Far away there is a nation of people with a peculiar way of deciding what to believe. In this nation everyone carries around a pack of tarot cards, which children are taught from a young age on how to read. When people in this nation argue with each other, they consult their cards, and demonstrate the truth of their positions by showing how the cards support them, for the cards are the highest authority on such matters (even if sometimes there are disagreements over whether one has actually read the cards correctly). These people call this practice of consulting the cards “tarotive logic.”
One day, you encounter a person from this nation. Without knowledge of their peculiar customs, you get into a debate with them. (The topic does not matter.) Not noticing their consultation of the cards (the people of this nation are so adept at reading the cards that it often looks to outsiders like they are idly shuffling decks, perhaps as a nervous habit), you become increasingly perplexed by the arguments this person is making: they are full of contradictions, non sequiters, and so on. And this person is equally perplexed by the arguments you are making. Finally, the two of you try to determine the source of this mutual confusion, at which point you learn tarotive logic, and they1 learn of deductive logic. You remark on what a silly method reading tarot cards is. Offended by your cultural insensitivity, the tarot-reader retorts that it is your method that is bizarre: for example, why would anyone think that from “if p then q” and p you should be able to infer q?
* * *
The question of how we should go about accepting, modifying, or rejecting beliefs is of deep importance. It is fundamental to philosophy, of course, both in that there are areas of philosophy specifically concerned with it (some areas in philosophy of science, metaethics, etc., and of course epistemology) and in that the rest of philosophy is the systematic examination of beliefs. It is of practical importance, for what we believe determines how we act in the world and so, consequently, our well-being – although many if not most people can go through their entire life and attain success without ever thinking in any deep way about how they reason (indeed they are likely to do better than the philosopher). Where its practical importance really comes to the fore is in the realm of politics, for what we believe affects our relations with our fellows and our desires and actions on behalf of the group and of humanity. And for many it is important on a personal level, for such people have a deep desire to weed out error and inconsistency in their beliefs, and if possible learn something true about the world.
Yet one often finds disagreement on precisely this question of how to determine what to believe. Fallacious lines of reasoning carry powerful force, and are often viewed by many as being unproblematic. On the flip side, what rational person hasn't experienced the frustration of developing an airtight argument, only to have their argumentative partner reject it? Or to point out the blatant contradiction in someone's views, only to have that person simply not care? We say “given that you believe this, you must believe this” and they reply “why should I?” Psychological research has shown that people, even highly educated people, consistently reason in defective ways (Stich pp. 4-9): furthermore, their errors are systematic. And often the fiercest disagreements exist because there is not a clear agreement on how to reason, in cases as diverse as religion vs. atheism, philosophy of mind, diverse systems of logic, and of course the infamous “Science Wars”.
In this essay I will explore the question of how we can justify norms of reason. I will not be answering the question of what the norms of reason are or might be. I want to ask the more general question of how we could justify certain norms of reason whatever they may be. Being two levels removed from the question of what we should in fact believe, this will of course seem to be a rather abstract discussion, but despite its abstraction it is important. For even if we disagree in our beliefs, if we agree in the right way to work out what to believe, we can resolve our disagreement. If, however, we disagree in how to reason properly about the subject in dispute we are stuck.
It is a long-standing tradition that the possibility of a civilized society is predicated on rational argumentation. The rules of reason are the one guide to adjudicate disputes, saving us from mere rhetorical flourish, force of authority, or violence. The last two we are particularly concerned with, for reason is what gives us ammunition against bad authorities, whether they be people or our entire, mistaken, community, and with reason, we can avoid coming to blows. Winning an argument through rhetoric proves our verbal ingenuity, through authority or violence our strength; it is only through reason that we prove our rightness.
Definitions & Other Preliminaries
Before we begin, it is, as always, useful to explain how I will use my terms, as much as I can.
By “reasoning” I mean the cognitive activity of updating ones beliefs according to some intendedly normative style or method that takes as its inputs previously and currently held beliefs.2 While some may want to make a stronger claim that in order to be “reasoning” the style or method must be normative, for the purposes of this essay I want a weaker but broader concept that makes it possible to ask the question of someone's “reasoning”: “Is it normative?” My definition of reasoning includes the examples of “defective” reasoning one find in psychological research (Stich pp. 4-9); indeed, it is in line with the definition such research employs, although it is in some respects broader, as it also includes such bizarre practices as believing contradictions on Tuesdays (Goldman, p. 60) and consulting tarot cards, which psychologists (at least those studying reasoning, as opposed to delusions) are unlikely to show much interest in.
“Norms of reason” I will use to signify those styles in or methods by which one ought to reason3. They constitute what it is to reason correctly. For the purposes of this discussion one should not have in mind any particular reasoning practice (such as logical reasoning) as defining what is normative. After all, that reasoning practice might be the very one that is in question and that must be justified according the the criteria our investigation hopes to discover. The reader must instead think of the norms of reason in the abstract: the correct way of reasoning, whatever it may be.
These “norms of reason” are very similar to “J-Rules” as proposed by A. Goldman, specifically intrapersonal “J-Rules”4. Goldman views justification as being a matter of having beliefs that are permitted by right J-Rules. Goldman describes J-Rules as follows:
J-Rules would expressly permit [or prohibit] certain beliefs, or would present schemas for belief permission [or prohibition]. For example, a rule might permit belief in any proposition that has a certain type of relation to other propositions already believed. (p. 74)
This is so similar to my “norms of reason” that the reader may wonder why I did not choose to simply use Goldman's terminology. The reason is that I think “justification” may have a broader meaning than Goldman gives to it. I must think it has a broader meaning, since if all it meant was “forming beliefs in permitted by the right J-Rules” and “J-Rules” and “norms of reason” are the same (which I do think they are) then my stated project would be ask how one can justify the rules of justification, which is a clearly circular enterprise (as opposed to the only possibly circular enterprise that is justifying norms of reason). This broader conception of “justification” could include such things as warrant, agreement, etc.
“Reason”, used in isolation as a noun, can mean one of two things: a belief that grounds some process of reasoning, or as a shorthand term for norms of reason and also that faculty by which we reason in accordance with the norms. It is the second meaning that the reader should usually assume when I use the term.
The Justification of Reason Must Be Public
In this section I will give a sketch of the argument that we must appeal to intersubjective agreement in order to determine whether our reasoning practices are correct. That is, in order for us to be justified in considering our reasoning practices to be normative it is at least necessary that our peers recognize them as such: the justification of our reasoning practices must be public. The question will then be asked: do our peers recognize certain reasoning practices as normative because they are justified (according to some further criteria), or does our peers' recognition of our reasoning practices as normative exhaust their justification?
Despite the enormity of the conclusions I will draw from it, the argument that the justification of ones reasoning practices must be public is in part making a thoroughly common-sense point; namely, that we can make errors in our reasoning, and that in order to catch those errors we present our reasoning to others for criticism. If we are prudent we seek the opinions of a fairly large number of people (or a small number of people who are themselves widely trusted), and it's only if they agree that we have not made an error that we can be justifiably (as opposed to blindly) confident that we've gotten things right. Of course, there are various addenda that can be made; for example, it's generally considered justifiable for us to be confident in our reasoning, even without checking in with others, if we've already demonstrated skill in reasoning correctly. But, of course, it's to others that we must demonstrate this skill. If we consistently can't demonstrate the correctness of our reasonings to others we become nervous; as Richard Rorty says (in respect to beliefs):
We need the respect of our peers because we cannot trust our own beliefs, nor maintain our self-respect, unless we are fairly sure that our conversational interlocutors agree among themselves on such propositions as “He's not crazy,” “He's one of us,” “He may have strange beliefs on certain topics, but he's basically sound,” and so on. (“Universalism and Truth”, p. 15)
To put this all in another way and more succinctly: crazy people are as (if not more) certain that they're reasoning correctly as anyone. How then do we know that we aren't crazy? Because we've talked to other people (and we try to talk to a lot of them, so that we don't just end up talking to people as crazy as we might be) and they don't think we're crazy!5
Or, to shift the emphasis somewhat and put the point even more succinctly: if everyone (or most people) think you're wrong, you should probably reconsider your position.
