We consider it to be a bad thing to be inconsistent. Similarly, wecriticize others for failing to appreciate (at least the more obvious)logical consequences of their beliefs. In both cases there is afailure to conform one’s attitudes to logical strictures. Wegenerally take agents who fall short of the demands of logic to berationally defective. This suggests that logic has a normative role toplay in our rational economy; it instructs us how we ought or oughtnot to think or reason. The notion that logic has such a normativerole to play is deeply anchored in the way we traditionally thinkabout and teach logic. To consider just two examples, Kantcharacterizes what he calls “pure general” logic asembodying the “absolutely necessary rules of thought withoutwhich there can be no employment whatsoever of theunderstanding” (A52/B76), which instruct us not “how theunderstanding is and thinks” but “how itought toproceed” (Kant 1974 [1800]: 16). Similarly, Frege, in hisvehement opposition to the psychologistic tendencies of his time,classifies logic, “like ethics” as a “normativescience” (Frege 1897/1979: 228), one whose laws “prescribeuniversally how one should think if one is to think at all”(Frege 1893/1903/2009: xv). This entry is concerned with the questionas to whether the tradition and the intuitions that appear tounderwrite it are correct. In other words, it is concerned with thequestion as to whether logic has normative authority over us. And ifit does, in what sense exactly it can be said to do so?

• 1. The normative status of what?
  • 1.1 Characterizing logical consequence in terms of its normative role
  • 1.2 Logical pluralism
• 2. Normative for what?
  • 2.1 Logic as normative for reasoning
  • 2.2 Logic as constitutively normative for thought
  • 2.3 Logic as normative for public practices
• 3. Harman’s challenge
  • 3.1 The objections
• 4. Bridge principles
  • 4.1 Evaluating bridge principles
  • 4.2 The Preface Paradox
• 5. Further challenges
  • 5.1 Kolodny’s challenge
  • 5.2 Consistency and coherence
  • 5.3 Logic vs. probability theory
• Bibliography
• Academic Tools
• Other Internet Resources
• Related Entries

1. The normative status of what?

Before we can hope to make any headway with these questions a numberof clarifications are in order. First and foremost, in asking afterthe normative status of logic, we had better get clearer on what wemean by “logic”. For present purposes, I will take a logicto be a specification of a relation of logical consequence on a set oftruth-bearers. Moreover, I will assume consequence relations tonecessarily preserve truth in virtue of logical form. For simplicity,I will use “\(\models\)” to denote such a consequencerelation. My default assumption will be to take the double turnstileto denote the semantic consequence relation of the classicalfirst-order predicate calculus. But not much hangs on this. Partisansof other types of non-classical consequence relations may read“\(\models\)” as referring to their preferred consequencerelation.

Presumably, if logic is normative for thinking or reasoning, itsnormative force will stem, at least in part, from the fact that truthbearers which act as the relata of our consequence relation and thebearers of other logical properties are identical to (or at least arevery closely related in some other way) to the objects of thinking orreasoning: the contents of one’s mental states or acts such asthe content of one’s beliefs or inferences, for example. Forpresent purposes I will assume the identity between truth-bearers andthe contents of our attitudes, and I will assume them to bepropositions.

1.1 Characterizing logical consequence in terms of its normative role

One may approach the question of the normativity of logic bytaking the notions of logical consequence and of validity to be settledand to then investigate how these (and perhaps related) notionsconstrain our attitudes towards the propositions standing in variouslogical relations to one another.^[1] An alternative approach has it that logic’s normative role inthinking or reasoning may be partly definitive of what logic is.Hartry Field, for one, advances an account of validity along thelatter lines. In his 2015, he argues that neither the standard model-or proof-theoretic accounts of validity nor the notion of necessarytruth-preservation in virtue of logical form succeed in capturing the notion of validity. Morespecifically, neither of these approaches is capable of capturing thenotion of validity in a way that does justice to logical disputes,i.e., debates over which logical system is the correct one. On thestandard approaches to validity, such disputes are reduced to merelyverbal disputes inasmuch as “validity” is defined relativeto the system of logic in question. No one, of course, ever disputedthat a given classical argument form is valid relative to the notionof validity-in-classical logic, where as an intuitionistically validargument is valid relative to the notion of validity-in-intuitionisticlogic. The problem is that there is no neutral notion of validity onecould appeal to that would enable one to make sense of logicaldisputes as genuine debates, which, arguably, they are. What is neededto capture the substantive nature of these disputes, therefore, is aworkable non-partisan notion of validity, one that is not internal toany particular system of logic. The key to availing ourselves of suchan ecumenical notion of validity, Field claims, resides in itsconceptual role. The conceptual role of the notion ofvalidity, in turn, is identified with the way in which avalid argument normatively constrains an agent’s doxasticattitudes. Roughly, in the case of full belief, in accepting anargument as valid, the agent is bound by the norm that she ought notbelieve the argument’s premises while at the same time notbelieving its conclusion. In other words, validity’s conceptualrole resides (at least in part) in the normative role played by validarguments in reasoning. Note that Field is not proposingtodefine validity in terms of its normative role. The notionof validity, Field contends, is best taken to be primitive. But evenonce we take it to be primitive, it still stands in need ofclarification. It is this clarificatory work that is done by acharacterization of validity’s conceptual role. And it is inthis sense that the normative role of logic is supposed tocharacterize the very nature of validity (understood as a notionshared by various distinct logics).

In a similar vein, John MacFarlane (2004, Other Internet Resources;henceforth cited as MF2004) contends that a fuller understanding ofhow logical consequence normatively constrains reasoning may help ussettle long-standing issues in the philosophy of logic, debates surrounding thevery nature of validity. Attempts at resolving such questions havebeen thwarted because of their suspect methodology: they relied on theunreliable (because theory-laden) testimony of our intuitions aboutvalidity. Appealing to the normative role of logic, MacFarlane hopes,would give us a new angle of attack and hence a potentially betterhandle on these vexed questions. MacFarlane, too, may therefore beread as suggesting that a proper account of logic’s normativerole in reasoning will ultimately enable us to hone in on the correctconception of logical consequence. As examples MacFarlane considersthe dispute between advocates of relevantist restrictions of thenotion validity and those who reject such restrictions (see entryrelevance logic), and the question of the formality of logical validity (see entrylogical consequence). The hope, in other words, is that an account of the normative role of logic, will help us pin down the correct concept of validity. In this respect, then, MacFarlane’s project may be thought to be more ambitious than Field’s whose aim is to provide a logic-neutral core concept of validity in terms of its normative role. For MacFarlane a correct account of the normativity of logic would constitute a potential avenue through which logical disputes may be decided; for Field such an account merely renders such disputes intelligible and so serves as a starting point for their resolution.^[2]

A potential problem with approaches like Field’s andMacFarlane’s is that logical consequence does not appear to havea unique normative profile that sets it apart from other, non-logicalconsequence relations. For instance, that one ought not believe eachmember of a set of premises while at the same time not believing (ordisbelieving) its conclusion, is a feature that logical consequenceseems to share with strict implication. At least in one sense of“ought”, I ought to believe that this is colored, if Ibelieve it to be red, just as much as I ought to believe \(A\), if Ibelieve \(A \land B\). If the general principles characterizinglogic’s normative role fail to discriminatelogicalconsequence among other types of consequence, we cannot identify theconceptual role of validity with its normative role as Fieldproposes. We cannot do so, at least, unless we impose furtherconditions to demarcate properly logical consequence (see entrylogical constants). The problem discussed here was raised (albeit in a different context)by Harman (1986: 17–20) when he argues that logic is not“specially relevant to reasoning”. One response, ofcourse, is simply to concede the point and so to simply broaden thescope of the inquiry: Instead of asking how logic (narrowly construed)normatively constrains us, we might ask how strict implication(Streumer 2007) or perhaps a priori implication does.^[3] A further response is that neither Field nor MacFarlane are committedto demarcating logic or carving out any “special” role forit. Their principles are left-to-right conditionals: the existence ofa logical entailment gives rise to a normative constraint on doxasticattitudes. One can thus question the operative notion of entailment byquestioning the normative constraint. This, it might reasonably bemaintained, is all that Field and MacFarlane need for theirpurposes.

