects can reason in accordance with at least some rules of inference without knowing or even being able to know in advance that such rules are valid. 

Once we acknowledge the existence of “blind but blameless reasoning” we can start to see how an inferentialist can skirt the charge of begging the question.  Since begging the question requires that one believe in advance that his conclusion is true, the Carrollian regress argument opens the door to there being a rule circular argument for the validity of MPP that is not question-begging.  But open doors often lead to vermin. 




III. Meaning-Constituting Rules   

If we allow that rules may be used to justify themselves, then won’t we have to allow that ridiculous inference rules such as tonk-introduction and tonk-elimination are justified?[9]  The validity of the rules governing ‘tonk’ can be "proven" as long as we avail ourselves of those rules.  If inferentialism is to have even a chance at succeeding, there must be some non-ad hoc way to avoid these consequences. 

Just as the inferentialist can independently motivate his rejection of SII by appeal to the Carrollian regress argument, this problem can be blocked on independent grounds by appeal to some apparatus from the philosophy of language.  Conceptual Role Semantics (CRS) is the idea that the meaning of a word or concept is determined by the role that it plays in a certain set of inferences.[10] The inferences that determine the meaning of a word or concept are the “meaning-constituting inferences” for that word or concept.  For example, a proponent of CRS might say that ‘bachelor’ means what it does in virtue of the fact that ‘x is a bachelor’ and ‘x is an unmarried man’ are interderivable. 

In addition to providing an account of the nature of concepts, an account of concept possession also drops out of CRS.  It is in virtue of understanding ‘x is a bachelor’ that thinkers who understand the terms are disposed to infer ‘x is an unmarried’ or 'x is a man'.  And since these inferences are meaning-constituting, the inferences can successfully transmit warrant from premises to conclusion even if the thinker in question has no beliefs concerning the nature of this inference.

 In the same way, if CRS is true, then the logical constant ‘if, then’ gets its meaning from a proper subset of the inferences that it participates in.  If MPP is a meaning-constituting inference for ‘if, then’, then there is a good explanation for the fact that Granny can employ MPP and arrive at justified beliefs blindly. It is simply in virtue of the fact that she possesses the concept ‘if, then’ that she is able to justifiably believe (6) on the basis of (4) and (5).  Contra SII, prior justified belief in the validity of MPP is not necessary.  These considerations motivate adoption of the following principle.

(E)       S is entitled to infer according to M, independently of having

supplied an explicit justification for M if and only if M is a genuinely meaning-constituting rule for S.[11]


To supply an 'explicit justification' for a deductive rule of inference M is to construct a cogent argument whose conclusion is that M is valid.  An anonymous referee has pointed out that E seems to contradict SII only if SII requires that inferences be justified explicitly.  According to SII, however, subjects must be in a position to justifiably believe that their inferences are good ones prior to carrying those inferences out.  E, on the other hand, does not have this requirement.  E allows that a subject might become justified in believing that his inference is a good one only after making that inference.  This, as we shall see, is why the acceptance of E and the rejection of SII are crucial to the inferentialist account of our knowledge of basic logical principles.      

E provides a way for the inferentialist to screen off counterexamples to his idea that rules may be used to justify claims of their own validity.  In the case of ‘tonk’ “it is readily shown, by attempting to construct a truth table for 'tonk', that its introduction and elimination rules do not determine a meaning for it; there is no proposition expressed by sentences of the form 'A tonk B'.”  (Boghossian, 2000, 251)  If ‘tonk’ is meaningless, its introduction and elimination rules cannot be meaning-constituting and therefore they cannot be employed in rule circular arguments.


IV.  Two Rule Circular Arguments and the Problem of Begging the Question Again

Before we sign on to the project, we should ask what exactly a rule circular argument for the validity of MPP would look like.  One might say that we can easily establish the validity of MPP by proving the truth of its corresponding material conditional (MPPC): ‘((P É Q) & P)) É Q’ in standard propositional logic (PL).  Although some of what Boghossian says suggests this route, it cannot be the whole story. 