So does the fact that we must justify our reasoning practices publicly mean that what justifies them just is agreement? Does the fact that in order to resolve doubts about the correctness of our reasoning practices we must appeal to others mean that the norms of reason are only those reasoning practices that are agreed upon – and that their being agreed upon exhausts their justification? For it may only be that we hope others will be better able to notice our errors – errors that are objectively errors. That is, there is some agreement independent standard for correct reasoning, but we simply cannot trust ourselves to independently recognize when we are or are not in accord with it, and so we appeal to the community, in the belief (hope?) that the perspective of others is likely to counteract our own errors. And does the fact that to reason correctly is to reason in the way we have learned mean that to reason correctly just is to reason in the way we have learned – the way, once again, that is agreed on? After all, one must learn to do all sorts of things correctly, such as operating a piece of machinery. Yet certainly the correct way to operate a piece of machinery is not something that is merely agreed upon: if one gets it wrong, the machine will not work (and someone may lose some important limb)!
What we have here really is an example of a Euthyphro-type dilemma. Are certain reasoning practices normative because our community endorses them, or does our community endorse them because they are normative? If our community endorses them because they are normative then there should be some further justification for them. It is the search for such a justification that will occupy the next section, up until we do consider the view that consensus is all there is.
As stated in “Definitions” my norms of reason are very similar to Goldman's J-Rules. This is useful at this moment because Goldman provides a list of possible criteria for the correctness of J-Rules, which helps us get a lay of the land for possible justifications of the norms of reason. Goldman's list (adapted for the norms of reason) is as follows:
(C1) The norms of reason are a system of rules derivable from logic (and probability theory).
(C1*) The norms of reason are a system of rules that would be chosen by someone who believes all truths about logic (and probability theory), but is ignorant of all contingent facts.
(C2) The norms of reason are those accepted by players of one's language game.
(C2*) The norms of reason are those accepted by members of one's disciplinary matrix (ala Kuhn)
(C2**) The norms of reason are those accepted by one's peers.
(C3) Conformity with the norms of reason would guarantee a coherent set of beliefs.
(C4) The norms of reason permit doxastic attitudes proportional to the strength of one's evidence.
(C5) Conformity with the norms of reason would maximize the total number of true beliefs a cognizer would obtain. (p. 66)
This is a nice list, but let us make it nicer. First, (C1) and (C1*). While these options make sense in regards to justification, they are circular for the norms of reason: logic and probability theory, insofar as they are meaningful, are reasoning practices. However, this suggests the option that the norms of reason are self-evidently correct. There are two ways that “self-evidence” can be meant. One is that the norms of reason are given (perhaps by God or the order of nature), and we have some sort of access to them: they can be seen to be correct (although maybe not by everybody). The second is that the norms of reason are analytically correct, that is, are correct in virtue of the meaning of certain terms, such as the logical operators and the term “reason” itself. I will call these two families of justifications “Intuitionist” and “Analytic”.
(C2), (C2*), and (C2**) all say roughly the same thing (hence Goldman calls them all “C2”), which is that the norms of reason are those accepted according to the standards of some community. I will call this family of justifications “Cultural”.
(C3) begs the question: coherent by what standards? Presumably, by the standards of some norms of reason: that is, the beliefs are coherent because they follow from (or at least do not contradict) each other according to some rules about how one is allowed to get from one belief to another. Either these norms of reason are external to the cognizer, in which case they need some other justification, or they are internal to the cognizer, in which case anyone's reasoning practices could be justified, since they lead to coherence according to their own standards. I do not want to forget the notion of coherence though, as it will play an important role in the discussion of analytic justifications.
(C4) again begs the question: proportioned to the evidence according to what standard? Why, some norm of reason. (I also do not see how this option is different from the “probability theory” referenced in (C1).)
(C5) Is reliabilism, which is a variety of what I (and Goldman) call “Consequentialism”. The other variety (which is curiously absent from Goldman's list, although he does discuss it elsewhere) is pragmatism. So I group reliabilist and pragmatic justifications in the “Consequentialist” family.
Finally, there are justifications that appeal to the notion of “Reflective Equilibrium”. Stich spends much time on these types of justifications. In reflective equilibrium, our reasoning practices are justified by being the outcome of balancing our intuitions and the rules that follow from them. From N. Goodman's Fact, Fiction, and Forecast:
...rules and particular inferences alike are justified by being brought into agreement with each other. A rule is amended if it yields and inference we are unwilling to accept; an inference is rejective if it violates a rule we are unwilling to amend.The process of justification [of the norms of reason6] is the delicate one of making mutual adjustments between rules and accepted inferences; and in the agreement achieved lies the only justification needed for either. (p. 66)
This is different from intuitionist justifications in that, in intuitionist justifications, the norms of reason are given to us by intuition: in reflective equilibrium, they are the outcome of this process of balancing.
Potential ultimate justifications of the norms of reason, then, can be divided into five major categories:
- Analytic: the norms of reason are what they are by virtue of definitions/meaning.
- Intuitionist: the norms of reason can be “seen” to be correct (they are self-evident or Platonic).
- Reflective Equilibrium: the norms of reason are the result of achieving a balance between our intuitions and posited rules.
- Consequentialist: the norms of reason are those reasoning practices that tend to produce beliefs with some sort of valuable quality (truth, pragmatic utility, etc.).
- Cultural: the norms of reason are those norms accepted/endorsed/declared by some community.
In this essay I will focus on three of these options: Analytic, Consequentialist, and Cultural. While I do this primarily for interest of space, I also think these are the three most viable options. While the intuitionist option is often appealed to in interactions (“Of course it's correct, just look at it!”), and is endorsed by some of history's most venerable philosophers, I think it is plain to see7 that it will not resolve any disagreements. Reflective equilibrium (which I do think plays some role in justification, just not any ultimate one) faces similar issues, and also shares many of the problems that analytic justifications will be shown to have. The greatest difficulty that it faces is that there is no guarantee that intuitions and rules will balance in the same way for different people.8
Analytic justifications of the norms of reason are those that take the norms to be justified by the meaning of various terms. The terms in question can range from reasoning terms (“and”, “or”, “if-then”, “implies”, etc.) to terms such as “justification” and “reason” themselves. I shall deal first with the analyticity of the norms as a system, that is, the idea that the norms of reason define what it is to reason correctly. Then I shall move on to the analyticity of rules of inferences, that is, the view the inferences the norms of reason allow are allowed because the are correct by virtue of the terms used. This discussion will not remain pure: considerations of systems will inevitably sneak back in. Finally I will make some passing remarks on issues of interpretation of alternative reasoning practices. In all of this discussion the focus will be on inductive and deductive logic, both because these provide the clearest examples of how analytic justifications are supposed to work and because they are the foundation of reasoning in general.
The Analyticity of the Norms as a System
The general sentiment behind analytic justifications is expressed nicely in P. F. Strawson's Introduction to Logical Theory, in regards to inductive and deductive procedures:
There is...a residual philosophical question which enters so largely into discussion of the subject that it must be discussed...What reason have we to place reliance on inductive procedures?...If someone asked what grounds there were for supposing that deductive reasoning was valid, we might answer that there were in fact no grounds for supposing that deductive reasoning was always valid; sometimes people made valid inferences, and sometimes they were guilty of logical fallacies. If he [sic] said that we had misunderstood his question, and that what he wanted to know was what grounds there were for regarding deduction in general as a valid method of argument, we should have to answer that his question was without sense, for to say that an argument, or a form or method of argument, was valid or invalid would imply that it was deductive; the concepts of validity and invalidity had application only to individual deductive arguments or forms of deductive argument. Similarly, if a man asked what grounds there were for thinking it reasonable to hold beliefs arrived at inductively, one might at first answer that there were good and bad inductive arguments, that sometimes it was reasonable to hold a belief arrived at inductively and sometimes it was not. If he, too, said his question had been misunderstood, that he wanted to know whether induction in general was a reasonable method of inference, then we might well think his question senseless in the same way as the question whether deduction is in general valid; for to call a particular belief reasonable or unreasonable is to apply inductive standards, just as to call a particular argument valid or invalid is to apply deductive standards...(pp. 248-249)
Let us...show that the demand for a justification [of induction] is mistaken...Sometimes it is expressed in the form of a request for proof that induction is a reasonable or rational procedure, that we had good grounds for placing reliance upon it. Consider the uses of the phrases 'good grounds', 'justification', 'reasonable', &c. Often we say such things as 'He has every justification for believing that p'; 'I have very good reasons for believing it'; 'There are good grounds for the view that q'; 'There is good evidence that r'. We often talk, in such ways as these, of justification, good grounds or reasons or evidence for certain beliefs. Suppose such a belief such a belief were one expressible in the form 'Every case of f is a case of g'; I think it would be felt to be a satisfactory answer if he replied: 'Well, in all my wide and varied experience I've come across innumerable cases of f and never a case of f which wasn't a case of g.' In saying this, he is clearly claiming to have inductive support, inductive evidence, of a certain kind, for his belief, and he is also giving a perfectly proper answer to the question, what he meant by saying that he had ample justification, good grounds, good reasons for his belief. It is a analytic [my emphasis] proposition that it is reasonable to have a degree of belief in a statement which is proportional to the strength of the evidence in its favour; and it is an analytic proposition...that...the evidence for a generalization is strong in proportion as the number of favourable instances, and the variety of circumstances in which they have been found, is great. So to ask whether it is reasonable to place reliance on inductive procedures is like asking whether it is reasonable to proportion the degree of one's convictions to the strength of the evidence. Doing this is what 'being reasonable' means in such a context.
