Peirce, Charles Sanders

Peirce, Charles Sanders
American pragmatism Peirce Cheryl Misak INTRODUCTION Charles Sanders Peirce (1839–1914), one of America’s greatest philosophers, mathematicians, and logicians, was a difficult and not altogether pleasant character. That, combined with what the establishment regarded as moral lapses, resulted in the fact that he was thwarted in his attempts to obtain a permanent academic post and died a malnourished and impoverished outcast. He was dismissed from his brief stint at Johns Hopkins University, dismissed from his service with the US Coast Survey (a job handed to him by his father, its superintendent), and ostracized by his alma mater—Harvard University. Despite this grim life, Peirce was the founder of pragmatism, semiotics, and a theory of truth and knowledge that is still popular today. He was a serious student of the history of philosophy and of science and he was generous in acknowledging the influence of others. One of the most important influences is Kant, of whom the young Peirce was a ‘passionate devotee’ ([12.1], 4:2).1 It is from Kant, for instance, that Peirce inherits a quest for the categories, a penchant for the notion of continuity and a desire to develop an ‘architectonic’ system. But there is also a strong gust of medieval philosophy blowing throughout his work, Duns Scotus in particular. It is from here that Peirce gets his Scholastic realism, which is set against the nominalism and individualism of the British empiricists. But there is also a clear affinity between Peirce and those empiricists. For instance, Peirce credits Berkeley’s arguments that all meaningful language be matched with sensory experience as the precursor of pragmatism: ‘Berkeley on the whole has more right to be considered the introducer of pragmatism into philosophy than any other one man, though I was more explicit in enunciating it (letter to William James, 1903 ([12.12], 2:425)). The volume and breadth of Peirce’s work is staggering. But because he was unsuccessful in securing a permanent academic position, most of it went unpublished in his time. It lies in a huge bulk of manuscripts and scraps. His best known papers are those of the 1870s series in Popular Science Monthly called ‘Illustrations of the Logic of Science’. These include ‘How To Make Our Ideas Clear’ and ‘The Fixation of Belief’. His Lowell Lectures in 1898 and 1903 and his Harvard Pragmatism Lectures in 1903 also contain essential material. But much of what is important is only now being published in the definitive chronological edition. THE PRAGMATIC MAXIM2 The ‘spirit’ of pragmatism is captured in the following maxim: ‘we must look to the upshot of our concepts in order rightly to apprehend them’ ([12.1], 5:4) There is, Peirce argues, a connection between knowing the meaning of a sentence or hypothesis and knowing what to expect if it is true. If a sentence has no consequences (if there isn’t anything one could expect would be the case if it were true) then it lacks an important dimension. It lacks a property that we would have had to get right if we were to know what it means. Pragmatism labels such a hypothesis defective. Understanding requires knowledge of consequences and a sentence is legitimate only if it has consequences. This criterion of legitimacy permeates Peirce’s work. Not only does he disparage certain philosophical positions as pragmatically meaningless, but he argues that if we focus on the consequences of ‘H is true’, ‘the probability of H is n’, ‘x is real’, etc., we will adopt the best accounts of truth, probability, reality, etc. So the pragmatic maxim serves as a standard for determining which expressions are ‘metaphysical rubbish’ or ‘gibberish’ ([12.1], 8:191) and it serves as a methodological principle for formulating philosophical theories. In ‘How To Make Our Ideas Clear’, Peirce publicly unveils pragmatism and sets out the maxim as follows: Consider what effects, which might conceivably have practical bearings, we conceive the object of our conception to have. Then, our conception of these is the whole of our conception of the object. ([12.2], 3:266) Peirce suggests in this paper that knowing the meaning of an expression is exhausted by knowing its ‘practical’ effects, which he characterizes as ‘effects, direct or indirect, upon our senses’ ([12.2], 3:266). These effects can be described by conditionals of the sort: if you were to do A, you would observe B. He says: we come down to what is tangible and practical, as the root of every real distinction of thought, no matter how subtile [sic] it may be; and there is no distinction of meaning so fine as to consist in anything but a possible difference of practice. ([12.2], 3:265) As an example of how the pragmatic maxim operates, Peirce examines the meaning of ‘this diamond is hard’. He says that it means that if you try to scratch it, you will find that ‘it will not be scratched by many other substances’. ([12.2], 3:266). Notice that the consequence in this example is formulated as an indicative conditional, as a matter of what will happen. Peirce sees that if he formulates consequences in this manner, it makes little sense to describe a diamond which is in fact never scratched as being hard. He seems to be content with this conclusion in ‘How To Make Our Ideas Clear’. But when he considers the matter later, he always insists on a subjunctive formulation. He chides himself for making the nominalist suggestion