First, the project is to justify the belief that MPP is valid where this is understood in some extrasystematic sense that is applicable to everyday reasoners such as Granny.  Inferentialists nowhere suggest that their project rides on the truth of the controversial thesis that ‘É’ is semantically equivalent to ‘if, then’.  Therefore a proof that MPP is valid for ‘É’ must not be what we are after.

An argument which serves to justify the belief that MPP is valid, at the very least, needs to have the claim that MPP is valid as its conclusion.  A proof of MPPC in PL, whose conclusion is a material conditional, clearly does not meet this requirement.  But this is not to say that such a proof is completely irrelevant for it does establish:

13.  MPPC is a theorem of PL.

To get from here to the claim that MPP is valid we need the additional premise:

14.  If MPPC is a theorem of PL then MPP is valid.

From these two we can rule circularly infer that MPP is valid. 

To know whether an inference from 13 and 14 to the claim that MPP is valid is question begging we need to know our grounds for accepting these premises.  Our basis for 13 is clear enough.  We can point to the proof in PL.  Our belief in 14, however, must rest ultimately on our belief that PL is a sound system.  And since MPP is a rule of PL, it would appear that we cannot be justified in accepting 14 without being antecedently justified in believing that MPP is valid.  If this is true, then an argument for the validity of MPP based on an inference from 13 and 14 would fail for the same reason that the argument from the Holy Text does, it begs the question.[12]   

Of course, a proof of the soundness of PL is readily available.  But there is a good deal of dispute about the philosophical significance of metalogical proofs.[13]  The most frequent and predictable complaint is that the reasoning used in the metalanguage is of the same sort as that used in the object language and thus the metalogical proofs beg the question.  But from what has been said so far, it is not at all clear that this charge sticks.  The inferentialist, armed with principles such as (E) and Granny-type cases, will insist that one can use a rule without assuming in advance that the rule is valid.   

            More pressing is the worry mentioned earlier.  We are after a justification of our belief that MPP is valid understood in an extrasystematic sense.  What is needed then is an argument to establish that MPP is valid for the ordinary ‘if, then’.  It is for this reason that inferentialists also offer an informal argument. [14]  This sort of argument, if successful, would allay the worries of those skeptical about the achievements of metalogic because it would provide a demonstration of the legitimacy of the reasoning that goes on in the metalanguage (provided of course that the metalanguage is English).  

15.  If ‘if, then’ means what it does, then MPP is valid.

16.  ‘If, then’ means what it does.

17.  Therefore, MPP is valid.     


This argument is obviously rule-circular.  To determine whether this argument is question begging, however, we must determine what our bases for believing the premises are supposed to be.  If our basis for believing one of the premises is a belief in 17 then the argument is also question begging. 

16 is another way of saying that ‘if, then’ does not have the same status as ‘tonk’.  It is meaningful.  Exactly how we are supposed to know something like this is a good question and may present problems[15], but I won’t quarrel with it here. 

            The problem with this argument concerns our basis for the first premise.  15 is equivalent to the claim that MPP is meaning-constituting for ‘if, then’.  In other words, 'if, then' picks out whatever it is that makes MPP inferences valid.  But what is our basis for believing that?  Part of the problem here stems from familiar worries over CRS. The standard objection to CRS is that it fails to provide any clear distinction between meaning-constituting inferences and all the rest.  (Fodor and Lepore, 1991)  But even if one can solve this fundamental problem and explain what generally distinguishes meaning-constituting from non-meaning-constituting inferences, we still need to know what reason there is for believing that MPP falls on one side of this distinction rather than the other. 

Suppose we know MPP to be meaning-constituting non-inferentially. Upon understanding ‘if, then’ we can look at MPP inferences and just see that they are valid in virtue of the fact that they are meaning-consituting. However plausible this view might seem to some, it is not available to the inferentialist.  The idea that we can intellectually “just see” certain things upon understanding them is the very sort of traditional view that inferentialists (and others) casually dismiss as being too obscure to be philosophically illuminating.  (Boghossian, 2000, 231)  If skepticism about the existence or justificatory power of “intuitions” or “rational insights” is warranted, then it applies to our beliefs about semantic content just as well as it does to our beliefs concerning the truths of logic themselves.     

