ORGANIGRAMA

I have been arguing that LSR makes two jointly unsatis able claims, for logic cannot ful l its universalist ambitions by disregarding ques- tions of content (by holding on to uncompromising topic-neutrality, that is). e CET-worries raised in chapter  are in fact ampli ed in the case of logic because of its need to carry out two tasks at once (in- dividuating content and codifying inference) which in fact presup- pose each other. Without an answer to CET, however, neither task can be carried out. Or so I have argued.

Let me now consider a typical move by the defender of LSR, namely, the further claim that logic idealises reasoning (LIR) and that there- fore the issue of a poor match between ‘natural’ and logical reasoning is no objection to the account.

Ideal reasoners, the proposal goes, would have no difficulty in se- curing determinacy (presumably because theywould have access to a magical language). Odd as it may sound,ourlogic trackstheir be- haviour. Andweare rational to the extent that we approximatetheir ideal standards of reasoning, precisely those encased in the logical laws (indeed, without that regulative ideal to aspire to, our reasoning practice would be a wholly random affair).

LIR, in effect, is a more radical form of CET. e claim now is that every reasoning step we take in our daily reasoningcouldalways be translated into reasoning steps between truths as expressed and grasped by ideal reasoners. Correct reasoning is reasoning in confor- mity to the logical laws stated by and meant for such reasoners.

Clearly LIR does not (yet) settle the issue of which logic isthelogic of reasoning. Indeed, as I’ll be arguing shortly, if we espouse LIR we do face the problem of saying why the particular idealisation we have chosen should be the one that we have to best approximate in our everyday reasoning—for unless we can have anindependenthold on the question (which seems doubtful), it is an arbitrary matter at which point we want to say that idealisation is misrepresenting our practices, given the proposed choice of ideal logic and the reason- ing modes that it commends to our attention (the question, that is, is whatindependentreasons can we nd in support of the selection of a speci c level of logical strength for our logic of choice).

LIR, however, is oen invoked to defend the claim that CL is the

_{A similar thesis is commonly held in epistemology with regard to the notion of epistemically}

ideal agents. See the recent Christensen (2007) for discussion.

_{Again, McDowell’s (1981a: 342) remark about the fantasy of a viewpoint external to our prac-}

 | Chapter 

one true logic, that it is not just the logic of science and mathematics, but also the logic that best regulates our (properly idealised) daily affairs. _{So let me say something more speci c about that claim.}

One obvious reply here is that it seems unclear why we should ac- cept CL as mandated by LIR when it endorses inferences (e.g. the im- plication paradoxes and monotonic reasoning more generally) that by the lights of that practice ought to be patently invalid, while also failing to account for inferences that again any reasonable account of that practice would classify as intuitively valid (e.g. various forms of meaning entailment that are no less logical than those attached to the traditional connectives and so on). Which prompts the question: why insist on a LIR strategy that falsely represents what our reason- ing is really like both procedurally and extensionally?

Here’s a counter-reply the LSR/LIR defender could give: my cri- tique of her position is assuming that reasoning modes and the re- quirements of ideal rationality must be fully user-transparent. _is assumption however is unrealistic: ideal rationality is a regulative ideal and may well elude our grasp in a given context (where, for in- stance, we may be overwhelmed by pragmatic noise in our reasoning). Reasoning, the reply continues, is oen a case of doing the best one can in the circumstances, and our cognitive limitations should not impact on what the regulative ideal is like. _{Conversely, the bad} arguments (e.g. positive paradoxes of implication) are onlypragmat- icallyfallacious. True, they would be neither persuasive norpractical.

_{Actually, and as already indicated, I think CL is the wrong logic for science and mathematics}

too and not just for their folk versions. It may be the mostconvenientproof-theoretically speaking, butthatdoes nothing to establish the claim that it istrueof those domains.

_{Read (2004: §5) defends a wider conception of validity and of the scope of logic: logic is the}

study of valid inference, and logical validity is only a sub-class of validity. Read (1988) gives a mild- mannered attack on the LIR-motivated defence of CL. Anderson and Belnap (1975: 5) and Routley

et al.(1982: xi) are a little less diplomatic.

_{Wittgenstein (1945/1953: §426) insists that a logic that would be unattainable in actual practice}

would be an idle wheel of dubious normative hold. I imagine LIR-defenders such as Williamson will remain unperturbed. See the text and footnote 46 for further discussion. e LIR strategist may also retreat to a second-order claim: CL (or whatever ideal logic we choose) regulates second-order disputes about validity. I doubt that would de ect the argument in the text.

_{It is worth mentioning a distinction between two conceptions of the requirements of ratio-}

nality made by Scanlon (1998: 30-31), namely, the one between being irrational (i.e. going against one’sbasicreasons, as it were) and failing to ful l the requirements of ideal rationality (what one hasmostreason to do). For Scanlon, decision theory and deductive logic only set standards for the second notion of rational requirements. e worry I’m endorsing in the text is that it is questionable whether CL sets even merely ideal standards of reasoning.

