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Notes toThe Normative Status of Logic

1. To be clear: an argument is valid just in case its conclusion is alogical consequence of its premises.

2. But even if an account of the normative status of logic does not aimto pin down the correct consequence relation, it may still play animportant role in settling disputes between advocates of differentlogics. For instance, Steinberger (2016), following the lead ofFitelson (2008), Harman (1986) and MacFarlane (MF2004),argues that an influential argument for paraconsistent logic isunsuccessful because it relies on a philosophically untenableconception of the normative role of logic in reasoning.

3. Indeed Peter Geach states the truth conditions for “\(p\)entails \(q\)” as “There is ana priori way ofgetting to know that \(p \supset q\) which is not a way of getting toknow either that \(\neg p\) or \(q\)” (Geach 1972 [1958]:180).

4. Indeed one might take the opposition between monism and pluralism andits ramifications for the question of logic’s normative statusas to some extent prefigured in Frege and Carnap’s philosophies of logic (seeSteinberger 2017).

5. To say that logic is normative for reasoning, is to say that there isa sense in which the materials of reasoning—doxastic attitudes,inferences, etc.—are normatively evaluable. However, thisassumption has been fiercely contested. It has been denied of doxasticattitudes, in particular, that they should qualify as proper subjectsof normative appraisal on account of the fact that they are not underthe agent’s direct voluntary control, and so are not responsiveto reasons in the right kind of way. It would lead too far to pursuethis important question here. (See entry onethics of belief (section 3.3).)

6. See MacFarlane (2000, 2002), Steinberger (2017), Taschek (2008). Fora dissenting view especially with respect to Kant having held thisview, see Tolley (2006) as well as Conant (1991) and Putnam(1994).

7. See MacFarlane (2000: 52) who attributes this conception of thoughtto Kant. Note, though, that elsewhere, in the context of discussingFrege’s views, he defines “thinking” more narrowlyas “forming beliefs on the basis of other beliefs”(MacFarlane 2002: 35, fn. 16).

8. Different manifestations of thought may of course be answerable tothe strictures of logic in different ways. For instance, it may beentirely proper for me to entertain an inconsistent set ofpropositions in the context of a supposition or as part of anantecedent in a conditional, whereas in other contexts I would be inbreach of logical norms. This is not to say that supposing andentertaining antecedents of conditionals are not acts of thinking, butsimply that logical norms constrain them differently than other modesof thinking.

9. See Tolley 2006 for a similar example and further illuminatingdiscussion.

10. See again Conant (1991), Putnam (1994) and especially Tolley (2006)for arguments that this view is misascribed to Kant.

11. Similar points are made by Taschek (2008: 384) in the case ofthinking and by Williamson (1996: 491) in the case of speaking alanguage and making assertions. MacFarlane (2002: 37) also emphasizes,in the case of thought, that one need not be aware of the norms towhich one is subject. What is required is merely that the agent be“assessable in light of these norms”. MacFarlane’sdescription of the thesis may thus be less demanding thanTaschek’s proposal below.

12. Notice that this difference in methodological approach need notcoincide with the internalism/externalism divide. Some externalistsare happy to explore “first-personal” epistemology so longas the status of beliefs formed in compliance with the theory’sdirectives is distinguished from justification conceived as anecessary condition of knowledge. See, e.g., Goldman (1980). On theother hand, there are internalists who do not regard epistemicjustification to be a matter of responsibly following precepts (see,e.g., Feldman & Conee 1985).

13. The following principles are roughly those discussed by Harman.Harman’s formulations ofIMP differ in the deontic modals they feature (e.g., in his 2002: 172,Harman’s mentions “should” and “may”, inhis 1986: 11, he uses “can be a reason for”.

14. Both assumptions can be challenged. On a more course-grainedconception of propositions we face Fregean puzzles. For instance, thepropositions expressed by “Superman can fly” and“Clark Kent can fly” might be taken to be one and thesame. Yet, Lois Lane does not appear to be irrational if she believesthat which is expressed by the former sentence, but disbelieves whatis expressed by the latter sentence. The second assumption is rejectedby advocates of paraconsistent logicians. See, e.g., Priest 2006: Ch.6 for discussion.

15. Harman also enlists the Liar Paradox as an example of unavoidableinconsistencies of our beliefs (Harman 1986: 16). The case of the Liarintroduces additional difficulties that would only obscure the issueat hand. I therefore will make no further mention of it in whatfollows.