If inferentialism is true, it must be that our belief that MPP is a meaning-constituting inference, insofar as it is a priori, is justified inferentially, by way of some other set of beliefs.  Therefore, the argument from 15 and 16 to 17 is non-question begging only if our belief that MPP is meaning-constituting (i.e., 15) is not based on our belief that MPP is valid.  This follows from the earlier analysis of what it is to beg the question.  If it turns out that part of our basis for believing that 15 is true is a belief that MPP is valid, then our basis for a premise of the argument for 17 is 17 itself and the argument is fallacious.  The challenge for inferentialism is to ground our acceptance of 15 in something other than our acceptance of 17.  As I will argue, this challenge has not been met.  There are several candidate bases for the belief that MPP is a meaning-constituting inference for 'if, then' but they turn out to either be too weak or ultimately grounded in the belief that MPP is valid.      

We might base the belief that MPP is meaning-constituting on the belief that anyone who understands ‘if, then’ is disposed to reason in accordance with it.  But there are philosophers such as Lycan (1993) and McGee (1985) who explicitly claim that MPP is invalid.  Whether they are correct is not the issue.  The point is rather that these philosophers understand ‘if, then’ if anyone does and yet they do not appear to meet CRS’s condition for doing so.  Following Williamson (2003), the example can be parlayed into a general objection to CRS.  For any particular rule of inference involving a concept C, there could be someone who rejects that rule for sophisticated theoretical reasons but still understands C.  The proponent of CRS may be able to slip out of trouble here depending on how he cashes out what it means to be “disposed” to infer in accordance with a certain rule of inference.  Philosophers often do not practice what they preach and it may be that even those who espouse disdain for MPP or other inferential rules still happily employ them outside the seminar room. 

A more pressing problem for any who hope to defend the claim that MPP is meaning-constituting for ‘if, then’ with the claim that all who understand ‘if, then’ are disposed to reason in accordance with MPP, is that we must again ask what the basis for this second claim is.  And, once again, I see nothing short of a belief that MPP is valid that could possibly serve justify a claim like this.  The disposition to infer according to MPP will most likely be taken as evidence of understanding 'if, then' and absence of that disposition as evidence of semantic ignorance.  If that is the case, then our belief that all who understand 'if, then' are disposed to reason in accord with MPP is grounded in our belief that MPP is valid and not vice versa.  In that case, our acceptance of 15 is ultimately grounded in prior acceptance of 17 and the argument begs the question. 

Furthermore, it is difficult to see why the fact that people are disposed to reason a certain way would provide an adequate basis for believing that way of reasoning to be constitutive of the meanings of the concepts involved.  Most would happily infer from ‘Joe is a bachelor’ that ‘Joe is a guy who likes to party’ but this, I take it, is merely a contingent aspect of bachelorhood.  Worse yet, people are often disposed to reason invalidly and therefore these dispositions don’t support the idea that MPP is constitutive of the meaning of ‘if, then’ any more then they do the idea that the fallacy of ignoring the base rates is constitutive of the meaning of ‘probability’.

A proponent of a rule circular argument for the validity of MPP can skirt the charge of begging the question only if he can show that the argument does not contain a premise which epistemically depends on the conclusion.  But inferentialists have failed to show how the crucial premise, that MPP is meaning-constituting for ‘if, then’ (i.e., 15 above), could be justified without appeal to the belief that MPP is valid.  In fact, Boghossian comes very close to admitting that the former must be based on the latter when he says that a rule circular argument can at best be “non-suasive”.  (2000, 252) Anyone who doubts the validity of MPP will also be rational in doubting that MPP is meaning-constituting and there is no independent argument that can rationally compel him to change his mind on either.  To say that anyone who doubts the validity of MPP will also doubt that MPP is meaning-constituting is not to say that the belief that MPP is meaning-constituting is based on the belief that MPP is valid, but it is difficult to see why the former would be true unless the latter were also. 