As for the other form in which the doubt may be expressed, viz., 'Is induction a justified, or justifiable, procedure?', it emerges in a still less favourable light. No sense has been given to it, though it is easy to see why it seems to have a sense. For it is generally proper to inquire of a particular belief, whether its adoption is justified; and, in asking this, we are asking whether there is good, bad, or any, evidence for it. In applying or withholding the epithets 'justified', 'well founded', &c., in the case of specific beliefs, we are appealing to, and applying, inductive standards. But to what standards are we appealing when we ask whether the application of inductive standards is justified or well grounded? If we cannot answer, then no sense has been given to the question. Compare it with the question: Is the law legal? It makes perfectly good sense to inquire of a particular action, of an administrative regulation, or even, in the case of some states, of a particular enactment of the legislature, whether or not it is legal. The question is answered by an appeal to a legal system, by the application of a set of legal...rules or standards. But it makes no sense to inquire in general whether the law of the land, the legal system as a whole, is or is not legal. (pp. 256-257)
Strawson's comments about the legality of the law help us make the essential distinction between intuitionist (the norms of reason are “given”) and analytic justifications (even if that is not his main intention). The statement “the law is legal because it defines what it means for something to be legal” says nothing about whether the law is given to us, saw by God or the natural order. Similarly to say that “the norms of reason are justified because they define what it means for anything to be justified” says nothing about whether those norms are given: indeed, it is not only irrelevant why the norms are what they are – the question of why they are what they are is meaningless, insofar as that question seeks a reason. The analogy of the legality of the law is also interesting because of a more direct connection with the question of the analyticity of the norms of reason. While it is meaningless to ask whether the law is legal, it is meaningful to ask whether it is right. This question will appeal to higher standards than legality: moral rightness, etc. The rightness of these standards can then be defended by appealing to still higher standards, and so on and so forth. But when we reach the question of the rightness of standards of reason there are no higher standards to appeal to (as the higher standards we might hope to appeal to would be appealed to as reasons), and all we can hope for is a loop, according to the analytic defense. As H. Feigl says: “Many analytic philosophers...consider the quest for a justification of induction as a pseudo problem because, in their view, this quest comes down to asking 'is it reasonable to be reasonable?” (1961, p. 212)
Another way to describe the point of analytic justifications is that they claim that “one should believe in accordance with the norms of reason because it is the reasonable thing to do” is, while circular, not viciously so. As H. Siegel says (describing the position of Rescher):
[A] rational defense of rationality is not question begging or viciously circular; it merely acknowledges, as any serious questioner must, that seriously asking 'Why be rational?' presupposed a commitment to rationality, i.e. to deciding the question on the basis of the best available reasons. Thus the presumption of rationality...does not beg the question against the sceptic, but rather presupposes that which the sceptic, and indeed any serious inquiry into the question 'Why be rational?', must presuppose: that the question must be settled on the basis of reasons if it is to be properly settled, and therefore that all parties to the debate must presume the potential force of reasons. (p. 28)
To some extent, I think this analytic defense of the norms of reason is right, but it only takes us so far. The issue is that analyticity, in this broad sense, does not discriminate between reasoning practices. The tarot-readers from the introduction should be quite happy with the Siegel/Rescher argument exactly as it stands. “Yes,” one can imagine such a person saying, “the question whether one should be rational 'must be settled on the basis of reasons and therefore all parties to the debate must presume the potential force of reasons', exactly as Siegel says. So, you see, if one is going to have any sort of debate about what the norms of reason are at all one must accept that reading tarot cards works!” One could also imagine these people formulating an argument in support of tarot cards similar to Strawson's argument in support of induction, although this flight of fancy is more difficult. For example, are we to allow the tarot-readers to say “that an argument, or a form or method of argument, is valid or invalid implies that it is tarotive; the concepts of validity and invalidity have application only to individual tarotive arguments or to 'forms'9 of tarotive arguments”? We might very well not, instead telling the tarot-card readers that they have misunderstood the meaning of “valid”: for an argument to be valid just is for it to have the right deductive form. But it it easy to see how this could be turned around: the tarot-readers simply reply that, in fact, we are the ones who misunderstand the meaning of “valid”!
At this point we would probably go back and forth a bit, haggling over the correct meaning of “valid”, until someone pointed out that what was at issue is that our two communities have different definitions of “valid”. In fact, the source of the disagreement is that the same word is being used to mean two different things: we are using it to mean “having the right deductive form” while they are using it to mean “having the right tarotive form.” All that needs to be done is to come up with two different words, so that it is clear that there is no disagreement. “Valid” we will keep for deductive correctness: tarotive correctness will be given the name “valit”. But while this does expose our disagreement as merely verbal, it also exposes the deeper disagreement that is not verbal: why should we prefer valid arguments of valit ones? One answer may be that valid arguments are truth preserving, while valit arguments are not (one could imagine that in tarotive logic the true statement “The cards say p” implies p, but p is false). But this merely shows a lack of imagination on our part: perhaps the tarot-readers have a conception of truth (or “truth”) that does make tarotive arguments truth-preserving. Perhaps, for example, “truth” is whatever the cards say. (One thinks of religious fundamentalists who take “truth” to be “whatever my holy text says”, and can therefore refuse to acknowledge “facts” that contradict the holy text.) What we find is that the answer as to whether we should prefer vailidity or valitity depends on whether we want to be classical logicians or tarot-card readers: and any further attempts at justifying this choice can no longer be analytic, but will instead be reliabilist, pragmatic, etc.
The Analyticity of Inferences
We have covered the view that the norms of reason are analytic because as a system they define what “reason” is. Now let us look at the possibility that it is the rules of inference allowed by the norms that are analytic, correct by virtue of the meaning of the terms used. For simplicity, I will consider the analytic validity of of deductive inferences employing logical connectives: if analytic justifications fail here, it is hard, if not impossible, to see where else they could succeed.
Let us begin with A. N. Prior's wonderful paper “ Runabout Inference-Ticket”:
It is sometimes alleged that there are inferences whose validity arises solely from the meanings of certain expressions occurring in them. The precise technicalities employed are not important, but let us say that such inferences,if any such there be, are analytically valid. One sort of inference which is sometimes said to be in this sense analytically valid is the passage from a conjunction to either of its conjuncts, e.g., the inference 'Grass is green and the sky is blue, therefore grass is green'. The validity of this inference is said to arise solely from the meaning of the word 'and'. For if we are asked what is the meaning of the word 'and'...the answer is said to be completely given by saying that (i) from any pair of statements P and Q we can infer the statement formed by joining P to Q by 'and' (which statement we hereafter describe as 'the statementP-and-Q'), that (ii) from any conjunctives tatement P-and-Q we can infer P, and (iii) from P-and-Q we can always infer Q. Anyone who has learnt to perform these inferences knows the meaning of 'and', for there is simply nothing more to knowing the meaning of 'and' than being able to perform these inferences.