_{An argument of this kind regarding epistemic virtues is for instance in Williamson (2000: §8.7)}

Situating Consequence |  But again, to think that this weakens the status of CL as the logic of reasoning is to confuse competence with performance (i.e. irrelevant truths are still truths and irrelevant truth-preserving transitions are still truth-preserving).

Now, I hear the appeal of a defence of this kind and I can see ways of adapting e.g. Zinda’s () notion of a linking structure between imperfect and perfect modes of reasoning to show how ideal stan- dards of logical thinking can still have normative force for practices that routinely incorporate incoherent beliefs—the trick (and it’s not an easy one to pull) is to make (formal) sense of the notion ofbetter approximationtowards the ideal.

Two obstacles however remain. Firstly, there is a difficulty here which is both highly speci c and highly general, namely the very pos- sibility of making sense of a notion of content determinate enough for us to make assessments about logicality (consequence is a relation be- tween pieces of content: no determinate, truth-evaluable content, no relation); if CL misses out on some subtleties of our thinking be- cause it carves content too grossly (e.g. it’s insensitive to relevance), that in itself is reason enough to ditch it (regardless of whetherany replacement might fare better against the indeterminacy issue). And what needs showing in any case is that the discrepancies between competence and performance are genuine cases of purely cognitive imperfections and not, rather, structural failures of the modelling tools.

Secondly, the possibility of eshing out the notion of better approxi- mation requiresantecedent agreementon what would constitute ideal reasoning. is latter difficulty, that is, concerns the fact that it seems implausible that we can individuate ideal reasoning patterns that we strive to ‘better approximate’ without rst coming to a decisionfrom our viewpoint as imperfect agentsas to whatwouldcount as ideal (for even in the philosophical closet we are far from infallible when we draw up the regulative ideals of rationality).

In short, evaluating judgements about the status of the primacy of

_{See e.g. the discussion in Williamson (1994: ch. 2).}

_{LIR, that is, should not disregard Chomsky’s (1965: 9) metaphor that competence is the basis}

for performance. And yet it seems as if LIR all too oen amounts to the claim that logic isthe

language ofpurecompetence (competenceirrespectiveof performance). at, however, would leave performanceungrounded.

_{is again requires care: of course we have some kind of antecedent grasp of patterns of rea-}

soning: that’swhywe nd, when we do, certain aspects of CL implausibly idealised. e point I’m making in this paragraph is simply thatthe very notion of approximationis normative (it’s easy to set up the maths to deal withsomeversion of approximation; the hard part is saying why a certain function would be acceptable and another wouldn’t).

 | Chapter 

CL (or ofanyother logic that would take its place on the throne) is not a matter that can be settled independently of judgements about what would count as ideal rationality—just re ect: what does the claim that ideally rational agents would obey the laws of the probability calculus amount to? Who set up that calculus? Was its precise shape given to us by some unforgiving god or was it the result of re ection on a reasoning base that can only beboththe judge and the judged on such matters?

I do not think that there are clear answers to these questions such that they could settle once and for all the question ofi)which laws are genuinely logical (in the LSR sense) andii)which are mere artefacts of a formal framework that, unless we canantecedently and indepen- dently establish the truth of a certain view of physics, may not have genuinely general normative import for us (for instance, outside of the mathematical domain).

Nevertheless, if we endorse LIR and accept something like the bet- ter approximation principle, then it seems as ifthe closer the gapbe- tween the ideal and our approximating efforts the more likely it will be that the idealcanindeed plausibly be seen as regulating behaviour. And so a logic that is demonstrably closer to our practices but that can still keep in place sufficient distance between our actual decisions and those that it mandates would beceteris paribuspreferable.

Whetherthisprovides enough grounds to uphold (or dislodge) CL from its privileged position is an argument for another day.

Still, our ability to carry out meta-logical assessments over these

_{I nd the discussion in Sainsbury (2002b) highly instructive in this respect.}

_{at is to say: unless we can establish that nature is appropriately uniform, comfortingly sys-}

tematic and fully deterministic, we can always question whether thelawswe posit for our various domains of discourse do in fact provide best t with the facts (classic case: the old Quine-Putnam dispute over the import of quantum logic). Again, Lewis’ (1982: 101) frankness is refreshing here: faced with genuinely radical challenges to the logicalstatus quo(such as Routley’s and Priest’s), the classicist can only stamp her foot and retrench into dogmatism. But why should inconceivability (to David Lewis in 1982) be a guide to (timeless) illogicality?

_{e LIR-arguments given in Williamson (2005: 480-1) strike an odd balance. On the one hand,}

we are told that it would be a mistake to expect an ideal theory to have practical import. On the other, we are told that such a theory would still enjoy normative force. In support of this, Williamson appeals to his usual anti-luminosity arguments. If transparency is not a determinant of best theory, however, it is unclear how we can evenchoosebetween competing theories. On what grounds is a theory that lacksdemonstrableconnections with our practices to be held to bethetheory we ought to respect in our epistemic activities? As a parenthetical remark, I should perhaps add that I nd it curious that the very same externalists who accuse internalists of over-intellectualising ourgrasp

of concepts and more generally of the normative features of our practices should then commend to our attention regulative ideals that severely over-intellectualise those verypractices(and not just our grasp of their normative features).