that habits, dispositions or ‘would-bes’ are not real. A ‘Scholastic realism’ about dispositions and subjunctive conditionals must be adopted: a disposition is more than the total of its realizations and a subjunctive conditional is determinately correct or incorrect, whether or not the antecedent is fulfilled. The consequences which concern pragmatism are those which would occur under certain conditions, not those which will actually occur. His considered view about the unscratched diamond is that ‘it is a real fact that it would resist pressure’ ([12.1], 8:208). This was not Peirce’s only amendment to the pragmatic maxim. In his struggle to arrive at a suitable criterion of understanding and meaning, he sometimes suggested one very similar to the criterion we find later in logical positivism. The positivists’ criterion effectively restricted knowledge to that which physical science is about; we can have knowledge only of that which is directly observable or verifiable. Anything else— metaphysics, for example—is literally meaningless. But Peirce is concerned with a much broader account of what is involved in linguistic competence and altered his maxim in order to make it more generous. For one thing, Peirce himself inclined toward metaphysics and he does not want to do away with it altogether. In metaphysics ‘one finds those questions that at first seem to offer no handle for reason’s clutch, but which readily yield to logical analysis’ ([12.1], 6:463). Metaphysics, ‘in its present condition’ is ‘a puny, rickety, and scrofulous science’ ([12.1], 6:6). But it need not be so, for many of its hypotheses are meaningful and important. It is the job of the pragmatic maxim to sweep ‘all metaphysical rubbish out of one’s house. Each abstraction is either pronounced to be gibberish or is provided with a plain, practical definition’ ([12.1], 8:191). Secondly, Peirce frequently claims that the pragmatic maxim captures only a part of what it is to know the meaning of an expression. In order to grasp a term, he argues, a threefold competence is required. The interpreter must be able to (1) pick out what objects the term refers to; that is, know Mill’s ‘denotation’, Hamilton’s ‘extension’ or ‘breadth’; (2) give a definition of the term; that is, know Mill’s ‘connotation’, Hamilton’s ‘intention’ or ‘depth’; (3) know what to expect if hypotheses containing the term are true; that is, know the consequences of hypotheses containing the term. Whereas his predecessors identified the first two sources of meaning, Peirce thinks that his contribution was to locate the important third source. He takes his three aspects of understanding to spell out completely what someone must be able to do if she grasps a concept or knows the meaning of an expression. But none the less, the pragmatic maxim is supposed to be a criterion for meaning identity. Peirce argues that a purported difference which makes no practical difference is spurious; if two hypotheses have the same set of subjunctive conditional consequences, then they express the same content. It is pointless to suggest that they differ in denotation or connotation. Thirdly, Peirce at times tries to divert the pragmatist’s gaze from sensory experience. His account of experience is very generous: any belief that is compelling, surprising, impinging, unchosen, involuntary or forceful is a perception. And such beliefs need not arise from the senses. He takes there to be two kinds of experience—‘ideal’ and ‘real’. The latter is sensory experience and the former includes experience in which ‘operations upon diagrams, whether external or imaginary, take the place of the experiments upon real things that one performs in chemical and physical research’ ([12.1], 4:530). These diagrammatic experiments or thought experiments figure in mathematical and deductive inquiry. They involve ‘experimenting upon [an] image in the imagination, and of observing the result so as to discover unnoticed and hidden relations among the parts’ ([12.1], 3:363). The mathematician, for instance, draws subsidiary lines in geometry or makes transformations in algebraic formulae and then observes the results: ‘his hypotheses are creatures of his own imagination; but he discovers in them relations which surprise him sometimes’. ([12.1], 5:567). Since surprise is the force of experience, the upshot of such reasoning counts as experience. What this means is that Peirce, unlike his verificationist predecessors (Hume, Comte) and successors (the logical positivists), wants all hypotheses to be exposed to the pragmatic maxim; he does not exempt formal (or what are now called ‘analytic’) sentences. Logical and mathematical hypotheses can meet the criterion because there is a kind of experience relevant to them. And some metaphysical hypotheses meet the criterion as well. They must have consequences, Peirce argues, for ordinary, everyday, experience, by contrast with experiences in technical experimental contexts and by contrast with experiences in diagrammatic contexts. TRUTH AND REALITY Peirce applies the pragmatic maxim to the metaphysical debate on the nature of truth and reality. The philosopher must look to our everyday practices and see what account of truth would be best suited for them: ‘We must not begin by talking of pure ideas,— vagabond thoughts that tramp the public roads without any human habitation,—but must begin with men and their conversation’ ([12.1], 8:112). The correspondence