1.2 Logical pluralism

We said that not much of our discussion below hinges on the choice ofone’s logic. However, while we countenanced the possibility ofdisagreement over which logic is correct, we have simply presupposedthat there must be a unique correct logic. And this latter assumptiondoes seem to bear on our question in potentially significant ways. Theissue has yet to be explored more fully. Here I offer a number of preliminary distinctionsand observations.

Logical pluralists maintain that there is more than one correct logic(see entry onlogical pluralism). Now, there are perfectly uncontroversial senses in which several distinctlogical systems might be thought to be equally legitimate: differentlogical formalisms might lend themselves more or less well todifferent applications, e.g., classical propositional logic may beused to model electric circuits, the Lambek calculus naturally modelsphrase structure grammars, and so forth. If “correct” or“legitimate” is merely understood as “having auseful application”, monists should have no complaints aboutsuch anodyne forms of “pluralism”. The monist may happily admit that there is a vast number of systems of logic that make forworthy objects of study, many of which will have usefulapplications. What monists must have in mind, then, is a more demanding sense of “correctness”.According to Priest, the monist takes there to be, over and abovequestions of local applicability, a core or “canonical”(Priest 2006: 196) application of logic. The canonical use of logicconsists in determining “what follows from what—whatpremises support what conclusion—and why” (idem). It isonly when the question is framed in these terms, that the full forceof the opposition between monists and pluralists can be appreciated.The monist maintains that there is but one logic fit to play this corerole; the pluralist insists that several logics have an equally goodclaim to playing it.

One consequence of pluralism, then, is that in a dispute betweenadvocates of different logics both of which lay claim to being thecorrect logic in this sense—say, a dispute between a classicallogician and an advocate of intuitionistic logic—neither partyto the dispute needs to be at fault. Each logic may be equallylegitimate. For this to be possible, it must be the case that even thecanonical application of logic can be realized in multiple ways.Pluralists differ in the accounts they offer of this multiplerealizability. Oneinfluential such account has been advanced by J.C. Beall and GregRestall (2005). According to their account, several logics may beequally qualified to fulfill the core function of logic, because “logical consequence” admits of several distinct interpretations (within a specified range). Roughly, \(A\) is a logical consequence of a set of formulas \(\Gamma\) if andonly if, in every case in which all of the members of \(\Gamma\) aretrue, so is \(A\). Depending on how we understand “case”in our definition—e.g., as Tarskian models (classical logic),stages (intuitionistic logic), situations (relevant logic),etc.—we arrive at different concepts of logical consequence.

What does this mean for the question of logic’s normativestatus? It follows that it is only once we choose to disambiguate“logical consequence” in a particular way—as classical orintuitionistic, say—that the normative import of that particularconception of consequence makes itself felt. After all, on thepluralist picture a given conception of consequence cannot benormatively binding in virtue of being (uniquely) correct, i.e., invirtue of being descriptively adequate with respect to the entailmentfacts, as it were. Hence, if I opt for an intuitionistic conception ofconsequence and you go in for a classical one, I have no grounds forcriticizing your move from, say, \(\neg \neg A\) to \(A\), saveperhaps pragmatic ones. To be sure, such a move would be impermissibleaccording to my preferred notion of consequence, but it is perfectlyacceptable according to yours. According to the pluralist, then, thereexists no absolute sense, but only system-relative senses, in which alogic can normatively bind us. Pluralism about logic thus seems to give riseto pluralism about logical normativity: If there are several equallylegitimate consequence relations, there are also several equally legitimate sets of logical norms. Consequently, it is hard to seeprimafacie how substantive normative conflicts can arise. If the consequencerelations of classical and intuitionistic logic are equallylegitimate, there is little to disagree about when it comes to thenorms they induce. The classicist and the intuitionist simply haveopted to play by different rules.

This line of thought leads to a potential worry, however. For logicalnorms do not merely bind us in the way that the rules of a game bindus. I hold myself to be answerable to the rules governing a game(of chess, say) so long as I wish to participate in it. However, thenormativity of logic does not seem to be optional in the same way. Thenorms of logic are themselves responsible to our broader epistemicaims (and would thus need to be coordinated with other epistemicnorms). Hence, if my epistemic aim is, say, acquiring true beliefs(and avoiding false ones), this may give me a reason to prefer one setof logical norms over another. For imagine I could choose either oftwo logics \(L_{1}\) and \(L_{2}\). Suppose, moreover, that \(A\) istrue and that \(A \models_{L_{1}} B\) but \(A \not \models_{L_{2}}B\), for some relevant proposition \(B\). Even according to Beall andRestall, not all logics are equal. To pass muster, a logic mustsatisfy certain core conditions. In particular, it must betruth-preserving. Assuming that both \(L_{1}\) and \(L_{2}\) aretruth-preserving, it follows that \(B\) is true. But then it wouldseem that there is a clear sense in which \(L_{1}\) outperforms\(L_{2}\) in terms of the guidance it affords us. According to thenorms \(L_{2}\) gives rise to, there is presumably nothing amiss aboutan agent who believes \(A\) but not \(B\); according to \(L_{1}\)there presumably is. Hence, \(L_{1}\) is more conducive to ourepistemic aims. It follows that whenever two putatively equallycorrect logics, \(L_{1}\) and \(L_{2}\) are such that \(L_{2}\) is aproper sub-system of \(L_{1}\), one would appear to have reason to optfor \(L_{1}\) since it is more conducive to one’s aim of havingtrue beliefs. In cases where we are dealing with two logics \(L_{1}\)and \(L_{2}\) such that \(\models_{L_{1}}\) and \(\models_{L_{2}}\)are not sub-relations of one another, things may be more complicated.All the same, even in such cases, it may well be that our overarchingepistemic aims and norms give us reason to prefer one logic overanother, and hence that from the standpoint of these epistemic aims,the logics are not equally good after all. The aim of theseconsiderations is not to undermine forms of logical pluralism like theone advanced by Beall and Restall, but merely to point out that oncewe take the normative dimension of logic into account, we must alsoreckon with the broader epistemic goals, which the norms of logicmay be thought to be subservient to.

Field (2009b) argues for a different form of logical pluralism, onewhich leaves more room for normative conflict. Logical pluralism isnot, for Field, the result of ambiguity in our notion of logicalconsequence. Rather, it has its source in non-factualism of epistemicnorms. His non-factualism, in turn, is fueled partly by generalconcerns, partly by the nature of how we choose such norms. Among thegeneral concerns Field (2009c) mentions are Hume-style worries aboutthe impossibility of integrating irreducible normative facts into anaturalistic world view, Benacerraf-style worries about our ability togain epistemic access to such facts, and Mackie-style worries aboutthe “queerness” of such facts (i.e., that they not onlyappear to have no room within our scientific picture of the world, butthat, furthermore, they are supposed to have a somewhat mysteriousmotivational pull to them). The latter issue of norm selection amountsto this. Given a set of epistemic goals, we evaluate candidate normsas better or worse depending how well they promote those goals.According to Field, we have no reason to assume that there should be afact of the matter as to which choice of logic is the uniquely correctone; there will typically not be a unique system that best optimizesour (often competing) constraints.

That being said, it seems that we can sensibly engage in rationaldebates over which logic to adopt in the light of various issues(vagueness, the semantic paradoxes, etc.). Consequently, there is aclear sense in which normative conflicts do arise. Now, since Fieldtakes it to be an essential component of the notion of logicalconsequence that it should induce norms (Field 2009a,b, 2015), wechoose a logic by finding out which logical norms it makes most sensefor us to adopt. But because Field does not take there to be a fact ofthe matter as to which set of norms is correct and since the questionas to which of the norms best promotes our epistemic ends is oftenunderdetermined, we may expect there to be several candidate sets oflogical norms all of which are equally well-motivated. We are thusleft with a (more modest) form of logical pluralism on our hands.