A doubt might be raised as to whether it is really the case that, for any pair of statements P and Q, there is always a statement R such that given P and given Q we can infer R, and given R we can inferP and can also inferQ. But on the view we are considering such a doubt is quite misplaced, once we have introduced a word, say the word 'and ', precisely in order to form a statement R with these properties from any pair of statements P and Q. The doubt reflects the old superstitious view that an expression must have some independently determined meaning before we can discover whether inferences involving it are valid or invalid. With analytically valid inferences this just isn't so. (p. 38)
So far so good. The meaning of “and” is defined by the inferences it allows, and this is true of the logical connectives in general: therefore, what it is reason correctly just is to make those inferences that define the the terms. The question “why, from P and Q, should I infer Q?” is silly in exactly the way that “why are all bachelors unmarried men?” is silly.
But problems arise:
I want now to draw attention to a point not generally noticed, namely that in this sense of 'analytically valid' any statement whatever may be inferred, in an analytically valid way, from any other. '2 and 2 are 5', for instance, from '2 and 2 are 4'. It is done in two steps, thus:
2 and 2 are4.
Therefore, 2 and 2 are 4 tonk 2 and 2 are 5.
Therefore, 2 and 2 are 5.
There may well be readers who have not previously encountered this conjunction 'tonk', it being a comparatively recent addition to the language; but it is the simplest matter in the world to explain what it means. Its meaning is completely given by the rules that (i) from any statement P we can infer any statement formed by joining P to any statement Q by 'tonk' (which compound statement we hereafter describe as 'the statementP-tonk-Q'), and that (ii) from any 'contonktive' statement P-tonk-Q we can infer the contained statement Q. A doubt might be raised as to whether it is really the case that, for any pair of statements P and Q, there is always a statement R such that given P we can infer R, and given R we can infer Q. But this doubt is of course quite misplaced, now that we have introduced the word 'tonk' precisely in order to form a statement R with these properties from any pair of statements P and Q. (pp. 38-39)
As Prior notes, “tonk” is quite useful, for in allowing us to infer any statement from any other, it “promises to banish falsch Spitzfindigkeit from Logic for ever [sic].” (p. 39)
Of course, Prior's paper is a lovely demonstration of philosophical sarcasm, and we certainly do not want to be able to infer any statement from any other. But on the face of it there is nothing wrong with the definition of “tonk”: it is defined, after all, in exactly the same sort of way as “and”. And so we can imagine, on telling someone that they have made an incorrect inference, them replying “not at all. I'm simply a fan of the 'tonk' connective, and so I can infer whatever I want.”
Although Prior states his point as being about analytic definitions of the meaning of logical terms his target can be more accurately described as syntactic definitions of logical terms. As such, there are two possible responses to Prior. One is to attempt to find syntactic considerations that would exclude “tonk”. The other is to defend a semantic notion of the logical connectives, that is, the notion that they are defined by their truth tables, and the inferences that follow from them follow because of the truth tables.
The syntactic move is endorsed by Belnap. It goes as follows:
It seems to me that the key to a solution lies in observing that even on the syhnthetic view, we are not definiting our connective ab intitio, but rather in terms of an antecedently given context of deducibility, concerning which we have some definite notions. By that I mean that before arriving at the the problem of characterizing connectives, we have already made some assumptions about the nature of deducibility. That this is so can be seen immediately by observing Prior's use of the transitivity of deducibility in order to secure his ingenious result.But if we not that we already have some assumptions about the context of deducibility within which we are operating, it becomes apparent that by a too careless use of definitions, it is possible to create a situation in which we are forced to say things inconsistent with those assumptions. (p. 131)
But as Belnap himself says, this only works if we assume a certain context of deducibility, certain basic presumptions about how it operates. As Haack points out systems that employ odd connectives (in her case a peculiar sort of material conditional) “can hardly be assumed to be otherwise conventional.” (p. 117)
The semantic move is the one endorsed by Stevenson. One can see that this would exclude “tonk” since “tonk” has no truth table that would allow one to make semantically valid inferences: “P-tonk-Q” is true whenever “P” is true, but has no truth value when “P” is false (and I mean no truth value: it is not “true and false”, “neither true or false”, or even “uncertain”, unless it is one of these by stipulation). Semantic definitions also have the advantage of showing why deductively valid arguments are truth-preserving: of course p is going to be true whenever “p and q” is true, because “x and y” is defined as being true only when x and y have the same truth value and that truth value is “true”. This is an analytic justification par excellence. And it would be incapable of resolving disputes over what the correct way to reason is. One can imagine someone saying the following: “certainly, if you define 'and' the way you have, then the argument 'p and q implies p' is truth preserving. But I am suspicious of your definition of 'and': can you please demonstrate to me that 'p and q' is in fact (by 'in fact' I mean 'independent of your definitions') true whenever p is true and q is true?” Of course, this request is silly: there is no “fact of the matter”, independent of our definition, as to whether “p and q” is true whenever p is true and q is true. But this means that if someone disagreed with our definition there would be nothing we could appeal to to defend it. The case is analogous to the dispute between the deductive and tarotive reasoners in regards to “valid/t”.
This can be hard to see in the case of “and”, which seems to have a pretty clear-cut truth table. Let us then turn to a more tangible disagreement: the dispute over the meaning of the conditional, that is, “if-then” statements. Conditionals are at the core of deductive logic, as any logical inference can be translated into a conditional, where the inference is valid iff the conditional is tautological: for example, the inference
p and q
which is valid, can be translated as
if (p and q) then q
which is tautological, and the inference
p or q
which is invalid, can be translated as
if (p or q) then q
which is not tautological. Yet there is disagreement over what “if-then” means (Priest, p. 12). In classical logic “if p then q” is interpreted as “not-p or q”. This means that “if p then q” is true in all cases except where p is true and q is false. At first glance this seems to capture what “if-then” means. Yet it may strike some as odd that “if p then q” is true if it just happens to be the case that, say, both p and q are true, and even odder still that it is true if p and q are both false. These facts lead to such seemingly strange truths as “If snow is white then 1+1=2” and “If unicorns exist then dragons also exist.”10 There are various responses to these “paradoxes of implication”, making reference to conversational norms, etc. One can also make distinctions between material conditionals and subjunctive/counterfactual conditionals, and point out that in these examples that distinction is being ignored (for example, when we say “If unicorns exist then dragons also exist” we actually mean “If unicorns did exist then dragons would also exist”) - although we then run into the problem that we cannot figure out the logic of subjunctive and counterfactual conditionals.11 But what justified making this distinction, beyond ad hoc considerations of wanting to preserve “not-p or q” as the correct analysis of “if p then q”? Furthermore, there are other examples which are more troublesome, for example, “if (p and q) then r” implies that “(if p then r) or (if q then r)”. This means that the following inference (from Priest) should be valid:
If you close switch x and switch y the light will go on. Hence, it is the case either that if you close switch x the light will go on, or that if you close switch y the light will go on. (p. 14)
As stated in English this argument seems blatantly invalid, as there is a situation in which the premise would be true and the conclusion false: the light only turns on when you close both switches.
These concerns, along with concerns about contradictions, vague truth values, and so on, have led to the proliferation of “alternative” logics (as described in Priest). I will not describe this work, and the arguments for and against classical logic, in detail: the point is that the work, and the dispute, exists. There is disagreement over the way that logic should operate.12 Furthermore, these alternative logics are internally consistent. As such, analytic considerations cannot choose between them. Something else must be doing the work: reliability, pragmatic considerations, consensus, etc.
However, it is important to note that the analytic defense of one's norms of reason is not exactly wrong. There is an important sense in which my reasoning practices are analytic, for the reasons given by those such as Strawson and Siegel and for another reason given below.
A Remark on Interpretation: Are Different Reasoning Practices Actually Different?
Let us reconsider the cases where we and the tarot-readers disagree about the meaning of “valid”, or where someone understands “if-then” in a peculiar way. In such situations is it actually the case the the other people are reasoning differently? After all, is it not the case what is at issue is a misunderstanding, which is cleared up by figuring out in one's own terms how the other is using their terms? But this does not indicate substantial disagreement any more than the fact that a certain sound might mean one thing in English and something else in another language indicates substantial disagreement. It seems possible that what is at issue is not that the the other people are reasoning differently from us in any substantial way but that they are just using different terminology.
For example, suppose that someone thought the inference from “if p then q” and q to p was valid. It is possible that what is at issue is that they understand by “if p then q” what we would understand by “if q then p”, or perhaps “p iff q” if this person also still thinks modus ponens is valid. Of course, with this new understanding of “if-then” other inferences employing it would no longer be valid, and if this person thought they were valid, we would have a real problem.