theory, he argues, lacks such human habitation. It holds that a true hypothesis is one which is in agreement with an unknowable ‘thing-in-itself’. But: You only puzzle yourself by talking of this metaphysical ‘truth’ and metaphysical ‘falsity’ that you know nothing about. All you have any dealings with are your doubts and beliefs… If your terms ‘truth’ and ‘falsity’ are taken in such senses as to be definable in terms of doubt and belief and the course of experience…well and good: in that case, you are only talking about doubt and belief. But if by truth and falsity you mean something not definable in terms of doubt and belief in any way, then you are talking of entities of whose existence you can know nothing, and which Ockham’s razor would clean shave off. Your problems would be greatly simplified, if, instead of saying that you want to know the ‘Truth’, you were simply to say that you want to attain a state of belief unassailable by doubt. ([12.1], 5:416). Peirce’s argument here is that if one offered an account of ‘H is true’ in terms of its consequences for doubt, belief and perceptual disappointment, one would be offering a pragmatic elucidation of truth. And that, if it were a correct specification of the consequences, would be a satisfactory account of truth. But a definition of truth which makes no reference to belief, doubt and experience is an empty definition of truth. It is useful only to those who have never encountered the notion. Peirce sometimes states this objection to the correspondence theory by labelling it a ‘transcendental’ account of truth ([12.1], 5:572). Such accounts regard truth ‘as the subject of metaphysics exclusively’—spurious metaphysics, not pragmatically legitimate metaphysics. On the correspondence definition, truth transcends experience; it has no consequences for inquiry. He says: The Ding an sich…can neither be indicated nor found. Consequently, no proposition can refer to it, and nothing true or false can be predicated of it. Therefore, all references to it must be thrown out as meaningless surplusage. ([12.1], 5:525) If we look at the experience of inquirers which seems most relevant to truth—the evidence they have for and against hypotheses—the correspondence theory is speechless. For on that account, there is an unbridgeable gap between what we can have evidence for and the inaccessible reality. We could have the best possible evidence for an hypothesis and yet that hypothesis might fail to be true. The correspondence theory does not tell us what we can expect of a true hypothesis and so it is not capable of guiding us in our actions and inquiries. If truth is the aim of inquiry, then on the correspondence construal, enquirers are left completely in the dark as to how they should conduct their investigations. The aim is not, Peirce says, ‘readily comprehensible’ ([12.1], 1:578). How could anyone aim for a sort of truth that transcends experience? How could an enquirer develop a means for achieving that aim? In anticipation of certain kinds of naturalized epistemologies, Peirce focuses on what he thinks the transcendentalist has lost sight of—the link between truth and inquiry. The pragmatic account deals with the common experience that constitutes inquiry, and so it offers a conception of truth that can be a guide for inquiry. On Peirce’s view, ‘A true proposition is a proposition belief in which would never lead to…disappointment’ ([12.1], 5:569). This is an account of what we can expect from a true belief: if we were to inquire into H, we would find that H would encounter no recalcitrant experience. We can predict that if we were diligently to inquire about H, H would not, in the end, be overturned by experience. An alternative way of making the point is to say that we would expect the following: if inquiry with respect to H were to be pursued as far as it could fruitfully go (i.e. far enough so that the hypothesis would no longer be improved upon), H would be believed (it would not be doubted). For if H would be believed after such a prolonged inquiry, then H would not have been overturned by experience; it would not have been put into doubt. A true belief is a permanently settled belief. Peirce’s view of reality is connected to his view of truth. The consequence of a thing’s being real is that the hypothesis asserting its reality would be, if inquiry relevant to it were pursued, perfectly stable or doubt-resistant. For a consequence of a thing’s being real is that, if we were to inquire into issues for which it is relevant, it would in the long run force itself on our attention. The pragmatic view is that reality is the ‘object’ of true beliefs—it is what true beliefs are about. Reality is what beliefs in the final opinion would fix on. This account of reality, Peirce argues, fulfils the definition of reality as that which is independent of whatever ‘you, I, or any number of men’ think. We have seen that Peirce is a realist about subjunctives. What would be believed to be real is thus independent of what is believed to be real at any particular time. The real ‘is that which, sooner or later, information and reasoning would result in, and which is therefore independent of the vagaries of you and me’ ([12.2], 2:239) Peirce thinks that this makes reality ‘objective’. ([12.2], 3:29). He makes the same point about truth. What would be ascertained to be true would be so ascertained whatever anyone here and now thinks. A hypothesis may be