V.  Granny, Carroll and Some Other Problems

            The fact that the inferentialist has failed to provide a non-question begging argument for the validity of MPP does not entail that no such argument could be made.  In one place, Boghossian (2001, 229) suggests that he doesn't wish to actually present and defend a particular rule circular justification for our belief that MPP is valid but only to defend the weaker claim that our basic logical beliefs could be justified in this way.  But neither Granny nor Carrollian considerations tell decisively in favor of this softer thesis.  Granny cases at most show only that it is possible to employ a rule of inference and arrive at justified belief without being antecedently justified in believing that the inference is valid for some propositions.  Since begging the question is not a formal fallacy of reasoning but depends on the content of the propositions believed and their epistemic bases, it is not at all clear that Granny cases generalize.  A very good candidate for an exception to Granny-motivated externalism would be a case where the reasoner is employing the very same rule she is attempting to justify.  Second, the intuitive appeal of Granny type cases also stems from the fact that the conceptually unsophisticated are typically not aware of the kinds of inferences they are employing and we do not expect them to be.  But the person who attempts to deduce the proposition that MPP is valid will certainly not be logically uninitiated and he will (or should be) well aware of the inference he employs.  This is another reason to think that Granny cases are not analogous and may be of no relevance here at all.     

The Carrollian regress argument also fails to support the inferentialist in an even more dramatic way.  SII stipulates a necessary condition on inferential knowledge.  Subjects are required to be in a position to know that the inferences they employ are good ones.  The regress argument gets up and running on the false assumption that this requisite knowledge must be stated as a premise in an argument somewhere.  If the mind/brain identity theory is true then a necessary condition on Granny having any beliefs at all (and thus any justified beliefs) is that she has a brain.  But the mind/brain identity theory clearly does not require that “I have a brain” be a premise in an argument for each belief that Granny has. 

In the same way, SII requires that S be in a position to know that his reasons for p are good ones but it does not require this second-order epistemological assessment to be included as a premise in the inference to p.  The Carrollian regress argument confuses reasons for believing that p (i.e., things from which p is inferred) with a necessary condition for justified belief in p.  The regress argument fails to support the sort of epistemological externalism that is designed to motivate adoption of the crucial principle E. 

Another problems concerns inferentialism's attempt to restrict what rules can be rule circularly justified.  The initial worry for those who think that circularity of any sort is epistemically acceptable was that if we allow it, then we can justify anything we wish and thus the distinction between justified and unjustified beliefs collapses.  The inferentialist attempts to prevent this collapse by focusing on rule circular arguments and by distinguishing meaning-constituting from non-meaning-constituting inferences.  We may be convinced that the latter distinction rules out the introduction and elimination rules for ‘tonk’.  It is important to note, however, that Boghossian’s own rejection of ‘tonk’ rests primarily on the claim that ‘tonk’ is inconsistent.  Even opponents of CRS can make that point.  Thus the appeal to “meaning-constituting rules” doesn’t provide any new reason to abjure the obviously absurd inferential rules either.

Consider less obviously absurd but still very controversial rules: the KK-rule (From ‘S knows that p’ infer ‘S knows that S knows that p’), the KJ-rule (From ‘S knows that p’ infer ‘S is justified in believing that p’) and the S5 rule (from ‘◊p’ infer ‘p’).  These can all be rule circularly defended.[16]  And, given that there is no clear procedure for determining when an inference is meaning-constituting, one can very easily assert that these rules are so without committing himself to any obvious contradiction.  Thus the inferentialist approach does little toward providing us with a way to distinguish good rules from bad ones because it all turns on whether the rule in question is meaning-constituting or not and we have, as yet, no way of determining that.  Even if worries over patently invalid rules such as those that govern 'tonk' are allayed, inferentialism makes the still justification of many inferential rules too easy. 


VI.  A Change of Heart

Remarks from Boghossian’s more recent (2003) suggest a way around this objection.  There, he gives up on unrestricted commitment to E and he rejects his earlier view that only a valid inference can be meaning-constituting.  He claims that there are concepts such as the pejorative ‘boche’ that, while not incoherent in the way ‘tonk’ is, nonetheless derive their meanings from invalid rules.[17]  Furthermore, he argues that there may be concepts whose introduction and elimination rules are not invalid but, nonetheless, one should not be entitled to rely on them simply in virtue of understanding the concept. 