Or would we? For we could interpret their usage of the other symbols in the system. We could even decide that “inference”, “validity”, and so on, have different meanings for the other person than they do for us (think of the tarot readers). We could then seek interpretations for these terms. And so we show that, “properly” interpreted, our fellow's deductive practice is actually perfectly in line with our own. So, if we want to, we can find some interpretation where someone who is reasoning oddly is in fact reasoning the same way we would, just with an idiosyncratic understanding of the terms employed.
Why would we want to do this? Because (given a certain theory of intentional attribution) the intentional content a cognitive states is characterized by its relationship to other cognitive states. As such, in order to attribute intentional states to someone at all we must assume that their cognitive states “hold together” to some degree.13 And cognitive states “hold together” through inference, that is, by following and/or not contradicting each other. (Hence my request that we not forget the notion of coherence.) This point – that intentional attribution requires that we interpret our subject's reasoning so it comes out somewhat, mostly, or even completely correct - is suggested by Quine (pp. 58-59) and developed more fully by Davidson (p. 324), Dennett (p. 73), and Stich (pp. 29-54) (although Stich then argues against it), among others.
The other, more direct reason is that the meaning of terms used in reasoning are (perhaps completely) a function of the role they play in inference. In fact, this is the same reason as above: to call what our subject believes “if p then q” or characterize what they are doing as “inferring”, for example, we have to be able to interpret their beliefs and reasoning practices as being in line with our own.
One important thing to note is the Quine, Davidson, and Dennett do not express this point in the same subjectivist way I have, where what is important is interpreting the reasoning practices of others according to our own standards. They instead seem to assume the rules of logic as basically given. I do not make that assumption, and as such, the only option left to me is the position that we interpret the reasoning practices of others according to our own standards. Of course, this goes both ways: insofar as the people who are reasoning oddly can understand what we are up to they can interpret our reasoning practices according to their standards. The point of all this, then, is that insofar as we can recognize what someone is doing as “reasoning” and “having beliefs” it is in principle possible for us to find a way to interpret what their reasoning practices as to so degree similar to our own. I cannot of course endorse the more radical position that their reasoning can be interpreted as flawless by our own standards, for then the entire project of this essay would no longer make any sense! So instead I will make the less impressive point that insofar as we can judge another's reasoning practices as being different from our own we must be able to interpret some aspect of their reasoning practices as being the same, for without that anchor of similarity we cannot compare their reasoning practices with our own at all. More generally, the sort of relativism that says that we cannot even understand viewpoints different from ours is wrong, for if we cannot understand someone we cannot identify what they “have” as a viewpoint. (Putnam 1981, pp. 114-119)
Consequentialist justifications of the norms of reason are those that say that certain reasoning practices are justified by their tendency to produce beliefs with some sort of valuable quality.14 The word “tendency” here is important: it is not typically justification if one reasons in some idiosyncratic way that just so happens to lead to valued type of beliefs in some situation (although in the case of pragmatism this is not so clear). Conversely, the norms of reason aren't expected to always lead to the right kind of beliefs: there may (indeed there are expected to) be situations in which they fail.
The most common proposed values, and the ones I will focus on here, are truth (reliabilist) and pragmatic utility (pragmatic). Of course, these are not the only possible values: perhaps, for example, the norms of reason are justified by their tendency to produce beliefs that give one a warm fuzzy feeling, or beliefs with explanatory power. I do think most of these possible values other than truth are actually varieties of pragmatic utility, but I will not discuss this issue in any sort of detail.
There is also the possible view that the norms are intrinsically valuable: following them is a good in and of itself, regardless of the nature of the beliefs that are produced. It is hard, though, to see exactly what this would mean. It is distinct from saying that they are intrinsically justified, as would be the case if they are, e.g., self-evident or analytic. The difficulty is that the norms of reason give us practices and methods, which cannot be intrinsically valuable in the sense that their existence is valuable. They must be valuable for some person(s) following them. For example, following them makes us feel good (no matter what the consequences). Or perhaps they are somehow beautiful. When divorced from self-evidence or analyticity and considered as being itself a justification of the norms, this strikes me as a complete dead-end.
Before we move on, a note on the connections between reliabilist and pragmatic justifications. The reliabilist and pragmatic justifications are often thought to go hand-in-hand: truth is thought to be pragmatically useful. This can go three ways:
- it is valuable to believe what is pragmatically useful, and it is pragmatically useful to believe truth
- it is valuable to believe what is true, which is additionally pragmatically useful
- “truth” is pragmatic utility.
It is important to note that in the first two of these options either truth or utility is the ultimate goal: in the first option, believing truth is a means to believing what is useful, and in the second, pragmatic utility is a happy (perhaps necessary) byproduct of believing truth. (There is also the option that the norms of reason are those that produce beliefs that are true and useful, or true or useful (where truth and usefulness are independent of each other) – options that, while intriguing, do not seem to have been much explored, and will continue to go unexplored in this essay (seeing as how I reject both reliabilism and pragmatism considered independently).
Ask a non-philosopher to justify their reasoning practices and, after you have convinced them that this is not a silly question, you will probably get a reliabilist response. Ask a scientist why they trust the scientific method, and they will tell you that it is because it gives us our best chance at figuring out how things actually work. Ask a Christian why they seek answers from the Bible, and they will tell you that it is because it is the true word of God. When people propose revisions in our reasoning practices the justification is usually that such revisions will help us better determine the truth. One can also find reliabilism underneath the surface of much philosophy: skepticism about our methods of inquiry, after all, only makes sense if one is concerned that they do not actually lead us to truth. Reliabilism is deeply embedded in our intuitions about justification and reason. Yet while reliability may be used to justify reasoning practices, it fails as an ultimate justification of the norms of reason. In this section I will argue for why that is the case.
For my reliabilist account I turn to Alvin I. Goldman's Epistemology and Cognition. Many of Goldman's criticisms of alternative views will be discussed in the context of those views. For now, let us focus on his positive proposal. This proposal is given in its final form on page 106:
A J-Rule (justificatory rule) system R is right if and only if....[they] would result in a truth ratio of beliefs that meets some specified high threshold.
J-Rules, we should remember, are the rules that permit and prohibit certain types of beliefs given other types of beliefs. Goldman also adds that in order for someone's beliefs to be justified the J-Rule system they employ must have secondary justification, that is itself be the result of a reliable process.
Goldman believes that this proposal best captures our intuitions about what it is for a belief to be justified. This proposal is focused on what makes a J-Rule system right: my concern is with how norms of reason are justified. Therefore I adapt his proposal, giving the following:
The norms of reason are justified if and only if they would result in a truth ratio of beliefs that meets some specified high threshold.
It is important to note that Goldman's reliabilism is not intended as a justification of a J-Rule, but a criteria for what makes a J-Rule system right. Goldman is very careful to exclude epistemological terms from this rightness criteria, to avoid circularity. Of course, one can wonder what exactly “right” means if it does not mean “justified”; it is odd if it means “true” (perhaps a J-Rule system can be “true” in the sense that the statements of permission and prohibition it makes are “true”, a.k.a. “It is true that you are permitted to form a belief in a scientific theory if that theory is endorsed by a respected scientist”, but this raises a whole set of meta-ethical worries). I will not concern myself with this question, as I am adapting Goldman's discussion for my own purposes, which are epistemological all the way down: I want to know how we can justify our norms of reason. This does mean that some of the objections I raise against my adaptation of Goldman's reliabilism may not hold against Goldman's reliabilism as he expresses it (although I think for the most part my objections do hold for the latter).
It is also worthwhile to note that I am not concerned with what the ratio of true beliefs should be. In fact, it does not matter much to my discussion whether the ratio is particularly high or even if the threshold is exact and/or definite. The main point is the claim that the norms of reason are justified by their ability to produce truths and avoid falsehoods.