believed, then doubted and then believed again, but this does not affect whether it would be believed at the end of a prolonged inquiry. Independently of whatever any ‘definite’ group of inquirers may think about the truth-value of H, H either would be or would not be a member of the final opinion (12.1], 5:565). Thus the truth-value of H is an objective matter—it does not depend on what anyone at any particular point happens to think. SEMIOTICS Peirce was a pioneer in semiotics. Not only is he responsible for the distinction between type (‘human’ as a general term) and token (‘human’ as applied to various objects), but he developed a complex map of signs which covers sixty-six classes, from which sprout 59,049 varieties. His theory of signs has interpretation at its centre. For Peirce holds that the signreferent relation is not able, on its own, to uphold a complete account of representation. Representation is triadic: it involves a sign, an object and an interpreter. Each aspect of this representation relation corresponds to one of the elements in Peirce’s division of signs into icons, indices and symbols. And in each of these, one or another aspect of linguistic competence is most prominent. Icons are signs that exhibit their objects by virtue of similarity or resemblance. A portrait is an icon of the person it portrays and a map is an icon of a certain geographical area. Peirce argues that the meaning of iconic signs lies mostly in their connotation; what makes a painting or a map an icon is that its qualities or attributes resemble the qualities or attributes of its object. Indices are signs that indicate their objects in a causal manner; an index ‘signifies its object solely by virtue of being really connected with it’ ([12.1], 3:360). A symptom is an index of a disease and smoke is an index of fire. The essential quality of an index is its ability to compel attention. A pointing finger, a knock on the door or a demonstrative pronoun, such as ‘there’ or ‘that’, draws attention to its object by getting the interpreter to focus on the object. So an index, by being object-directed, has its denotation or extension as its ‘most prominent feature’ ([12.1], 8:119). An index picks out or indicates its object; it points to ‘that, that and that’ as its extension. A symbol is a word, hypothesis or argument which depends on a conventional or habitual rule; a symbol is a sign ‘because it is used and understood as such’ ([12.1], 2:307) Symbols have ‘principle’ or pragmatic meaning; they have ‘intellectual purport’. Peirce contrasts pragmatic meaning with ‘internal’ meaning (which he relates to icons and connotation) and with ‘external’ meaning (which he relates to indices and denotation). He suggests that the pragmatic meaning of symbols has to do with a ‘purpose’ ([12.1], 8:119). A symbol has pragmatic meaning because if the utterer knows how interpreters habitually interpret a sign, she can use the sign to cause a specific effect in the interpreter. And Peirce calls this effect the ‘interpretant’ of the sign. If, for instance, I write ‘dog’, I intend the sign to cause a certain effect in the interpreter (perhaps I want the interpreter to think of a dog) whereas if I write ‘odg’, I do not, as ‘odg’ is not a conventional sign. Or if I assert ‘That bridge has a loose plank’, I might want the interpreter to be careful when crossing the bridge. Peirce characterizes an assertion as the attempt to produce a disposition in an interpreter; it is ‘the deliberate exercise, in uttering the proposition, of a force tending to determine a belief in it in the mind of an interpreter’ ([12.4], 4:249). Notice that if pragmatic meaning is about this sort of practical consequence, it is no longer about ‘effects, direct or indirect, upon our senses’. Pragmatic meaning, rather, involves consequences for action or thought. In 1905 we find Peirce offering this version of the pragmatic maxim: ‘The entire intellectual purport of any symbol consists in the total of all general modes of rational conduct which, conditionally upon all the possible different circumstances and desires, would ensue upon the acceptance of the symbol’ ([12.1], 5:438). ‘Rational conduct’, although Peirce thinks that it will eventually manifest itself in a modification of the interpreter’s disposition to behave, includes the conduct of one’s thought. This twist in the pragmatic maxim—that the acceptance of a hypothesis must have effects on an interpreter’s train of thought—coincides with a development in the early 1900s in Peirce’s theory of signs. That development is a theory of interpretants and Peirce at times locates pragmatic meaning within this theory. He distinguishes three types of interpretants. The ‘immediate’ interpretant is the fitness of a sign to be understood in a certain way; the ‘dynamical’ interpretant is the actual effect a sign has on an interpreter, and the ‘final’ interpretant is the effect which eventually would be decided to be the correct interpretation. Pragmatic meaning, Peirce says, lies in a kind of dynamical interpretant: the ‘ultimate logical interpretant’. A sign, Peirce argues, sparks a subsequent sign, or a logical interpretant, in the mind of the interpreter, and since the logical interpretant is itself a sign, an infinite chain of interpretation, development, or thought, is begun. Peirce stops the regress by introducing the notion of an ‘ultimate logical interpretant’ or a ‘habit-change’. He follows Alexander Bain