What both of these types of pluralism have in common from thepoint of view of the question of the normativity of logic, though, istheir rejection of the view that logical norms might impose themselvesupon us simply as a result of the correctness of the correspondinglogical principles. As such, pluralist views stand diametricallyopposed to realist forms of monism such as the one championed by GilaSher (2011). According to Sher, logical principles are grounded,ultimately, in “formal laws” and so in reality. It isthese formal laws that ultimately also ground the correspondinglogical norms.^[4]

2. Normative for what?

Next let us ask what it is that logic is normative for, if indeed itis normative. The paradigmatic objects of normative appraisal areactions, behaviors or practices. What, then, is the activity orpractice that logical norms apply to?

2.1 Logic as normative for reasoning

One response—perhaps the most common one—is that logicsets forth norms for (theoretical)reasoning. Unlikethinking, which might consist merely of disconnected sequences ofconceptual activity, reasoning is presumably a connected, usuallygoal-directed, process by which we form, reinstate or revise doxasticattitudes (and perhaps other types of states) through inference.Consider the following two examples of how logic might give rise tonorms. First, suppose I am trying to find Ann and that I can be surethat Ann is either in the museum or at the concert. I am now reliablyinformed that she is not in the museum. Using logic, I conclude thatAnn is at the concert. Thus, by inferring in conformity with the valid(by the standards of classical logic) logical principle of disjunctivesyllogism, I have arrived at a true belief about Ann’swhereabouts. Second, if I believe that Ann is either at the concert orthe museum, while at the same time disbelieving both of the disjuncts,it would seem that there is a tension in my belief set, which I havereason to rectify by revising my beliefs appropriately. Logic may thusbe thought to normatively constrain the ways we form and revisedoxastic attitudes. And it does so, presumably, in our everydaycognitive lives (as in our example), as well as in the context of moreself-conscious forms of theoretical inquiry, as in mathematics, thesciences, law, philosophy and so on, where its normative grip on uswould seem to be even tighter.^[5]

2.2 Logic as constitutively normative for thought

Other philosophers have taken the normativity of logic to kick in atan even more fundamental level. According to them, the normative forceof logic does not merely constrain reasoning, it applies to allthinking. The thesis deserves our attention both because of itshistorical interest—it has been attributed in various ways toKant, Frege and Carnap^[6]—and because of its connections to contemporary views in epistemology andthe philosophy of mind (see Cherniak 1986: §2.5; Goldman 1986:Ch. 13; Milne 2009; as well as the references below).

To get a better handle on the thesis in question, let us agree tounderstand “thought” broadly as conceptual activity.^[7] Judging, believing, inferring, for example, are all instances ofthinking in this sense. It may seem puzzling at first how logic is toget a normative grip onthinking: Why merely by engaging inconceptual activity should one automatically be answerable to thestrictures of logic?^[8] After all, at least on the picture of thought we are currentlyconsidering, any disconnected stream-of-consciousness of imaginingsqualifies as thinking. One answer is that logic is thought to putforth norms that are constitutive for thinking. That is, in order fora mental episode to count as an episode of thinking at all, it must,in a sense to be made precise, be “assessable in light of thelaws of logic” (MacFarlane 2002: 37). Underlying this thesis isa distinction between two types of rules or norms: constitutive onesand regulative ones.

The distinction between regulative and constitutive norms is Kantianat root (KRV A179/B222). Here, however, I refer primarily to a relateddistinction due to John Searle. According to Searle, regulative norms“regulate antecedently or independently existing forms ofbehavior”, such as rules of etiquette or traffic laws.Constitutive norms, by contrast

create or define new forms of behavior. The rules of football orchess, for example, do not merely regulate playing football or chessbut as it were they create the very possibility of playing such games.(Searle 1969: 33–34; see also Searle 2010: 97)

Take the case of traffic rules.^[9] While I ought to abide by traffic rules in normal circumstances, Ican choose to ignore them. Of course, rowdy driving in violation ofthe traffic code might well get me in trouble. Yet no matter howcavalier my attitude towards traffic laws is, my activity still countsas driving. Contrast this with the rules governing the game of chess.I cannot in the same way opt out of conforming to the rules of chesswhile continuing to count as playing chess; in systematicallyviolating the rules of chess and persisting in doing so even in theface of criticism, I forfeit my right to count as partaking in theactivity of playing chess. Unless one’s moves are appropriatelyassessable in light of the rules of chess, one’s activitydoes not qualify as playing chess.

According to the constitutive conception of logic’s normativitythe principles of logic are to thought what the rules of chess are tothe game of chess: I cannot persistently fail to acknowledge that thelaws of logic set standards of correctness for my thinking withoutthereby jeopardizing my status as a thinker (i.e., someone presentlyengaged in the act of thinking).

Two important clarifications are in order. For one, on its mostplausible reading, the thesis of the constitutive normativity of logicfor thought must be understood so as to leave room for the possibilityof logical error: an agent’s mental activity may continue tocount as thinking, despite his committing logical blunders.^[10]

That is, although one may at times (perhaps even frequently andsystematically) stray from the path prescribed by logic in one’sthinking, one nevertheless counts as a thinker provided oneappropriately acknowledges logic’s normative authority overone’s thinking. Consider again the game of chess. In violatingthe rules of chess, deliberately or out of ignorance, I can plausiblystill be said to count as playing chess, so long, at least, as Iacknowledge that my activity is answerable to the rules; for example,by being disposed to correct myself when an illegal move is brought tomy attention.^[11] Similarly, all that is necessary to count as a thinker is to besensitive to the fact that my practice of judging, inferring,believing, etc., is normatively constrained by the laws of logic. Itis not easy to specify, in any detail, what the requisiteacknowledgment or sensitivity consists in. A reasonable startingpoint, however, is provided by William Taschek who, in hisinterpretation of Frege, proposes that acknowledging

the categorical authority of logic will involve one’s possessinga capacity to recognize—when being sincere and reflective, andpossibly with appropriate prompting—logical mistakes both inone’s own judgmental and inferential practice and that of others.(Taschek 2008: 384)

A second point of clarification is that the agent need not be able toexplicitly represent to herself the logical norms by which she isbound. For instance, it may be that my reasoning ought to conform todisjunctive syllogism in appropriate ways. I may be able to displaythe right kind of sensitivity to the principle by which I am bound(with the right prompting if need be), without my having to possessthe conceptual resources to entertain the metalogical proposition that\(\neg A, A\lor B \models B\). Nor must I otherwise explicitlyrepresent that proposition and the normative constraint to which itgives rise.

With these clarifications in place, let us turn to a centralpresupposition of the approach I have been sketching. What is beingpresupposed, of course, is a conception of thinking that does notreduce to brute psychological or neurophysiological processes orevents. If this naturalistic level of description were the only oneavailable, the constitutive account of the normativity of logic wouldbe a non-starter. What is being presupposed, therefore, is thepermissibility of irreducibly normative levels of descriptions of ourmental lives. In particular, it is assumed that the boundary betweenthe kinds of mental activity that constitute thinking and other kindsof mental activity (non-conceptual activity like being in pain, forinstance) is a boundary best characterizable in normative terms. Thisis not to deny that much can be learned about mental phenomena throughdescriptions that operate at different, non-normative levels—the“symbolic” or the neurological level of description,say—the claim is merely that if we are interested in demarcatingconceptual activity from other types of mental phenomena, we shouldlook to the constitutive norms governing it. Davidson (1980, 1984),Dennett (1987), and Millar (2004) all hold views according to whichhaving concepts and hence thinking requires that the agent beinterpretable as at least minimally sensitive to logical norms. Also,certain contemporary “normativist approaches” according to whichaccounts of certain intentional states involve ineliminable appeals tonormative concepts may advocate the constitutive conception of logic’s normativity(e.g., Wedgwood 2007, 2009; Zangwill 2005).