So we have the position that the norms of reason are justified if following them produces some high ratio of true beliefs. As Stich (p. 94) points out, the difficulty with this position is that it leaves open the question of which world(s) our reasoning15 should lead to truth in. The obvious option is that they should lead to a high ratio of truth in the actual world, or the world in which the cognizer is operating.16 But this option quickly runs into difficulties. What if the world is being run by a Cartesian demon intent on deceiving us as to reality's actual nature? (Goldman, p. 110) One can imagine all sorts of ways our demon does this. Perhaps, for example, the demon systematically provides us with perceptual information that, were we to follow the customary reasoning practices, would lead us to beliefs that are the negative of whatever is actually the case. If this is the world we live in, then the norms of reason would be to believe the negation of whatever we would be led to believe by following the customary reasoning practices. This is just an example: there are all sorts of ways the demon could be distorting reality, each justifying more or less bizarre reasoning practices. This demon could even prevent any reasoning practice(s) from being reliable, by arranging things such that any particular practice that we might choose would lead us to truth in one and only one (perhaps randomly determined) situation. For all we know, any of these descriptions is the way our world actually is: as such, we have no way of knowing whether any reasoning practice is justified! Of course, a skeptic may be quite happy with this conclusion, but most people are not. If nothing else, what these considerations show is that even if reliability in the actual world “justifies” norms of reason in some sense we do not have access to this justification. And as I have stated my concern is with how we can justify the norms of reason.
These problems arise when we tie the justification of reason to what is reliable in the in the actual world, as the actual world may not work the way we think it does (there may actually be a Cartesian demon). What about possible worlds? Of course, requiring our reasoning practices to be justified across all possible worlds is a non-starter: there are all sorts of bizarre ways that a world might work, with all sorts of bizarre reasoning practices being consequently justified within it. Even if we take “reliable across possible worlds” to mean “leading to a large proportion of true beliefs in all possible worlds considered as a whole” - that is, leads to a high ratio of true beliefs in a high ratio of possible worlds – we still run into problems, because of the simple fact that the number of possible worlds, and the number of possible worlds that work in any particular way, is indeterminate.
Instead, what we could try to do is to link the justification of reasoning practices to their reliability in worlds that work in some sort of particular way, specifically, in roughly the basic way we presume the world to work. Then, we would have solutions to our problems: Cartesian demons are out of the picture. I will spend a lot of time on this proposal, as, despite the fact that it does not work, I do think that if it did work it would best capture our intuitions in regards to justification, since it would allow us to avoid universal skepticism.
Goldman calls those worlds that work in roughly the basic way we presume our world to work “normal worlds” (p. 108-109). As Goldman admits, the normality of a world is quite a vague predicate, but that is not my major concern. My concern is with the fact that the normality of worlds is linked with the way we presume our world to work. This sounds subjectivist, which the reliabilist account was not supposed to be. Goldman argues that it is not subjectivist, as it is still an objective fact as to whether some reasoning practice is reliable in these normal worlds. I will grant that the reliability of some reasoning practice is objective in this sense. But still, a normal world is defined as a world which operates according to the the fundamental physical regularities we presume, and these presumptions are subjective. Indeed, they may be different from person to person. Whose presumptions define normal worlds? As Stich (p. 95) points out, there are many ways we could choose to characterize what makes a world normal, each of which would lead us to decide on a different reasoning practice as being reliable, and as he points out, there is no prima facie reason to prefer one characterization to another. Different people are going to have all sorts of different presumptions about the way the world works: one assumes that what we are looking for is the right set of presumptions. Right, according to what?17 Not the way the world actually works: then we just have actual-world reliabilism, with all its problems. The way reason tells us the world works? But then we have a circularity.18
In fact, I think Goldman's characterization of normal-worlds reliabilism does lead to circularity, particularly if one assumes that we can change (in a reasoned way) our presumptions about the way the world works.
According to Goldman, “the fundamental world regularities that define the class of normal worlds [do not] extend to properties of our cognitive processes,” and because of this “what we believe about our cognitive processes in the actual world need not hold in (all) normal worlds...[the] proposal does not imply that the processes believed to be reliable (in the actual world) are reliable in normal worlds.” (p. 108) I will grant that the correctness of our reasoning practices may not be one of the “fundamental physical regularities” that we presume about normal worlds. But why do we presume this set of fundamental physical regularities? Because they are the ones described by our current science (or whatever corpus of “knowledge” one puts ones faith in – religion, etc.)? But science is a reasoning practice, and we discovered these fundamental physical regularities by engaging in it! More generally, our presumptions about what the fundamental physical regularities are are going to be the outcome of some reasoning practice. One senses that we are at the cusp of a circularity: the correctness of our reasoning practices are determined by the way that we presume the world to work, but the way we presume to world to work is the outcome of our reasoning practices. The situation becomes even worse if we note (as above) that normal worlds are to be those that accord with not just any presumptions, but the right presumptions.
Can we tighten this circularity further, so that our belief that our reasoning practices are correct justifies them, and all it takes for our reasoning practices to be normative is for us to believe they are? I think we can. This is where I bring in the principle that we want to be able to change our presumptions in a reasoned way. Yet in Goldman's normal worlds the fundamental physical regularities of normal worlds match whatever our current19 presumptions are about the such regularities. As such, it is always unreasonable to change our presumptions about the way the world fundamentally works, as our current presumptions define what makes a normal world and reliability in normal worlds determines the norms of reason. How then do we make it possible to discover new fundamental physical regularities? By presuming (pace Goldman) the correctness of our reasoning practices as a still more basic fact than those regularities. But then normal worlds are those worlds in which the reasoning practices we assume to be normative are normative. Therefore if our reasoning practices are justified by being reliable in normal worlds, then our reasoning practices are justified by our assumption that they are justified!
Of course, one could also imagine that the norms of reason and the fundamental physical regularities are mutually evolving: the norms lead us to discover and so presume new regularities, which in turn lead to a change in the norms.20 I actually think this could very well be right; but it has stopped looking very much like reliabilism, at least not as an ultimate justification for the norms of reason, for in such a situation whatever the current system of presumed-physical-regularities-and-norms-of-reason is would be (to some essential degree) a function of current consensus.
There is a premise that all the proposals we have considered so far take for granted, namely, that truth is independent of our means of accessing it, that is, whether a proposition is true and whether it can be determined to be true are completely separate questions. This is what allows for situations such as the Cartesian demon, which were what led us, along with Goldman, to consider the normal worlds approach in the first place. What if, instead, we link truth to our means of accessing it? That is, what it is for a proposition to be true is for it to be verified, acceptable to an ideal epistemic community, etc. These are internalist conceptions of truth, and what they all have in common is that the truth of a proposition is its acceptability according to some sort of standards - norms - of reason. Not much time needs be spent on this, for if this is our conception of truth then the reliabilist thesis quickly collapses into vacuity: the norms of reason are justified by their ability to produce beliefs that are acceptable according to the norms of reason (Putnam 1982, p. 5).21 While my opinion is that this has to be our conception of truth, not only because otherwise we have no way of identifying truth, but because of the semantics of truth, this broad topic will not be discussed in detail here. I do not need to discuss it, because what this section has shown is that it does not matter whether or not truth is independent of our means of accessing it: reliabilism fails either way.
After reliabilism, the second most popular response one gets to the request to justify reasoning practices is pragmatism. Scientists of a more instrumentalist bent will tell you that the value of scientific reasoning is not that it leads us to truth but that it helps us make predictions, and control our environment. One hears religious belief justified by the fact that it helps people get through their lives. In fact, I would not be surprised if pragmatism is implicitly appealed to by more people more often than reliabilism, or any other proffered justification of reason. People reason in whatever way best helps them cope.
“Pragmatism” as a philosophical tradition is hard to pin down: being used by those such as Stich to describe the justification of reasoning practices by their utility and by those such as Rorty to describe the view that justification comes through agreement. For this discussion I shall discuss pragmatism as it is understood by Stich. This variety of philosophical pragmatism has the advantage of also matching up with the normal meaning of “pragmatism”. In this variety of pragmatism reasoning is justified by how well it helps the cognizer get something that they value (Stich, p. 131).
The difficulty I see with this approach is that one wonders who is evaluating how well the reasoning practice does at getting what is valued. If it is the person employing the reasoning practice then worries of circularity appear: for one would have to employ one's reasoning practices in making such an evaluation. However, there are possible responses to this: for example, Stich, amongst other replies, makes the interesting suggestion that one might in employing one reasoning practice determine that another one is better (pp. 146-147). But a problem still remains: for in order to put our trust in a reasoning practice we also believe that it will continue to be successful. And we justify the belief in continued success through the use of inductive reason. And this would need to be justified, and if we attempt to justify it pragmatically we end up back where we started.