16. We will soon also encounter what I callattitudinal bridgeprinciples. They take the slightly different form:

• (\(\star \gamma\)) If\(\gamma(A_1,\dots, A_n \models C)\), then \(N(\alpha(A_1), \dots,\alpha(A_n), \beta(C))\).

where \(\gamma\) designates a particular attitude of the agent towardsthe instance of \(\models\).

17. I will set suspension of belief aside for present purposes.

18. Notice that MacFarlane’s classification only recognizesB-principles in which the deontic operator occurring in the antecedentand the operator occurring in the consequent are identical.MacFarlane’s classificatory scheme might thus be extended byallowing for “mixed” Bs in which the deontic operatorsfeaturing in the antecedent and in the consequent of the embeddedconditional could be distinct. For example, in addition to (Bo+), wecould consider also

• (Bop+) If \(A_1,\dots, A_n\models B\), then if \(S\) ought to believe all the \(A_i\),\(S\) may believe \(B\).
• (Bor+) If \(A_1,\dots, A_n\models B\), then if \(S\) ought to believe all the \(A_i\),\(S\) has reason to believe \(B\).

and so on for all the possible combinations. Intuitively, only thosemixed principles have any plausibility in which the deontic operatorin the consequent is of equal strength or weaker than the operator inthe antecedent: It would seem odd, for instance, if my having a reasonto believe a proposition, should have the entailment that I ought tobelieve its logical consequences. Whatever epistemic goodness thepremises enjoy may be thought to be inherited by their logicalconsequences. Epistemic goodness, presumably, can be diminished or, at best, preserved in this way. It would be strange, however, if we, as it were, gotmore epistemic goodness out of the conclusion than we put into thepremises (assuming the logical consequence is a contingentproposition).

19. See MacFarlane (MF2004: 7) for an exhaustive list of all bridgeprinciples that can be generated in this way.

20. See David Christensen (2004) for a lucid discussion of the importanceand inevitability of the Preface Paradox. Milne 2009: 285 is aparticularly relevant example of a dissenting view.

21. See Boghossian (2003), Gibbard (2003, 2005), Shah (2003), Wedgwood(2002) to name but a few proponents of versions of the truth norm.Others have opted for the closely related knowledge norm to the effectthat one ought to have knowledgeable beliefs, e.g., Williamson 2000:47, 255–56.

22. For example, Easwaran (2015) and Titelbaum (2015) are very clearthat it is such evaluative norms of perfect rationality that they areafter.

23. One might also consider comparative beliefs. That is, doxastic stateswhich are partially ordered according to relative certainty. The ideagoes back at least to Keynes (1921). More recently, it has receivedrenewed attention in Hawthorne (2009) and Fitelson [BFMS]. For reasons of space I donot pursue comparative beliefs further here.

24. This claim is backed by an impressive array of arguments: so-calledDutch-book arguments, representation theorem-based arguments andaccuracy-dominance arguments. See entry epistemic utility argumentsfor probabilism.

25. Though not necessarily. For there are generalizations of probabilitymeasures—what Joseph Halpern has calledplausibilitymeasures (Halpern 2003)—which satisfy the constraintsimposed by Field’s principle, but which are notprobabilistic.

Notes to the Supplement “Bridge Principles – Surveying the Options”

S1. The only attitudinal principles MacFarlane (MF2004) considers arefactive ones.

S2. Arguably, this is a feature of what Harman (2002) has dubbedgeneral foundations theories in epistemology. Such theoriespromote what we might call an innocent-until-proven-guilty policyconcerning belief maintenance. The approach amounts to a type ofconservatism about belief: An agent’s belief set enjoys a kindof default justification until she encounters sufficiently strongcountervailing evidence. On such views, then, it seems proper to say,at first blush at least, that Ido have reason to believe anyproposition I in fact believe. I have reason to stick to my beliefsunless and until I am presented with sufficiently strong grounds forabandoning them. It may well be that the best case for the (Cr)s canbe made in the context of such theories.

S3. Notice that it would not be enough merely to add the clause“and \(S\) takes an attitude towards \(C\)” because theremay be cases in which an agent fails to take an attitude to a logicalconsequences she has good reason to consider. For example, I might,out of intellectual dishonesty, fail to take into account a damningconsequence of my philosophical position of which I am otherwiseaware.