2.3 Logic as normative for public practices

So far the answers to the question “What is logic normativefor?” we considered had in common that the “activities” inquestion—reasoning and thinking—are internal, mentalprocesses of individual agents. But logic also seems to exertnormative force on the external manifestations of theseprocesses—for instance, it codifies the standards to which wehold ourselves in our practices of assertion, rational dialogue andthe like. While much of the literature on the normativity of logicfocuses on internal processes of individuals, some authors haveinstead emphasized logic’s role as a purveyor of public standards for normatively regulated practices.

Take the practice of asserting. Assertion is often said to “aimat truth” (or knowledge, Williamson 2000: Ch. 11) as well asbeing a “matter of putting forward propositions for others touse as evidence in the furtherance of their epistemic projects”(Milne 2009: 282). Since I take the asserted propositions to be trueand since truths entail further truths, I am “committed tostanding by” the logical consequences of my assertions or elseto retract them if I am unable to meet challenges to my assertion orits consequences. Similarly, if the set of propositions I assert isinconsistent at least one of my assertions must fall short of beingtrue and the set as a whole cannot be regarded as part of my evidence.Plausibly, therefore, logic does have a normative role to play ingoverning the practice of assertion.

Peter Milne takes an interest in assertion mainly in order to“work back” from there to how logic constrains belief. Heconcludes that logic exerts normative force at least on the stock ofbeliefs that constitute the agent’s evidence (Milne 2009: 286).Other authors explicitly prioritize the external dimension ofreasoning, conceived of as a social, inter-personal phenomenon.According to them, it is reasoning in this external sense (as opposedto intra-personal processes of belief revision, etc.) that is theprimary locus of logical normativity (MacKenzie 1989). The normsgovern our rational interactions with our peers. For instance, theymight be thought to codify the permissions and obligations governingcertain kinds of dialogues. Viewed from this perspective,logic’s normative impact on the intra-personal activity ofreasoning is merely derivative, arrived at through a process ofinteriorization. A view along these lines has been advanced byCatarina Dutilh Novaes (2015). In a similar vein Sinan Dogramaci(2012, 2015) has proposed a view he calls “epistemiccommunism”. According to epistemic communism our use of“rational” applied to certain deductive rules has aspecific functional role. Its role is to coordinate our epistemicrules with a view to maximizing the efficiency of our communalepistemic practices. On the basis of this view, he then elaborates anargument for the pessimistic conclusion that no general theory ofrationality is to be had.

We will here follow the bulk of the literature in asking after thenormative role logic might play in reasoning understood as anintra-personal activity. Yet, much of the discussion to follow appliesmutatis mutandis to the other approaches.

3. Harman’s challenge

Despite its venerable pedigree and its intuitive force, the thesis thatlogic should have a normative role to play in reasoning has not goneunchallenged. Gilbert Harman’s criticisms have been particularlyinfluential. Harman’s skeptical challenge is rooted in adiagnosis: our deep-seated intuition that logic has a specialnormative connection with reasoning is rooted in a confusion. We haveconflated two very different kinds of enterprises, viz. that offormulating a theory of deductive logic, on the one hand, and whatHarman calls “a theory of reasoning” (Harman 2002) on the other. Beginwith the latter. A theory of reasoning is a normative account abouthow ordinary agents should go about forming, revising and maintainingtheir beliefs. Its aim is to formulate general guidelines as to whichmental actions (judgments and inferences) to perform in whichcircumstances and which beliefs to adopt or to abandon (Harman 2009:333). As such, the subject matter of a theory of reasoning are thedynamic “psychological events or processes” thatconstitute reasoning. In contrast, “the sort of implication andargument studied in deductive logic have to do with [static,non-psychological] relations among propositions” (idem). Consequently,

logical principles are not directly rules ofbelief revision.They are not particularly about belief [or the other mental states andacts that constitute reasoning] at all. (Harman 1984: 107)

Once we disabuse ourselves of this confusion, Harman maintains, it ishard to see how the resulting gap between logic and reasoning can bebridged. This is Harman’s challenge.

At least two lines of response come to mind. One reaction toHarman’s skeptical challenge is to take issue with his way ofsetting up the problem. In particular, we might reject his explanation of the provenanceof our intuitions to the effect that logic has a normative role toplay in reasoning as stemming from a mistaken identification ofdeductive logic and theories of reasoning. It might be thought, forinstance, that Harman is led to exaggerate the gulf between deductivelogic and theories of reasoning as a result of acontestable—because overly narrow—conception of eitherlogic or reasoning, or both. Advocates of broadly logical accounts ofbelief revision (belief revision theories, non-monotonic logics,dynamic doxastic logic, etc.) may feel that Harman is driven to hisskepticism out of a failure to consider more sophisticated logicaltools. Unlike standard first-order classical logic, some of theseformalisms do make explicit mention of beliefs (and possibly othermental states). Some formalisms do seek to capture the dynamiccharacter of reasoning in which beliefs are not merely accumulated butmay also be revised. Harman’s response, it would seem (Harman1986: 6), is that such formalisms either tacitly rely on mistakenassumptions about the normative role of logic or else fall short oftheir objectives in other ways. But even if one disagrees withHarman’s assessment, one can still agree that such formalmodels of belief revision do not obviate the need for a philosophicalaccount of the normativity of logic. That is because such models do typically tacitly rely on assumptions concerning the normative role of logic. An account of the normativity of logic would thus afford us a fullerunderstanding of the presuppositions that undergird such theories.

On the other hand, some philosophers—externalists of variousstripes, for instance—may find fault with the epistemologicalpresuppositions underlying Harman’s conception of a theory ofreasoning. Harman views the aim of epistemology as closely linked tohis project of providing a theory of reasoning. According toHarman’s “general conservatism”, centralepistemological notions, like that of justification are approachedfrom the first-personal standpoint: “general conservatism is amethodological principle, offering methodological advice of a sort aperson can take” (Harman 2010: 154). As such Harman's approach contrasts with much ofcontemporary epistemology which, unconcerned with direct epistemicadvice, is mainly in the business of seeking to lay down explanatorilyilluminating necessary and sufficient conditions for epistemic justification.^[12] Summarizing the first line of response, then, Harman's skepticism is partly premised on particular conceptions of logic and of epistemological methodology both of which may be called into question.

The second line of response is to (largely) accept Harman’sassumptions regarding the natures of deductive logic and of epistemologybut to try to meet his challenge by showing that there is ainteresting normative link between the two after all. In what follows, I focusprimarily on this second line of response.

Of course, saying that deductive logic and theories of reasoning aredistinct is one thing, affirming that there could not be aninteresting normative connection between them is quite another. As afirst stab at articulating such a connection, we might try thefollowing simple line of thought: theoretical reasoning aims toprovide an accurate representation of the world. We accuratelyrepresent the world by having true (or perhaps knowledgeable) beliefsand by avoiding false ones. But our doxastic states havecontents—propositions—and these contents stand in certainlogical relations to one another. Having an awareness of these logicalrelations would appear to be conducive to the end of having truebeliefs and so is relevant to theoretical reasoning. In particular,the logical notions of consequence and consistency seem to be relevant.If I believe truly, the truth of my belief will carry over to itslogical consequences. Conversely, if my belief entails a falsehood itcannot be true. Similarly, if the set of propositions I believe (ingeneral or in a particular domain) is inconsistent, they cannotpossibly afford an accurate representation of the world; at least oneof my beliefs must be false. Harman may be able to agree with all of this. Hisskepticism pertains also (and perhaps primarily) to the question whether logic has a privileged role to play in reasoning; that the principles of logic are relevant to reasoning in a way that principles of other sciences are not (Harman 1986: 20). However, I want to set this further issue to one side for now.