Situating Consequence |  matters does depend on the tenability of some form of CET. And that’s why an answer to the CET puzzle I discussed in chapter  is due.

e LIR strategy, then, is at the service of the choice ofsomelogic as the regulative ideal. But any such choice must be justi ed on the basis of an argument thatit, and no other, is the logic of choice forus. And I am questioning that this can be done independently of existing theoreticalbiasandof a solution to the CET puzzle.

Let me now conclude the discussion of idealising strategies by mak- ing two more remarks.

Firstly, it seems clear that our theory (our logic as science of reason- ing) should have as much structure as the subject matter can support and no more, but also as much as it demands,and no less.

If so, the generality requirement will force pretty severe restric- tions on certain structural constraints that cause havoc when ap- plied to natural reasoning (say, transitivity, re exivity, exchange, di- lution, idempotency). _{For on any plausible reading of those con-} straints, they are in fact best construed aslocal, i.e. domain-speci c constraints on reasoning (good in some domains, undesirable in oth- ers) and should not burden our inferential practices more widely.

e upshot is that the idea of a truly universal logic, a logic that sets reasoning canons of absolutely unrestricted generality, _{is unlikely} to be achievable (by invoking LIR we lose applicability; by keeping applicability, we lose generality). e reason is that there are very few genuinely universal patterns of reasoning that can truly be said to disregardcontent (most likely none at all)—the resulting logic would therefore be extremely weak, and certainly much weaker than CL.

_{is is a principle that goes back at least toNichomachean Ethics, I, 7, 1098}a_{25-29 (“we must}

[…] not look for precision in all things alike, but in each class of things such precision as accords with the subject matter, and so much as is appropriate to the inquiry”), and resurfaces in Peacocke’s (1999) Integration Challenge.

_{If we accept that importantlylogicalfeatures of our everyday reasoning are best modelled by}

some form of dynamic, non-monotonic or resource conscious logic, then some (or all) of these structural rules will fail. See e.g. van Benthem (1996: 26), Marek and Truszczyński (1993) and Troelstra (1992) for details.

_{Note that once again efforts to keep these structural constraints in place would involve a revi-}

sion of the notion of content at hand. To de ect e.g. Girard’s (1995: 2) argument against idempo- tency for ‘and’, that is, one would need to posit a richer notion of content (implemented by some variety of LFI- or of Clause-indexicalism) to keep track of the events involved (and thus discrimi- nate between the two alleged co-occurrences of the same token).

_{For one extreme form of this claim, one that includes illogical, inconsistent and paradoxical}

situations, see Routley (1980).

_{As I discussed in the previous chapter, wecouldrig up domain-speci c connectives that be-}

have content-insensitivelywithin their domain(a point pressed on me by Ole Hjortland and Colin Caret in discussion). e trouble for that suggestion is that, the case of quanti ers notwithstanding,

 | Chapter 

And even if we had settled on an appropriately weak and appropri- ately general logic, one crucial point would still remain: we pack into the meaning of the logical connectivesjust as muchas we think serves the purpose of identifying what we take to be genuinely logical infer- ence; but the issue of how much structure weshouldpack into those connectives isnotindependent of what wedecideto treat as logical.

In short, and unsurprisingly, logic cannot tell us what logicis and which logic is the true one—there is no hope of detaching evalua- tive considerations from logical ones when we are testing both the tenability of LSR and its implementation through the selection of a particular (and privileged) set of logical tools.

Secondly, I want to note that behind LIR there oen (or perhaps invariably) lies the assumption that no other account (and certainly no weaker account than the classical one) would give us the required systematicity.

We can now see the connection between the insistence on PoC and the LIR/LSR approach to our conception of logic. For it seems to me that the PoC rules do encapsulate both the idea that we can (and must) give a systematic account of linguisticpractices (and henceof rationality as a whole) and that it isthoserules (and nothing less than those rules) that can (and do) embody the logic of choice that regu- lates our thinking and our agenthood (here, nally, we come to the standard reply to the CLB question that I le hanging from the last chapter).

Imposing the speci c PoC rules that one does impose on NL se- mantics is thus of a piece with imposing a logic on our thinking and our reasoning practices in general. And it is almost uncanny how the LIR strategy is invoked in precisely the same terms to defend PoC and UaGS on the one hand, as it is in the case of LSR and CL on the other. But again, whether systematicity is to be imposed on a theory of logicality (whether there can be no reasoning and linguistic compe- tence without systematicity) is precisely the point at issue and one on which logic itself cannot offer us counsel.

logical connectives are supposed to bedomain-insensitive too (their logicality is not supposed to be domain-relative, that is).

_{See Field (1977) and Field (2000).}

_{See for instance the instructive conclusion of Williamson (2005: 483). I’m certainly overlook-}

ing all the subtleties in his account, but that conclusion, and the preceding discussion, seems to come close to saying: we give a description that doesn’t t our practices (or even explain them) but we do it becauseotherwisewe would have no systematic account for the facts. Well, perhaps we should instead come to accept that there is no systematic account that would do full justice tothose