For example, following Ramsey, Carnap and Lewis, we might represent neutrino theory, T(neutrino), as the conjunction of the Ramsey sentence

(S) ($x) Tx

and the Carnap sentence

(C) ($x) Tx ą T(neutrino).[18]

We could then say that possession of the concept neutrino requires only acceptance only of C.  But now suppose someone introduces the concept neutrino+ and says that possession of this concept requires acceptance of the conjunction S & C.  Anyone who possesses this concept must thereby commit himself to the existence of neutrinos.  But even if neutrino theory is perfectly true, we should not say that one is entitled to believe in the existence of neutrinos simply in virtue of possessing a concept. 

Boghossian’s way of handling such cases is to restrict E to only those concepts that cannot be “conditionalized”.  Carnap sentences give us a way to state possession conditions for the concept neutrino without thereby committing ourselves to the existence of neutrinos.  And when such a route is available, we should take it because otherwise we “foreclose on the possible falsity of some particular set of claims about the world” (246).   The possession conditions for our basic logical concepts such as the conditional, however, cannot be stated in such a way because “if the conditional is one of your primitive logical constants you couldn’t conditionalize on the existence of an appropriate truth function for it, for you would need it in order to conditionalize on anything.” (247)

Something similar could be said of the rules mentioned earlier.  For example, someone who thinks that the S5 rule is meaning-constituting for the modal concepts, we might say, is conditionalizing on the truth of “S5 Theory”.  Our understanding of possibility and necessity need not commit us to this theory because we can always state the rule as the consequent of a conditional. 

This modification seems to resolve some problems in conceptual role semantics but it has dire consequences for the inferentialist account of the a priori.  Recall that the motivation for that view was on the one hand, to grant that radical empiricists are correct to reject traditional rationalism’s reliance on a priori “intuitions” but, on the other hand, to maintain that there is such a thing as a priori knowledge and justification.  The latter is supposed to be explained by appeal to the resources of conceptual role semantics and rule circular inference.  Now, if the blind entitlement to rely on an inferential rule is restricted to those rules that cannot be conditionalized on, it follows that rule circular argurments will be acceptable only for those rules.  It follows from this that the only things we know a priori are basic principles of logic, in fact, it seems to follow that the only things we know a priori are that modus ponens and conditional proof are valid.  Even if the KJ rule, the KK rule, the S5 rule are valid, we cannot know this a priori.  For the same reason, we can’t know a priori that double negation is valid (since this rule can also be stated conditionally).  We can’t even know a priori that all bachelors are unmarried or that all oculists are eyedoctors.  Anyone who thinks that the inference from ‘x is a bachelor’ to ‘x is unmarried’ can be seen as conditionalizing on the truth of “Bachelor Theory” and we need not join him.  Whatever this modification does for the plausibility of CRS, it spells doom for the inferentialist view of the a priori. 


VII.  A Concluding Ad Hominem

            One of the main motivations behind the traditional view of the a priori has always been the claim that one cannot account for our knowledge of basic truths of logic and mathematics without appealing to some non-empirical source of justification such as rational insight or intuition.  While inferentialism is designed to acknowledge the existence of a priori knowledge without commitment to such faculties, some of Boghossian’s own comments surprisingly suggest that his view cannot fulfill its promise of providing a complete account of the a priori.  Boghossian considers a pseudo-rule (R) which says: from any proposition p, infer all snow is white.  This rule could be used to prove its corresponding conditional.  Boghossian hopes to dismiss any attempt to rule circularly justify this rule by appeal to the condition that we can rule circularly justify only those rules that are meaning-constituting.  To show that this condition is not met he says, “it is obviously not part of the meaning of ‘all’ that ‘all snow is white’ can be inferred from any proposition”.  (2000, 251)  To call some claim about meaning “obvious” in a way that is clearly not perceptual and to assume that this carries any epistemic weight is just to endorse something that is, if not equivalent to old fashioned rationalism, no better than it.  It is to say that some of our beliefs are justified not because we base them on other beliefs but just because they are “obvious”.  In the same essay, Boghossian also attempts to defend some of the principles that he uses to support his allegedly novel view of the a priori by calling them “quite intuitive” (234).  This appears only three pages after he derides the traditional view's appeal to a faculty of intuition for being obscurantist.  Of course, none of this shows that the rationalist is right to think that appeal to something like intellectual insight or intuition is epistemologically indispensable.  But it is suggestive.    