In this section I will discuss the possibility, hinted at throughout this essay, that the norms of reason are justified by consensus, that is, by describing those reasoning practices endorsed by our community. This is view I call “Cultural Justification”. Although this is the view that has been suggested in the rejection of alternatives and although I think there is much to be said in favor of it, we will ultimately find that it too fails.
Justification by Consensus
As we saw before, in order to be justified in our reasoning practices we must consult our peers. We then asked the question whether this is because our peers are likely to get the norms of reason right or because the endorsement of our peers is what determines correct norms of reason. We explored various options for how norms of reason could be justified beyond consensus, and found them wanting. In the course of these explorations we often found reasons to suggest a cultural view. The rejection of alternatives can be considered an argument in favor of the cultural view. But is there also a positive argument for it?
There are, of course, many, particularly those offered by Rorty in his various writings. I, however, want to offer an “original” argument. I put “original” in quote, for my argument is really just a rephrasing of Wittgenstein's arguments against private language and rule following in terms of reasoning and justification. Specifically, my argument is an expansion of §202, which reads as follows:
...'following a rule' is a practice. And to think one is following a rule is not to follow a rule. And that's why it's not possible to follow a rule 'privately'; otherwise, thinking one was following a rule would be the same thing as following it. [my italics]
Simply replace “following a rule” with “reasoning correctly” or “justifying ones reasoning practices” and you have the core points:\
To think one is reasoning correctly is not to reason correctly. And that's why it's not possible to reason correctly 'privately'; otherwise, thinking one was reasoning correctly would be the same thing as reasoning correctly.
To think one is justified (in their reasoning practices) is not to be justified. And that's why it's not possible to justify a belief/the norms of reason 'privately'; otherwise, thinking one was justified would be the same thing as being justified.
From this I can construct the following argument:
THE JUSTIFICATION OF OUR REASONING PRACTICES MUST BE PUBLIC
- If one could justify their reasoning practices privately, then thinking that their reasoning practices were justified would be the same thing as them being justified.
- Therefore thinking one was reasoning correctly would be the same thing as reasoning correctly.
- But thinking one is reasoning correctly is not the same thing as reasoning correctly.
- Therefore, one cannot justify their reasoning practices privately.
- Therefore, one must justify their reasoning practices publicly.
When we ask how it is that we can justify our reasoning practices, we are asking how we can determine whether we are reasoning correctly. To reason correctly is to reason in accordance with the norms. So the question is: can we determine that we are reasoning correctly privately? No. Much as in order to know that we are understand a word correctly we must see if others agree with our use of it, in order to know if we are reasoning correctly we must express our reasonings to others and seek their approval. Moreover, unless we accept a sort of anarchism about reasoning, we seek their endorsement; they must not only allow that we may reason in our way, they must agree that that way is correct.
There are two reasons for this. One is that a justification to oneself does not do any work. It is like Wittgenstein's case of the left hand giving the right hand a gift (§268) or buying several copies of the same newspaper to confirm what it says (§265). What is at doubt is our ability to think through things correctly – a doubt that we are trying to resolve by thinking through things! The second is that what it is to reason correctly is something that we learn. The analogy is once again with Wittgenstein. As he points out, we learn how to apply a word correctly – that is one reason why a word like “pain” cannot refer to some private object. In his example of the beetle in the box, if everyone learns the word “beetle” without knowing what is in anyone's box then the word cannot refer to what is inside the box.22 Similarly, we learn what it is to reason correctly by engaging in reasoning with others. Therefore it cannot be some fundamentally private activity. Just as to use the word “pain” correctly just is to use it in a way that others would agree is correct, to reason correctly just is to reason in a way that others would agree is correct.23
I have stated that the justification on the norms of reason is public, and it comes through expressing our reasoning to others and having it endorsed by them. Yet most of our reasoning is never so expressed. In fact, it is likely that the majority of what any person believes came about through reasonings that were never tested against the court of public agreement. So what is going on here? Let us speak for a moment of justifying beliefs. We do often justify beliefs to ourselves: indeed, this is common, whereas the practice of justifying our beliefs to others is relatively rare. But despite its commonness, our ability to justify beliefs to ourselves is parasitic upon the possibility of our justifying them to others. When we justify beliefs to ourselves it is in some sense in preparation to justify them to others. We think of arguments we could marshal that would be convincing to the sort of people we care about convincing. And we trust that our ability to defend beliefs to an supposed argumentative partner will translate into the ability to defend beliefs to a real argumentative partner. But here I point out – in a very Wittgensteinian fashion (§§265, 267) – that imagining oneself successfully defending a belief is not to successfully defend a belief.
This may not seem quite right. For example, when we justify a result in mathematics, do we really need to suppose someone other than ourselves who needs convincing? Do we not simply demonstrate that that result comes from following the proper rules? Yes, we do demonstrate that – but who is the demonstration for? As earlier considerations show, it cannot be merely for ourselves: we may have missed something. If we are confident in our result, we are confident that that result could be demonstrated to whoever we feel we should demonstrate it to!
The point of all this is that when we we reason “privately”, if we are confident in our reasoning, we are likewise confident that we could defend that reasoning against others. And that confidence is justified by our evidenced tendency to reason correctly (we will assume for now). Private reasoning is, in a sense, preparation for public reasoning. And the correctness of reasoning is dispositional: even if it never is expressed in a way so that the community may endorse it, if the community would have endorsed it it is normative.
Another objection comes from the question: what constitutes a community? What if, say, there is one other person who agrees with you? This cannot justify your reasoning practices: they may be as crazy as you are! Well, what if we add yet another person. One can see that this quickly expands into a Sorites-type problem: just as the grains of sand never become a pile, the group of people never becomes a community capable of justifying reasoning practices. Every person added may be just as crazy as the last, yet at some point it is impossible that they are all crazy, for they have come to define the standard by which sanity is measured. So what is this point?
I do not think an inability to define a point at which a group of people becomes a justifying community is all that worrying. I think the comparison to the Sorites cases evidencses why. Despite the efforts to prove otherwise, piles do exist, even though one, two, three, or whatever small number of grains do not constitute a pile; similarly, communities capable of justifying reasoning practices exist, although an arbitrary but small number of people may all be wrong. All this shows is that the hope that there might be some algorithm, a set of rules, that we could use to make distinctions is misplaced.
This is connected to perhaps the most common objection against cultural justifications, which is that everyone could be wrong. This is Goldman's main challenge to cultural justifications (p. 68). The point is usually made by noting that any arbitrary number of people have been wrong, so why could not everybody be wrong? Stated thusly, I think one can see how this is the same sort of fallacious reasoning one sees in Sorites cases. An analogy can be made with language: any arbitrary number of people may be mistaken about the meaning of a certain word, so everybody can be mistaken about the meaning of a certain word. Furthermore, it is important to note that when we declare some group of people or past culture to have all been wrong, we are evaluating their positions according to the standards of our culture.
I promised in the introduction to this section that cultural justifications of the norms of reason would turn out to fail. I have fended off various common objections to the cultural view: now is the time for the objection that resists counter, and so proves fatal the the cultural view, at least as a theory of ultimate justification.
In Reason, Truth, and History Hilary Putnam discusses what he calls “criterial” conceptions of rationality (p. 110). These are theories of rationality such as Carnapian positivism, Wittgensteinianism, and my own theory, that define rationality according to institutionalized norms. He argues that such theories always undermine rationality. To do this, he expands an argument made against the positivists. The positivists claimed that the only statements that are meaningful are those that are testable by the methods of logic, math, or science. The difficulty is that according to the positivist criterion of meaning that very criterion is meaningless: it is not a truth of logic or mathematics and it cannot be scientifically tested. Putnam argues that any similar criterial theory is going to fail because the criteria itself cannot be rationally acceptable. I am not sure what Putnam's point is here. His attack seems to be on theories of rationality which link it to publicly institutionalized norms but if his attack works it works on any theory of rationality. It would always be the case that one cannot use a theory to argue for the theory. Yet Putnam states that the conclusion of his argument is not that “rational argumentation and rational justification are impossible in philosophy” but that “we cannot appeal to public norms to decide” what is rational. So do we appeal to private norms? But those are going to be just as incapable of justifying themselves as public norms are. Do we simply take our private norms as given?