Notice that this simple reflection on the connection between logic andnorms of reasoning leads us right back to the basic intuitions at the beginning of this entry: that there is something wrong with us whenwe hold inconsistent beliefs or when we fail to endorse the logicalconsequences of our beliefs (at least when we can be expected to beaware of them). Let us spell these intuitions out by way of the following two principles. Let \(S\) be an agent and \(P\)a proposition.^[13]

• Logical implication principle (IMP): If \(S\)’s beliefslogically imply \(A\), then \(S\) ought to believe that\(A\).

• Logical consistency principle (CON): \(S\) ought to avoid havinglogically inconsistent beliefs.

Notice that on the face of itIMP andCON are distinct.IMP, in and of itself, does not prohibit inconsistent or evencontradictory beliefs, all it requires is that my beliefs be closedunder logical consequence.CON, on the other hand, does not require that I believe the consequencesof the propositions I believe, it merely demands that the set ofpropositions I believe be consistent. However, given certainassumptions,IMP does entailCON. Against the background of classical logic, the entailment obtainsprovided we allow the following two assumptions: (i) one cannot (and,via the principle that “ought” implies “can”,ought not) both believe and disbelieve one and the sameproposition simultaneously; and (ii) that disbelieving a proposition istantamount to believing its negation.^[14] For let \(\{ A_{1}, \dots, A_{n}\}\) be \(S\)’s inconsistentbelief set. By classical logic, we have \(A_{1}, \dots, A_{n-1}\models\neg A_{n}\). Since \(S\)’s beliefs are closed under logicalconsequence, \(S\) believes \(\neg A_{n}\) and hence, by (ii), disbelieves \(A_{n}\). So, \(S\) both believes anddisbelieves \(A_{n}\).

3.1 The objections

IMP andCON are thus a first—if rather flatfooted—attempt at pinningdown the elusive normative connection between logic and norms ofreasoning. Harman considers these responses and responds in turn. Thefollowing four objections against our provisional principles can, inlarge part, be found in the writings of Harman.

So much for the objections toIMP andCON. The question raised by these considerations is whether these principles can be improved upon.

4. Bridge principles

Let us focus onIMP for now. Harman’s objections establish thatIMP—in its current form, at least—is untenable. The question iswhetherIMP can be improved upon in a way that is invulnerable to Harman’sobjections. In other words, the question is whether a tenable versionof what MacFarlane (MF2004) calls abridge principle is to behad. A bridge principle, in this context, is a general principle thatarticulates a substantive relation between “facts” aboutlogical consequence (or perhaps an agent’s attitudes towardssuch facts) on the one hand, and norms governing the agent’sdoxastic attitudesvis-à-vis the propositions standingin these logical relations on the other.IMP is a bridge principle, albeit not a promising one.

Harman’s skepticism about the normativity of logic can thus beunderstood as skepticism as to whether a serviceable bridge principleis to be had. In order properly to adjudicate whether Harman’sskepticism is justified, we need to know what “the optionsare”. But how? John MacFarlane (MF2004) offers a helpful taxonomy of bridge principles which constitutes a very goodfirst approximation of the range of options. This section brieflysummarizes MacFarlane’s classification, as well as subsequentdevelopments in the literature.

Let us begin with a general blue print for constructing bridge principles:^[16]

• (\(\star\))If \(A_{1},\dots, A_{n} \models C, \textrm{ then } N(\alpha(A_{1}),\dots, \alpha(A_{n}), \beta(C))\).

A bridge principle thus takes the form of a material conditional. Theconditional’s antecedent states “facts” aboutlogical consequence (or attitudes toward such “facts”).Its consequent contains a (broadly) normative claim concerning theagent’s doxastic attitudes towards the relevant propositions.Doxastic attitudes, as I use the term, include belief, disbelief, anddegree of belief.^[17] Here \(\alpha\) may (but need not) represent the same attitude as\(\beta\). In fact, for principles with negative polarity, it mayrepresent the negation of an attitude: “do not disbelieve theconclusion, if you believe the premises”.

In what ways, now, can we vary this schema so as to generate the spaceof possible bridge principles? MacFarlane introduces three parametersalong which the schema may be varied. Each parameter allows formultiple “discrete settings”. We can think of the logicalspace of bridge principles as the range of possible combinations amongthese parameter settings.

1. In order to express the normative claims, we will need deonticvocabulary. Bridge principles may differ in the deontic operator theydeploy: does the normative constraint take the form of anought (o), a permission (p) or merely of having (defeasible)reason (r)?

2. What is thepolarity of the normative claim? Is it apositive obligation/permission/reasonto believe acertain proposition given one’s belief in a number of premises (+)? Or rather is it anegative obligation/prohibition/reasonnot todisbelieve (−)?

3. What is the scope of the deontic operator? Different bridge principlesresult from varying the scope of the deontic operator. Let \(O\) standgenerically for one of the above deontic operators. Given that theconsequent of a bridge principle will typically itself take the formof a conditional, the operator can take

   • narrow scope with respect to the consequent (C):\(A\supset O(B)\)
   • wide scope (W):\(O(A \supsetB)\)
   • or it can govern both the antecedent and the consequent of theconditional (B):^[18]\(O(A) \supset O(B)\)

These three parameters admit of a total of eighteen combinations oftheir settings and hence eighteen bridge principles. The symbols inparentheses associated with each parameter setting combine todetermine a unique label for each of the principles: The first letterindicates the scope of the deontic operator (C, W or B), the secondletter indicates the type of deontic operator (o[bligation],p[ermissions], r[easons]) and the “+” or“−” indicate positive and negative polarity respectively.^[19] For example, the label “Co+” corresponds to our originalprincipleIMP:

• If \(A_{1}, A_{2}, \dots, A_{n} \models C\), then if \(S\) believes\(A_{1}, A_{2}, \dots, A_{n}\), \(S\)ought to believe\(C\).

And “Wr−” designates:

• If \(A_{1}, A_{2}, \dots, A_{n} \models C\), then \(S\) has reason to(believe \(A_{1}, A_{2}, \dots, A_{n}\), only if \(S\) does notdisbelieve \(C\)).

Many will regard the bridge principles we have presented thus far tobe problematic. They all relate “facts” about logicalentailment—assuming there are such things—to certainnormative constraints on the agent’s attitudes. The trouble, they will say, isthat these principles are not sensitive to the cognitive limitationsof ordinary agents. Agents, if they are even remotely like us, are notapprised of all entailment “facts”. Consequently,especially the “ought”-based principles (at least on someunderstanding of “ought”) are therefore vulnerable toHarman’sObjection from Excessive Demands.

A natural response is to consider attitudinal bridge principles. Icallattitudinal bridge principles whose antecedents arerestricted to logical implications to which the agent bears anattitude. For instance, to take the type of attitudinal principleconsidered by MacFarlane, Co+ may be transformed into:

• (Co+k) If\(S\) knows that \(A_{1},\dots, A_{n} \models C\), then if \(S\)believes the \(A_{i}\), \(S\) ought to believe \(C\).

According to (Co+k), the agent’s belief set ought to be closedonly underknown logical consequence. Let us call this anattitudinally constrained or, more specifically, theepistemically constrained variant of Co+ (whence the“k” in the label). Different authors may go in fordifferent types of attitudes. Knowledge, of course, is a factiveattitude. Some will wish to leave room for the possibility of(systematic) logical error. For instance, an agent might mistakenlycomply with the principle \(A\supset B, B \models A\). Perhaps evensomeone with erroneous logical convictions such as this should, forthe sake of internal coherence, comply with the principles he deemscorrect. An agent who sincerely took an erroneous principle to becorrect but failed to reason in accordance with it may be seen tomanifest a greater degree of irrationality than someone who at leastconformed to principles he endorses. But we can also imagine moreinteresting cases of systematic error. Suppose I am impressed with anargument for a particular non-classical logic as a means of parryingthe semantic paradoxes. I thus come to espouse the logic in questionand begin to manage my doxastic attitudes accordingly. But now supposein addition that unbeknownst to me the arguments that persuaded me arenot in fact sound. Again, it might be thought that though I ammistaken in my adherence to the logic, so long as I had good reasonsto espouse it, it may nevertheless be proper for me to comply with itsprinciples. If logical error in either of these two senses is to beaccommodated, the appropriate attitude would have to benon-factive.