in taking a belief to be a habit or disposition to behave. And so this new habit is a belief or a modification of the interpreter’s tendencies towards action. The pragmatic meaning of an expression, according to Peirce’s theory of signs, is the action (which includes the action of subsequent thought, and which ends in a disposition to behave) that arises after an interpreter accepts it. THEORY OF INQUIRY The notion of inquiry occupies a central place in Peirce’s thought. For the most part, his income was from employment in the United States Coast and Geodetic Survey, where he made numerous and significant contributions. Philosophy, he insisted, must get along with other branches of inquiry. The following motto ‘deserves to be inscribed upon every wall of the city of philosophy: Do not block the path of inquiry’ ([12.1] 1:135). Peirce characterizes inquiry as the struggle to rid ourselves of doubt and achieve a state of belief. An inquirer has a body of settled belief; a set of beliefs which are, in fact, not doubted. These beliefs, however, are susceptible to doubt, if it is prompted by some ‘positive reason’, such as a surprising experience ([12.1], 5:51). We have seen that Peirce takes experience to be that which impinges upon us—experience, he says, teaches us ‘by practical jokes, mostly cruel’ ([12.1], 5:51). When experience conflicts with an inquirer’s belief, doubt is immediately sparked. And doubt ‘essentially involves a struggle to escape’ ([12.1], 5:372 n.2). Inquiry is that struggle to regain belief. The path of inquiry is as follows: belief…surprise…doubt…inquiry… belief…. Peirce does not take these points to be mere observations about human psychology; he thinks that psychology should be kept out of logic and the theory of inquiry. Doubt and belief, although they do have psychological aspects, such as making the inquirer feel comfortable or uncomfortable, are best thought of in terms of habits. A ‘belief-habit’ manifests itself in an expectation: if we believe H, then we habitually expect the consequences or the predictions we derive from H to come about when the appropriate occasion arises. Thus inquirers are thrown into doubt when a recalcitrant experience upsets or disrupts a belief or expectation. There are three stances an inquirer may have with respect to a hypothesis: believe it, believe its negation or consider the matter open to inquiry. Only in the third stance are we left without a habit of expectation and thus it is agnosticism which is the undesirable state. That is, doubting whether an hypothesis is true is not equivalent to believing that it is false, rather, it is not knowing what to believe. What is wrong with this state is that it leads to paralysis of action. An inquirer has some end in view, and two different and inconsistent lines of action present themselves, bringing the inquirer to a halt: ‘he waits at the fork for an indication, and kicks his heels… A true doubt is accordingly a doubt which really interferes with the smooth working of the belief-habit’ ([12.1], 5:510). Doubt arises because of not knowing how to act. And action can include action in diagrammatic and thought experiments. Peirce’s theory of inquiry has a certain kind of empiricism at its core. Inquirers aim for beliefs that fit with experience. When we replace a belief which has come into doubt, that new belief stands up better than the old one. So we accept it, act on it and think that it is true. But we know very well that it eventually might be overthrown and shown to be false by experience. Peirce adds the more contentious claim that what we aim for is permanently settled beliefs. When we have beliefs that would for ever withstand the tests of experience and argument, he holds that there is no point of refusing to confer upon them the title ‘true’. Only a spurious desire for transcendental metaphysics will make one want to distinguish perfectly good beliefs from true beliefs. A problem faces Peirce here. If beliefs could be settled by a religious authority, or by a charismatic guru or by astrology, so that they were permanently resistant to doubt, there seems to be, on his account, no reason for criticizing them. Peirce considers different methods of fixing belief and suggests that it is hard really to end the irritation of doubt. The method of tenacity, or holding on to your beliefs come what may, will not work, Peirce says, because doubt will be sparked when one notices that the opinions of others differ from one’s own. Beliefs produced by the method of authority (fixing beliefs according to the dictates of a State, religion, etc.) will similarly be subject to doubt when one notices that those in other States or religions believe different things. Beliefs produced by the a priori method (adopting beliefs which are agreeable to reason) will eventually be doubted when it is seen that what the experts take as being agreeable to reason shifts like a pendulum and is really a matter of intellectual taste. None of these methods will produce permanently settled belief because they have a self-destructive design; the beliefs settled by them eventually would be assailed by doubt. The agent of destruction which Peirce sees in each of the specious methods seems to be a purported fact about our psychological makeup: if an inquirer believes an hypothesis, and notices that other inquirers do not believe it, that first inquirer will be thrown into doubt. This impulse, Peirce says, is ‘too