While I find it difficult to understand Putnam's point as he expresses it, it suggests to me what I consider to be the fatal argument against cultural justifications. The argument springs from the question: how do we know that our reasonings are endorsed by the community? If, for example, we are worried that we might be reasoning incorrectly because we are crazy, why might not that insanity extend to thinking that the community agrees with us when the community, in fact, does not? Or perhaps we are not insane, but there is a massive conspiracy where everyone is lying to us about whether they agree with our reasonings. What we find is that in attempting to determine whether our reasoning practices are in fact endorsed by our community we encounter the same problem we encountered for the reliabilist and pragmatic justifications: we must employ reasoning in order to determine if our reasoning practices do in fact obey the criterion of justification.
Finally, there is the issue that the cultural justification of the norms of reason does not do the work we wanted it to do: it would not convince someone who disputed our norms to go along with them. A cognitive rebel is not going to be brought into line by being made aware of the cultural norms – they are, after all, a rebel. If anything an attempt at a cultural justification will just strengthen their resolve. Similarly, cultural justifications would be useless against the tarot-readers, for their culture endorses different norms. The same goes for any of the communities discussed in the introduction. In this respect cultural justifications face the same problems as analytic ones. And so, despite the fact that attempts to justify reason other than cultural seemed to tend towards depending on cultural justifications, cultural justifications share all the problems of the alternatives.
Conclusion and Further Work
And so we come to the rather disheartening conclusion that none of our attempts to justify reason are successful. Do we throw up our hands and say that “anything goes”? I think not. For, as Putnam notes, this sort of anarchical relativism is self-refuting (1981 pp. 113-121). Are we instead trapped inside our own understanding of reason, incapable of change? Again, I think not. For one, there is the empirical fact that we do change our views about what is reasonable, and furthermore that we proffer reasons for these changes. Secondly, as we have seen the incommensurability thesis is incorrect: anything that can be counted as reasoning can, in principle, be understood. The only limits are our willingness to try to understand.
This observation, I think, points to the way out of parochialism. We have been looking in the wrong place for a way to resolve disputes over the norms of reason: we sought some theory whereby a criterion could be applied that would tell us whether our reasoning practices were justified. Instead, I would like to propose that what these explorations we have taken show is that the process of justifying our reasoning practices to each other is going to be irreducibly messy. It is going to involve adjusting our presumptions through mutual understanding and conversation, while acknowledging, with Putnam, that our concept of reason informs this very conversation. And this, I would like to suggest, is OK.
Due to this primacy of conversation that I am proposing, I think that the next steps would be to continue the work of those such as J. Habermas and, instead of worrying about norms of reason, instead focus on norms of discourse, that is, how can we talk to each other in a productive way? I want to caution against too-quick conclusions about what such norms of discourse may be: for example, many would immediately assume that we should advocate compromise and the preservation of harmonious relationships. While I do think those goals have their place, I also think there is a place for the ruthless and uncompromising advocation of opposing viewpoints. There are other complicated questions: for example, should we try to listen to the viewpoints of everybody, or of only some people, perhaps those that play by our rules of discourse? But I do not think this should discourage us. As I said, this work is messy, and that is, I think, as it should be. For its messiness is the result of its immense importance.
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1In this essay I will use the singular “they” as a gender-neutral pronoun in cases where it would not lead to confusion.
2Reasoning might not necessarily include the formation of beliefs, as beliefs may be formed in all sorts of ways that are not reasoning - for example, as the automatic result of perceptual stimuli – although once those beliefs are formed it is a matter of reasoning of whether they are accepted, rejected, or modified. I say it might not necessarily include such processes as one might very well claim that, for example in the case of automatic beliefs resulting from perceptual stimuli, we infer from colored blotches in our visual field that there is, say, a rhinoceros, and that inference is a case of reasoning. While I do not necessarily agree with this position, I also do not necessarily disagree with it, and as such want to leave the question open. (One could argue, in a Wittgensteinian fashion, that we assume that some reasoning must be going on.)
3There may be different norms of reason that regard different kinds of beliefs: for example, the norms for reasoning about ethics might be different from the norms for reasoning about science. But as my discussion concerns not what the norms of reason should be but the general question of justifying norms of reason whatever they may be I do not think this issue is relevant.
4Of course, I think that in some important respect the intrapersonal depends on the interpersonal.
5Of course, it may just be part of our delusion that we think other people don't think we're crazy. A variant of this problem will, in time, come back to haunt us.
6In my own case: Goodman in this passage is talking specifically about deductive inference.
7A perhaps amusing choice of phrase in this context.
8For a detailed account of the problems with reflective equilibrium as a method of justification see Stich (1990), pp. 75-100.
9By “forms” our tarot-card reader might mean something like “ways of laying out the cards, interpreting them, etc.”
10Even stranger: true statements are implied by their negations.
11A real problem, as almost all of our reasoning at some point depends on them: even deductive inference relies on the notion that if the premises were true the conclusion would be true, whether they (the premises or conclusion) are true or not.
12These disagreements are often about capturing what “if-then” means in English. But why should we be particularly concerned with what it means in English? Of course, it is an English word, and if our goal is simply to explicate the meaning of an English word, then this concern makes sense. But our goal would seem to be more than that: we want to find the correct logic, which should be universal. (In Spanish double-negation is used for emphasis: does this mean that the should be a Spanish logic where “not-not p” does not imply p, but instead implies “extra-not p”?)
13One can see in the practice of psychologists investigating “defective” reasoning that they hope for, if not believe in, the possibility of making this sort of interpretation (and in a not-too convoluted way), as they are not content to simply say that their subjects are reasoning defectively and leave it at that: they seek some explanation as to why the reasoning is defective, and proposed explanations usually have the character of attempting to demonstrate how the defective reasoning makes sense – that is, is reasonable – given the way that our cognitive machinery characterizes the problems it is presented with. Similarly, one can see this commitment to interpretation in the practice of anthropologists, who, in the interest of understanding a culture with seemingly odd reasoning practices and odd beliefs, try to show how those reasoning practices and beliefs are reasonable given the basic assumptions of the culture.
14 An interesting question, which will not be explored here, is whether it is more important to maximize the number of beliefs of the valued type or to minimize the number of beliefs of the unvalued type. William James expressed this as one of the disagreements between him and Clifford: while the latter was obsessed with avoiding error in one's beliefs, the former felt that the possibility of believing truth was worth the risk of being wrong, and furthermore that refusing to believe truth because of one's concern with avoiding error would be to do oneself a great disservice.
15Stich of course speaks of “justification”.
16I will ignore the distinction between “actual world” and “world in which the cognizer is operating” and simply talk about the “actual world”, since even though the following discussion imagines states of the world that (we hope!) do not hold, and so would describe other worlds, the discussion also imagines that we inhabit one of these worlds, and so that for us it would actually be the actual world.
17And, returning to the vagueness problem, how exact does this rightness need to be? Stich has a field day with this, pointing out that “our concept of justification occupies a small region in a large space of more or less similar concepts [my italics] that can be generated by altering the specification of [normal worlds].” (p. 95)
18If we reject these two options then it seems that the only option we have left is that the right presumptions are the presumptions we agree upon. And so it seems we face the possibility, as we did with analytic justifications, that, even if reliability justifies the norms of reason at a lower level, it is consensus gives the ultimate justification.
19One could dispute this, for example by saying that normal world are those worlds that obey the fundamental physical regularities we would presume once we have a final and complete science. But these may not be the physical regularities the world actually obeys, for then this position becomes actual-world reliabilism. (The Cartesian demon could arrange things such that our final and complete science is still wrong.) So the only reason we would presume those regularities is that they are the ones that the method of science – a reasoning practice – will lead us to discover.
20One thinks of how the discovery of quantum mechanics has led some to propose a revision in logic. (Putnam 1968)
21It is interesting how similar this is to the result we got by following the normal-worlds approach. One wonders whether the normal-worlds approach is just disguised internalism (or vice-versa).
22§293: “It would be quite possible for everyone to have something different in his box...But what if these people's word “beetle” had a use nonetheless. - If so, it would not be the name of a thing. The thing in the box doesn't belong to the language game at all; not even as a Something: for the box might even be empty.”
23We see here that there is actually something quite correct in the analytic defense of the norms of reason. Our norms of reason are analytic: what it is to reason correctly just is to reason in accordance with them. There just is not anything special about this analyticity. If we were in some different community some other set of norms might be analytic.