A further issue is that ordinary agents are presumably normativelybound by logical principles without being able to articulate orrepresent those principles to themselves explicitly. Assumingotherwise runs the risk of overly intellectualizing our ability toconform to logical norms. The attitudes borne by such logicallyuntrained agents to the logical principles therefore presumably arenot belief-like. Perhaps such agents are better thought of asexercising an ability or having a disposition to take certain forms ofentailment to be correct. See Corine Besson 2012 for a criticism ofdispositionalist accounts of logical competence, and Murzi &Steinberger 2013 for a partial defense.

Having thus outlined the classificatory scheme, a number of additionalcomments are in order. Notice that disbelieving \(A\) is to bedistinguished from not believing \(A\). One cannot rationally believeand disbelieve the same proposition (although seenote 12). Hence, I ought to ensure that when I disbelieve \(A\), I do notbelieve \(A\). The converse, however, obviously does not hold since Ican fail to believe \(A\) without actively disbelieving it. I may, forinstance, choose to suspend my judgment as to whether \(A\) pendingfurther evidence, or I may simply never have considered whether \(A\).Furthermore, I will remain neutral on the question as to whether theattitude of disbelieving \(A\) should be identified with that ofbelieving \(\neg A\).

Moreover, a note on deontic modals is in order. “You ought not\(\Phi\)” (\(O\neg \Phi\)) is not the same as saying “Itis not the case that you ought to \(\Phi\)” (\(\neg O \Phi\)).But rather “You are forbidden from \(\Phi\)ing”.Consequently, “You ought not disbelieve \(A\)” should beread as “disbelieving \(A\) would be a mistake”, asopposed to “it is not the case that you ought to disbelieve\(A\)”, which is compatible with the permissibility ofdisbelieving \(A\).

Ought andmay are understood to be strict notions. By contrast,reason is apro tanto or contributory notion. Havingreason to \(\Phi\) is compatible with simultaneously having reason notto \(\Phi\) and indeed with it being the case that I ought not to\(\Phi\). Reasons, unlikeoughts, may be weighed against eachother; the side that wins out determines what ought to be done.Finally, I am here treating all deontic modals as propositionaloperators. This too is not uncontroversial. Peter Geach (1982) andmore recently Mark Schroeder (2011) have argued that so-calleddeliberative or practicaloughts are best analyzed not asoperators acting on propositions but rather as expressing relationsbetween agents and actions. (Interestingly, MacFarlane (2014: Ch. 11)has recently followed suit.) Nevertheless, I will assume withoutargument that the operator-reading can be made to work even in the case of deliberativeoughts. For defensesof this position see e.g., Broome 2000, 2013; Chrisman 2012; andWedgwood 2006. We can capture the particular connection between anagent and the obligation she has towards a proposition at a particulartime, by indexing the operator: \(O_{S, t}\). I will drop the indicesin what follows.

A last comment: MacFarlane is not explicit as to whether bridgeprinciples are to be understood assynchronicnorms—norms that instruct us which patterns of doxasticattitudes are, in a specified sense, obligatory, permissible orreasonable at a given point in time; or whether they are to providediachronic norms—norms that instruct us how anagent’s doxastic state should or may evolve over time. Toillustrate the distinction, let us consider Co+ (akaIMP) once again. Understood synchronically, the principle should bespelled out as follows.

• If \(A_{1}, A_{2}, \dots, A_{n} \models C\), then if, at time \(t\),\(S\) believes \(A_{1}, A_{2}, \dots, A_{n}\), then \(S\)ought to believe \(C\) at time \(t\).

In other words, the principle demands that one’s beliefs be, atall times, closed under logical consequence. Alternatively, on mightinterpret Co+ as a diachronic norm as follows:

• If \(A_{1}, A_{2}, \dots, A_{n} \models C\), then if, at time \(t\),\(S\) believes \(A_{1}, A_{2}, \dots, A_{n}\), then \(S\)ought to believe \(C\) at time \(t'\) (where \(t\) precedes\(t'\) suitably closely).

Different principles lend themselves more or less well to these tworeadings. \(C\)- and \(B\)-type principles can be interpreted aseither synchronic or diachronic principles on account of the fact thatthey make explicit claims as to what an agent ought, may or has reasonto believe or disbelieve given her other beliefs. The \(W\)s, bycontrast, are most plausibly read as synchronic principles. Suchprinciples do not, in and of themselves, instruct the subject whichinferences to make. Rather, they tend to proscribe certain patterns ofbelief (and, perhaps, disbelief) or distributions of degrees of belief.

4.1 Evaluating bridge principles

With the logical terrain of bridge principles charted, the questionnow arises as to which principles (if any) are philosophically viable.This is discussed in the following supplementary document:

Bridge Principles – Surveying the Options

In that supplement we discuss a variety of desiderata thathave been put forward and consider candidate principleswith respect to those desiderata.

4.2 The Preface Paradox

Given that the Preface Paradox constitutes a major stumbling block formany otherwise plausible principles, we do well to explore the ways inwhich the Preface Paradox might be dealt with. One way, of course, ofdealing with the Preface Paradox is to deny it its force. That is,one might try to outright solve, or in some way dissolve, theparadox. Since it seems fair to say that no such approach has won theday (see entryepistemic paradoxes), I will assume that the Preface Paradox intuitions are to be take seriously.^[20]

Alternatively, one might acknowledge the force of the Prefaceintuitions while at the same time trying to hold on to a strict,ought-based principle. But how? According to all such principles, I,the author of a non-trivial non-fiction book (let us assume), ought to believe (or atleast not disbelieve) the conjunction of the propositions in my book,given that I firmly endorse each conjunct individually.MacFarlane’s response is that we must simply reconcile ourselvesto the irreconcilable: the existence of an ineliminable normative conflict. Our strictlogical obligations clash with other epistemic obligations, namely,the obligation to believe that some of my beliefs must be mistaken.Our agent becomes a tragic heroine. Through no fault of her own, shefinds herself in a situation in which, no matter what she does, shewill fall short of what, epistemically speaking, she ought to do.

It might be retorted that, as a matter of sound methodology, admittingan irresolvable normative clash should only be our last resort. Abetter approach (all other things being equal) would consist infinding a way of reconciling the conflicting epistemic norms.

Among the qualitative principles we have been considering, the onlyway out is via non-strict principles like (Wr+b*), which we consideredat the end of the previous section. On this principle, I, the author,merely have reason (as opposed to having sufficient reason) forbelieving the conjunction of the claims that make up the body of mybook, given that I believe each of the claims individually. Thecrucial difference resides in the fact that this leaves open thepossibility that my reason for being logically coherent can beoverridden. In particular, it can be outweighed by reasons stemmingfrom other epistemic norms. In the case at hand, it might be thoughtthat our logical obligations are superseded by a norm of epistemicmodesty. This, of course, is not uncontroversial. Some maintain thatwhat the Preface Paradox shows is not merely that the normative gripof logic does not take the form of a strictought, but ratherthat we in fact haveno reason at all to believe inmulti-premise closure of belief under logical consequence: my reasonsfor believing in the conjunction of my claims are not being trumped byweightier reasons for disbelieving it; I have no logic-based reasonwhatsoever to believe the conjunction in the first place.