strong in man to be suppressed, without danger of destroying the human species’ ([12.2], 3:250). If this psychological hypothesis expresses a universal fact about us, then the unsatisfactory methods will indeed prove unreliable in the long run. They will not produce permanently settled belief and we should refrain from using them.3 There are two other cornerstones to Peirce’s theory of inquiry: critical commonsensism and fallibilism. Critical commonsensism is a position about how we ought to regard those beliefs which are settled. It holds that there are many things which inquirers do not doubt and that inquiry must start with a background of beliefs which are not doubted. A body of settled belief is presupposed for the operation of inquiry in that there has to be something settled for surprise to stir up. This doctrine arose as a response to Peirce’s conception of Descartes’ project—a systematic attempt to bring into doubt all hypotheses about which error is conceivable. Peirce argued that such doubts would be ‘paper’ doubts. They are not genuine and they cannot motivate inquiry. The mere possibility of being mistaken with respect to what one believes is never a reason to revise those beliefs. Any of our beliefs might be false, but it would be absurd to doubt them all because of this. If we did, we would not possess a body of stable belief by which to judge new evidence and hypotheses, and hence, we would block the path of inquiry. We can doubt one belief and inquire, but we cannot doubt all of our beliefs and inquire. Peirce’s point against Descartes is that if we were to set the requirements on knowledge as high as Descartes does, we would have nothing left to go on. He says, there is but one state of mind from which you can ‘set out’, namely, the very state of mind in which you actually find yourself at the time you do ‘set out’—a state in which you are laden with an immense mass of cognition already formed, of which you cannot divest yourself if you would… Do you call it doubting to write down on a piece of paper that you doubt? If so, doubt has nothing to do with any serious business. ([12.1], 5:416) So Peirce is not concerned with sceptical questions about foundations for certainty, and his arguments are not addressed to those who are. But he is also a ‘contrite fallibilist’, holding that all our beliefs can be doubted; that is, that none of them are certain. There is a tension here: how can it be that all our beliefs are fallible, or subject to doubt, but, nevertheless, some of our beliefs must not be doubted if inquiry is to be possible? Peirce’s reconciliation of fallibilism with critical commonsensism is made in terms of his notion of truth. He thinks that many of our beliefs are indeed those which would be included in the final opinion, but since we cannot know for any given belief whether or not it would be in that opinion, we cannot know that it is true. That is, we do not know if the antecedent of this subjunctive conditional is fulfilled: ‘if inquiry were pursued as far as it could fruitfully go, then H would be believed’. Inquiry may or may not have been pursued far enough with respect to H, and so we cannot have certainty with respect to any belief. But the uncertainty or fallibility that in principle accompanies every one of our beliefs does not mean that we should doubt our settled beliefs. ‘Practically speaking’, he says, many things are ‘substantially certain’ ([12.1], 1:152); we do not doubt them. While ‘it is possible that twice two is not four…it would be difficult to imagine a greater folly than to attach any serious importance to such a doubt’ ([12.1], 7:108). But substantial certainty is different from the ‘absolute certainty’ which would result from knowing that we have permanently settled belief. We may have this settled opinion about many questions, but we must not infer that we ‘perfectly know when we know’. Again, we cannot know that any given hypothesis is permanently settled upon or true— we cannot have absolute certainty. Nevertheless, in every state of intellectual development and information, there are things that seem to us sure ‘so that even though we tell ourselves that we are not sure, we cannot clearly see how we fail of being so’ ([12.1], 4:64). Practi-cally, we must treat some hypotheses as certain. Settled beliefs must be regarded as infallible, in the sense that the inquirer does not doubt them for the purposes of inquiry; science has ‘established truths’ to be used as premisses in further deliberation ([12.1], 1:635). In this sense, we do not doubt what we believe, but in another sense, each of our beliefs can, or could, be doubted. Peirce’s theory of inquiry provides the key to understanding his view of the growth of knowledge and the progress of science. His position is that science ‘is not standing upon the bedrock of fact. It is walking upon a bog, and can only say, this ground seems to hold for the present. Here I will stay till it begins to give way’ ([12.1], 5:589). Accepted hypotheses and theories are stable until they are upset by experience. They are as good as they can be, given the state of evidence, technology, argument, etc. Knowledge is rebuilt bit by bit when experience forces inquirers to revise their beliefs. The rebuilding principle requires modification of our beliefs in the light of recalcitrant experience and Peirce argues that we cannot help but adopt this principle. We do have some reason to believe that, in