            To summarize, a rule circular argument will be non-question begging only if we can be justified in believing the premises of this argument without already being justified in believing the conclusion.  Two types of rule circular arguments have been proposed and they have shown to be question begging in the usual sense.  While Granny cases seem to support the claim that one can sometimes reason in accordance with a rule without being justified in believing anything about that rule, they do not provide adequate support for the claim one could justify the belief that MPP is valid using MPP; nor does the Carollian regress argument.  Furthermore, the inferentialist appeal to meaning-constituting inferences is unnecessary for dismissing obviously absurd rules and insufficient to curtail the problem of making justification of inferential rules too easy.  Inferentialists have provided no cogent rule circular argument for any of our fundamental logical beliefs nor have they given us good reason to believe that such an argument waits to be discovered.  Recent modifications to the underlying semantics of inferentialism only serve to destroy it as a general account of the a priori.  And in the end, some inferentialists seem committed to a more or less traditional view of the a priori anyway.[19]



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[1] The ‘we’ here excludes some philosophers such as Lycan and McGee who have argued that MPP is invalid.  But even they take it that some inferences are valid.  The comments here apply mutatis mutandis to whatever inference form(s) they happen to accept.

[2] For example, Devitt, (2005).

[3] Providing an account of epistemic dependence is outside the scope of this paper.  For a discussion of this issue see Korcz (1997).

[4] A subject might accept (1) because he has taken himself to have established it independently, perhaps by induction.  This would not result in a question begging argument (but of course it might be bad for some other reason).   

[5] This definition of ‘argument’ can be found in Sinnot-Armstong (1999).

[6] A consequence of this sort of account is that the same argument might be question begging in one usage context but not in another.  But as the case described in footnote 4 shows, this is exactly as things should be. 

[7] Boghossian (2004), p. 229.

[8] Boghossian (2001). 

[9] ‘Tonk’ is Prior’s (1960) logical pseudo-constant which is stipulated to have the same introduction rule as disjunction and the same elimination rule as conjunction.  ‘Tonk’ has the unhappy consequence that if anything is true then everything is true. 

[10] Boghossian (2000) prefers to construe it in terms of words in the language of thought.  Whether one understands the basic idea as applying to concepts or words is not important for the purposes of this paper.

[11] Boghossian, (2000).  The biconditional (E) is not explicitly stated by Boghossian in this paper but it is entailed by two conditionals that he endorses.  

[12] It is important to note that this criticism does not assume any commitment to SII.  The point is only that the formal proof by itself is not an argument for the validity of MPP.  Other principles are needed and our acceptance of these principles is clearly based on a prior belief in the validity of MPP. 

[13] For starters, see Haack (1982).

[14] Boghossian (1996, 376). 

[15] One problem concerns whether the justification for this is supposed to be empirical or a priori.  If it is the former then, it would seem, the justification for the belief that MPP is valid is also partly empirical.  Which may not be objectionable in itself but it would be a problem for Boghossian since his aim is to show that this justification is a priori.  This sort of criticism is developed some in Laurence and Margolis (2001).  On the other hand, if the basis for believing 16 is a priori then Boghossian’s account requires that it be based on some other beliefs.  We are then left wondering what those could be.   

[16] On the assumption that a proof of the corresponding conditional constitutes an argument for the validity of the rule the arguments should be obvious.  On the informal approach, we only need say something like  “If ‘knowledge’ means what it does then KK must be valid …”

[17] Boghossian suggests that the introduction rule for 'boche' is "From 'x is German' infer 'x is boche'" and the elimination rule is "From 'x is boche' infer 'x is cruel'".  Since it is false that all Germans are cruel, at least one of these rules is invalid. 

[18] For the unfamiliar, S essentially says that there is something which does what neutrino theory says that neutrinos do and C says that if S is true then neutrinos are what does what neutrino theory says that neutrinos do. 

[19] Versions of this paper were presented at the 2004 meeting of the Canadian Society for Epistemology and at the 2005 meeting of the European Congress of Analytic Philosophy.  The author thanks Albert Casullo, Max Deutsch, Ed Erwin, Michael Shaffer and Umit Yalcin for their comments and criticisms.