So far, then, we have considered the following reactions to thePreface Paradox: reject the Preface Paradox altogether; followMacFarlane and cling to the strict ought-based principle at the costof accepting an irresolvable normative clash; or opt for the weakerreason operator and give up the intuition motivating theStrictness Test. But none of these proposals incorporates what is perhaps the mostnatural response to the Preface Paradox outside of the debatesurrounding the normativity of logic. A standard response to thePreface Paradox consists in appealing to graded credal states in lieuof “full” (“qualitative”, “binary”or “all-or-nothing”) beliefs. Such “credences”or “degrees of belief” (I will use the two labelsinterchangeably) are typically modeled by means of a (possiblypartial) credence function (which we will denote by“\(cr\)”) that maps the set of propositions into the unitinterval.Probabilists maintain that an ideally rationalagent’s credence function ought to be (or at least ought to beextendable to) a probability function (i.e., it ought to satisfy thestandard axioms of probability theory). In other words, an ideallyrational agent should have probabilistically coherent credences.

Probabilists have no trouble accounting for the Preface phenomena: thesubjective probability of a (large) conjunction may well below—even zero, as in the case of the Lottery Paradox (see entryepistemic paradoxes)—evenif the probability assigned to each of the individual conjuncts isvery high (reflecting the high degree of confidence the author rightlyhas in each of her claims).

A tempting strategy for formulating a bridge principle capable ofcoping with the Preface Paradox is to incorporate these insights. Thismight be done by going beyond MacFarlane’s classification anddevising instead aquantitative bridge principle: one inwhich logical principles directly constrain the agent’s degreesof belief (as opposed to constraining her full beliefs).

Hartry Field (2009a,b, 2015} proposes a bridge principles of just thisform. Here is a formulation of such a principle:

• (DB) If\(A_{1}, \dots, A_{n} \models C\), then \(S\)’s degrees ofbelief ought to be such that: \(cr(C) \geq \sum_{1 \leq i \leq n}cr(A_{i}) - (n - 1)\)

Note first thatDB is a wide scope principle: it requires that our degrees of beliefrespect the specified inequality, which can be achieved in one of twoways: by suitably raising one’s degree of belief in theconclusion or else by readjusting one’s degrees of belief in thepremises.

DB is based on a well-known result in probability logic, which isusually stated in terms of “uncertainties” (see Adams 1998for more details; for a helpful overview, see Hájek 2001).Define theuncertainty of a proposition \(A\), \(u(A)\) as\(u(A) = 1-cr(A)\). Put in this way,DB says that the uncertainty of the conclusion must not exceed the sum of the uncertainties of the premises.DB can be seen to share a number of important features with standardprobability theory. Plug in \(0\) for \(n\) and you get that oneshould assign \(1\) to any logical truth. Plug in \(1\) and you getthat one’s degree of belief in the premise of a validsingle-premise argument should not exceed your degree of belief in theconclusion. The idea underlyingDB is that uncertainties can add up and therefore need to be accountedfor when we are trying to determine how the logical relations betweenour belief contents should affect our degrees of belief in thosecontents. Even if my uncertainty about each of a large number ofpremises is next to negligible when taken individually, theuncertainty may accumulate so as to make the conclusion highly(perhaps even maximally) uncertain. It is for this reason thatDB gets us around the Preface Paradox; in the Preface case the number ofpremises is sufficiently high for the conclusion to admit of a verylow credence.

5. Further challenges

5.1 Kolodny’s challenge

Logical norms are naturally regarded as a species of rationalrequirements. If I believe a set of propositions and at the same timedisbelieve an obvious logical consequence thereof my set of beliefspresumably exhibits a rational defect. Rational requirements arecharacterized by their demand for coherence: they demand either aparticular kind of coherence among our attitudes or else coherencebetween our attitudes and the evidence. Niko Kolodny has dubbed theformer “requirements of formal coherence as such” (Kolodny2007: 229). They areformal in the sense that they concernlogical relationships between attitude contents or the arithmeticalrelationships between the degrees of confidence we invest in thosecontents. The qualification “as such” indicates that aninternal coherence among the attitudes is demanded to the exclusion ofother epistemologically relevant factors (evidential considerations,for example). Requirements of this type, it has been argued (Broome2000; Dancy 1977), take the form of wide scope principles. Hence, theydo not generally prescribe a particular attitude, but are satisfiablein a number of ways. Or, to put it another way, they prohibitparticular constellations of attitudes. For instance, Wo−proscribes states like the one just imagined, in which the agentbelieves all of the premises of a valid argument while disbelieving its conclusion. It maybe satisfied, as we have seen, by either coming to believe theconclusion or by abandoning some of the premises.

The status of logical norms as a species of rational requirementraises weighty questions. For one, Kolodny (2005) has challenged theseemingly natural assumption that rationality is normative at all.That is, he has questioned whether we in fact havereason todo what rational requirements require of us. It might be thatrationality makes certain demands on us, but that it is an openquestion as to whether we should want to be rational. Here is not theplace to develop these ideas, let alone to try to resolve the“normative question” for rationality (see Way 2010 for anoverview). In the absence of a convincing response to Kolodny’schallenge, some might take umbrage at our talk of logicalnorms. Strictly speaking, we should speak of them asnecessary conditions for rationality, leaving open whether we havereason to be rational.

While it would take us too far afield to address the question of thenormativity of rationality, there is a related strand of Kolodny’sargument that is more directly relevant to our discussion. The claimin question, put forth in Kolodny 2007 & 2008, is that theresimply is no reason for postulating the existence of formal coherencerequirements as such at all. This may seem surprising. After all, totake Kolodny’s simplest example, we certainly do have theintuition that an agent who, at a given time, believes both \(p\) and\(\neg p\) is violating a requirement—a requirement, presumably,of something like the following form:

• (NC) \(S\)is required not to both believe \(A\) and \(\neg A\) at \(t\) (for anytime \(t\)).

If Kolodny is right that there are no pure formal coherencerequirements like(NC), how are we to explain our intuitions? Kolodny’s strategy is todevise an error theory, thereby seeking to show how coherence (or near enoughcoherence) in the relevant sense emerges as a by-product of ourcompliance with other norms, norms that are not themselves pure formalcoherence requirements, thus obviating the need for postulating pureformal coherence requirements.

Consider how this plays out in the case of(NC). Kolodny proposes an evidentialist response. Any violation of(NC) is indeed a violation of a norm, but the relevant norm being violatedis a (narrow scope) evidential norm: the norm, roughly, that one hasreason to believe a proposition only in so far as “the evidenceindicates, or makes likely, that” the proposition is true. Anorm, in other words, much like(EN) (in the supplement on Bridge Principles). The thought is that any instance of my violating(NC) iseo ipso an instance in which my beliefs are out of whackwith the evidence. For when I hold contradictory beliefs, at least oneof the beliefs must be unsupported by the evidence. As Kolodny putsit,

The attitudes that reason requires, in any given situation, areformally coherent. Thus, if one has formally incoherent attitudes, itfollows that one must be violating some requirement of reason. Theproblem is not, as the idea of requirements of formal coherence assuch suggests, that incoherent attitudes are at odds witheach other.It is instead that when attitudes are incoherent, it follows that oneof these attitudes is at odds with thereason for it—as it wouldbe even if it were not part of an incoherent set. (Kolodny 2007: 231)

Another way of making Kolodny’s point is to note the following.Suppose I find myself believing both \(p\) and \(\neg p\), but thatthe evidence supports \(p\) (over its negation). If(NC) were the operative norm, I could satisfy it “againstreason”, i.e., by coming to believe \(\neg p\). But adherence to(NC)contra the evidence seems like an unjustified“fetish” for “psychic tidiness”. (Kolodnyproposes similar maneuvers for other types of putative formalcoherence norms, and for norms of logical coherence inparticular.)