rebuilding, we are in some sense getting closer to the truth. For the new beliefs will get along with experience better than the old ones. True beliefs are those which would, in the end, get along with experience and one explanation of our beliefs achieving more and more fit with experience is that a good number of them are true. A good number of them would be permanently doubt-resistant. But Peirce’s picture is not one of placing indubitable building blocks upon each other as we progress towards the truth. Rather, the picture is one of doubt (recalcitrant experience) forcing us to inquire until we reach another tentative doubt-resistant belief. The ground upon which inquiry walks is tenuous and it is only the danger of losing our footing that makes us go forward. Doubt and uncertainty provide the motive for inquiry. All our beliefs are fallible and when an agent accepts a belief, she does so with the knowledge that it might very well prove to succumb to surprise. But if the agent knows that the belief is the result of a method which takes experience seriously, then she is warranted in accepting it, asserting it and acting upon it. In addition, Peirce’s theory of inquiry invokes two regulative hopes; assumptions, such that, without making them, the participants in a practice could make no sense of that practice. We must, Peirce says, hope or assume that the community will continue indefinitely and we must hope that there would be, if inquiry were pursued far enough, a final settled answer to ‘the particular questions with which our inquiries are busied’ ([12.1], 6:610). He says, a reasonable disputant disputes because he hopes, or at least, goes upon the assumption that the dispute will come to something; that is to say, that both parties will at length find themselves forced to a common belief which will be definitive and final. For otherwise, why dispute? ([12.1], 2:29) Inquiry is the asking of questions, and a presupposition of inquiry is that the questioner hopes for an answer. We have, Peirce says, some ground for this hope because all sorts of questions that seemed at one time to be completely resistant to resolution have been resolved. LOGIC: DEDUCTION, INDUCTION, ABDUCTION Peirce described himself first and foremost as a logician and despaired that the current state of philosophy in America was such that most found formal logic to be too difficult. He classified inference into three types: deduction, induction and abduction (which he also called retroduction or hypothesis) and made significant contributions to the study, of each. Indeed, the very study of abduction, what is today known as inference to the best explanation, is due to Peirce. Peirce’s contributions to deductive logic are very impressive, although today it is Frege, not Peirce, who is regarded as bringing modern logic into the world. Peirce developed a logic of relations and quantifiers independently of, and at roughly the same time as, Frege, discovered the Sheffer Stroke twenty years before Sheffer, and invented a notation (utilizing normal forms) very similar to the one still in use. In mathematics, he anticipated Dedekind on the difference between finite and infinite sets and independently developed arguments about infinity similar to Cantor’s. Unfortunately, setting out the background to these developments and adequately characterizing them is beyond the scope of this chapter (See Dauben [12.6], Putnam [12.13] and Dipert [12.7]). Peirce is also known for his work on induction. Some see in his writing an anticipation of Reichenbach’s probabilistic response to Hume’s scepticism about induction while others see an anticipation of the Neyman-Pearson confidence interval approach to testing statistical hypotheses (see Ayer [12.5], Lenz [12.9], Levi [12.10] and Hacking [12.8]). Peirce called the sort of inference which concludes that all As are Bs because there are no known instances to the contrary ‘crude induction’. It assumes that future experience will not be ‘utterly at variance’ with past experience ([12.1], 7:756). This is, Peirce says, the only kind of induction in which we are able to infer the truth of a universal generalization. Its flaw is that ‘it is liable at any moment to be utterly shattered by a single experience’ ([12.1], 7:157). The problem of induction, as Hume characterizes it, is about crude induction; it is about the legitimacy of concluding that all As are Bs or the next A will be a B from the fact that all observed As have been Bs. Peirce assumes that Hume’s problem is straightforwardly settled by fallibilism and critical commonsensism. We do, and should, believe that, say, the sun will rise tomorrow, yet it is by no means certain that it will. To show that induction is valid, we need not show that we can be certain about the correctness of the conclusion of a crude inductive inference. Fallibilism holds that this is a pipe dream. What we have to show, rather, is that induction is a reliable method in inquiry. Peirce holds that it is a mistake, anyway, to think that all inductive reasoning is aimed at conclusions which are universal generalizations. The strongest sort of induction is ‘quantitative induction’ and it deals with statistical ratios. For instance: Case: These beans have been randomly taken from this bag Result: Two-thirds of these beans are white Rule: Therefore two-thirds of the beans in the bag are white That is, one can argue that if, in a random sampling of some group of Ss, a