What Kolodny assumes here is that there are, in Broome’s words,“no optional pairs of beliefs” (Broome 2013: 85). That is,it is never the case that belief in \(A\) and belief in \(\neg A\) isequally permissible in light of the evidence. As Broome points out,Kolodny’s assumption is founded on a commitment toevidentialism, which may cause some to get off the bus. Notice,though, that even if we accept Kolodny’s argument along with itsevidentialist presuppositions, there may still be room for logicalnorms. Such norms would not constrain beliefs directly, since onlyevidence constrains our beliefs on Kolodny’s view. Yet, theevidence itself would be structured by logic. For instance, if \(A\)entails \(B\), then since \(A\) cannot be true without \(B\) beingtrue, any evidence that counts in favor of \(A\) should also count infavor of \(B\). Logic would then still exert normative force. However,its normative force would get only an indirect grip on theagent’s doxastic attitudes by constraining the evidence. It is not clear how robust the distinction is, especially against the background of conceptions that take evidence to be constituted largely (or entirely) by one's beliefs. Moreover, Alex Worsnip 2015 has argued that in cases of misleading higher-order evidence, failures of coherence cannot ultimately be explained in terms of failures to respond adequately to the evidence.

5.2 Consistency and coherence

At the outset we identified two logical properties as the two centralprotagonists in any story about the normative status of logic:consistency and logical consequence. So far our focus has been almostexclusively on consequence. Let us now briefly turn to norms ofconsistency.

The most natural and straightforward argument for consistency is thatthe corresponding norm—something along the lines ofCON—is entailed by the truth norm for belief:

• (TN) For anyproposition \(A\), if an agent \(S\) considers or has reason to consider\(A\), \(S\) ought to believe \(A\) if and only if \(A\) is true.^[21]

The truth norm entails theconsistency norm (given certainassumptions):

• (CN) For anyagent \(S\), the set of propositions believed by \(S\) at any giventime ought to be logically consistent.

For if the set of propositions I believe at a particular point in timeis inconsistent, they cannot all be true, which is to say that I amviolating the truth norm with respect to at least one of mybeliefs.

Some objections to the consistency norm are closely related to theconsiderations ofExcessive Demands. And even in cases where it would be within our powers to discover aninconsistency given our resources of computational power, time and soon, it may still be reasonable to prioritize other cognitive aimsrather than expending significant resources to resolve a minorinconsistency (Harman 1986). However, many authors who invoke(CN) do so in a highly idealized context. They think of the norm not asreason-giving or as a basis for attributing blame, but merely as anevaluative norm: an agent with an inconsistent belief set is less thanperfectly rational.^[22]

Another reason for rejectingCON is dialetheism (see entry ondialetheism). Clearly, if there are true contradictions, there are special cases in which one ought to have inconsistent beliefs.

But there is a further worry about consistency borne out of lesscontroversial assumptions. It stems from the aforementioned fact thatwe do not only evaluate our beliefs according to their truth statusbut also in terms of their reasonableness in light of the evidence.Accordingly, there would seem to be an epistemic norm, like(EN) in the supplement on Bridge Principles, that one ought to (or may) believe a proposition only if thatproposition is likely to be true given the evidence. But if that isso, the following well-known scenario may arise: it may be that, for aset of propositions, I ought to (may) believe each of them in light ofthe evidence, yet—because evidential support is notfactive—the resulting belief set turns out to be inconsistent.Therefore, if rationality demands that I align my beliefs with theevidence, rationality is no guarantee for logical consistency. Ofcourse, it is precisely this clash between our (local) evidential normand the (global) coherence norm of logical consistency that isdramatized in the Preface and in the Lottery paradoxes.

In light of such considerations, no small number ofauthors have come to reject the consistency norm (seeinteralia Kyburg 1970 and Christensen 2004). A particularlyinteresting positive alternative proposal was recently made by BrandenFitelson and Kenny Easwaran (Fitelson and Easwaran 2015, Easwaran 2015). They advancea range of sub-consistency coherence norms for full belief inspired byJoyce-style accuracy-dominance arguments for probabilism as a norm forcredences (see Joyce 1998, 2009 and also the entry onepistemic utility arguments for probabilism). One important such norm is based on the following conception ofcoherence. Roughly, a belief set is coherent just in case there is noalternative belief set that outperforms it in terms of its lowermeasure of inaccuracy across all possible worlds, i.e., just in caseit is not weakly dominated with respect to accuracy.

5.3 Logic vs. probability theory

Even if there is a plausible sense in which logic can be said to benormative for thought or reasoning, there remains a worry aboutcompetition. Logic-based norms usually target full beliefs. If thatis correct, a significant range of rationally assessable doxasticphenomena fall outside of the purview of logic—mostsignificantly for present purposes, degrees of belief.^[23] Degrees of belief, according to the popular probabilist picture, aresubject not to logical, but to probabilistic norms, in particular thesynchronic norm of probabilistic coherence.^[24] Consequently, the normative reach of logic would seem (at best) to be limited;it does not exhaust the range of doxastic phenomena.

Worse still, some philosophers maintain that degrees of belief are theonly doxastic attitudes that are, in some sense, “real”,or at least the only ones that genuinely matter. According to them,only degrees of belief are deserving of a place in our most promisingaccounts of both theoretical (broadly Bayesian) and practical (broadlydecision-theoretic) accounts of rationality. Full belief talk iseither to be eliminated altogether (Jeffrey 1970), or reduced to talkof degrees of belief (ontologically, explanatorily or otherwise).Others still acknowledge that the concept of full belief plays anindispensable role in our folk-psychological practices, butnevertheless deem it to be too blunt an instrument to earn its keep inrespectable philosophical and scientific theorizing (Christensen2004). Virtually all such “credence-first” approaches havein common that they threaten to eliminate the normative role of logic,which is superseded or “embedded” (Williams 2015) inprobabilism.

A number of replies might be envisaged. Here we mention but a few.First, one may question the assumption that logical norms really haveno say when it comes to credences. Field’s quantitative bridgeprinciple is a case in point. As we have seen, it does directlyconnect logical principles (or our attitudes towards them) withconstraints on the allowable ways of investing confidence in thepropositions in question. To this it might be retorted, however, thatField’s proposal in effect presupposes some (possiblynon-classical) form of subjective probability theory. After all, inorder to align one’s credences with the demands of logic, onemust be capable of determining the numerical values of one’scredences in logically complex propositions on the basis ofone’s degrees of belief in simple propositions. This is mostnaturally done by appealing to probability theory.^[25] But if so, it looks as if probability theory is really doing all ofthe normative work and hence that logic would seem to be little morethan a redundant tag-along. Second, one might try to downplay theimportance of degrees of belief in our cognitive economy. In itsstrongest form such a position amounts to a form of eliminativism orreduction in the opposite direction: against credences and in favor offull belief. Harman (1986), for instance, rejects the idea thatordinary agents operate with anything like credences. Harman does notdeny that beliefs may come in varying degrees of strength. However, hemaintains that this feature can be explained wholly in terms of fullbeliefs: either as belief in a proposition whose content isprobabilistic or else

as a kind of epiphenomenon resulting from the operation of rules ofrevision [e.g., you believe \(P\) to a higher degree than \(Q\) iff itis harder to stop believing \(P\) than to stop believing \(Q\)].(Harman 1986: 22)

More moderate positions accord both graded and categorical beliefsalong with their respective attendant norms a firm place in ourcognitive economies, either by seeking to give a unified account ofboth concepts (Foley 1993; Sturgeon 2008; Leitgeb 2013) or else byreconciling themselves to what Christensen (2004) calls a“bifurcation account”, i.e., the view that there is nounifying account to be had and hence that both types of belief andtheir attendant norms operate autonomously (Buchak 2014; Kaplan 1996;Maher 1993; Stalnaker 1984). Summarizing, then, so long, at least, asfull belief continues to occupy an ineliminable theoretical role to inour best theories, there still is a case to be made that it is tologic that we should continue to look in seeking to articulate thenorms governing these qualitative doxastic states.

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• [BFMS] Branden Fitelson, m.s.,Coherence, book manuscript.
• [MF2004] John MacFarlane, 2004, ““In What Sense (If Any) is Logic Normative for Thought?”, presented at the 2004 Central Division APA symposium on thenormativity of logic.
• John MacFarlane, 2017, m.s. “Is Logic a Normative Discipline?”, unpublished paper.

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