certain proportion r/n has the character P, the same proportion r/n of the Ss have P. One concludes from an observed relative frequency in a randomly drawn sample a hypothesis about the relative frequency in the population. Peirce is concerned with how inductive inference forms a part of the scientific method; how inductive inferences can fulfil their role as the testing ground for hypotheses. Quantitative induction can be seen as a kind of experiment. We ask what the probability is that a member of the experimental class of the Ss will have the character P. The experimenter then obtains a fair sample of Ss and draws from it at random. The value of the proportion of Ss sampled that are P approximates the value of the probability in question. When we test, we infer that if a sample passes the test, the entire population would pass the test. Or we infer that if 10 per cent of the sample has a certain feature, then 10 per cent of the population has that feature. Peirce took the three types of inference to form the scientific method. The role played by induction is to test hypotheses. The job of abductive inference is to provide hypotheses for this testing. Peirce’s settled view on abduction is that it is ‘where we find some very curious circumstance, which would be explained by the supposition that it was a case of a certain general rule, and thereupon adopt that supposition’ ([12.2], 3:326). The form it takes is: The surprising fact, C, is observed; But if A were true, C would be a matter of course. Hence, there is reason to suspect that A is true. ([12.1], 5:189) Peirce argued with Paul Carus about when an explanation is called for. Carus claimed that irregularity demands an explanation and Peirce disagreed. Nobody, he says, is ‘surprised that the trees in a forest do not form a regular pattern, or asks for any explanation of such a fact’ ([12.1], 189). Peirce suggests that irregularity is ‘the overwhelmingly preponderant rule of experience, and regularity only the strange exception’. A mere irregularity, where no definite regularity is expected, he says, creates no surprise; it excites no curiosity. And it is a surprise or an anomaly that throws us into doubt or demands an inquiry to explain the phenomenon. It is an unexpected regularity or the breach of an existing regularity that makes a demand for explanation. It is the interruption of a habit of expectation (a belief) that calls for an explanation. Abduction is ‘the process of forming an explanatory hypothesis’ ([12.1], 5:171) for such regularities. These hypotheses, however, are merely conjectures; we must ‘hold ourselves ready to throw them overboard at a moment’s notice from experience’ ([12.1], 1:634). For an abductive inference ‘commits us to nothing. It merely causes a hypothesis to be set down upon our docket of cases to be tried’ ([12.1], 5:602). So the first stage of inquiry is arriving at a conjecture or an explanatory hypothesis. Peirce argued that abduction and induction are ‘ampliative’ and deduction is ‘explicative’. In explicative inference, the conclusion follows from the premisses necessarily; in ampliative inference, the conclusion amplifies rather than explicates what is stated in the premisses. He argues that ampliative inference is the only kind that can introduce new ideas into our body of belief. Being a form of ampliative inference, abduction allows us to infer, or at least conjecture, from the known to the unknown. We can infer a hypothesis to explain why we observed what we did. The second stage is to deduce consequences or predictions from the hypothesis. The ‘purpose’ of deduction is ‘that of collecting consequents of the hypothesis’. The third stage is that of ‘ascertaining how far those consequents accord with Experience’ ([12.3], 841:44). By induction we test the hypothesis: if it passes, it is added to our body of belief. Peirce sees that the validity of abductive inference is hard to characterize. Its conclusion is not even asserted to be true, for it is a mere conjecture. He says: The hypothesis which it problematically concludes is frequently utterly wrong in itself, and even the method need not ever lead to the truth; for it may be that the features of the phenomena which it aims to explain have no rational explanation at all. Its only justification is that its method is the only way in which there can be any hope of attaining a rational explanation. ([12.1], 2:777) He argues that the reason we are justified in making abductive inferences is that, if we are to have any knowledge at all, we must make them. A logician, Peirce says, should have two goals—he or she should ‘bring out the amount and kind of security…of each kind of reasoning’ and should bring out the ‘uberty, or value in productiveness, of each kind’. ([12.1], 8:384) Abduction is such that ‘though its security is low, its uberty is high’. ([12.1], 8:388). It is the other two kinds of inference to which the notions of security and validity more aptly apply. THE CATEGORIES Peirce expended a great deal of intellectual energy engaging in a project which absorbed Aristotle and Kant—the categories. Peirce’s ubiquitous classificatory scheme—the categories of firstness, secondness, and thirdness—is designed to cover any object of thought. It is a classificatory scheme that takes each category to be an ‘independent and distinct element of the triune Reality’ ([12.1] 5:431). The doctrine is extremely complex, vague and difficult to understand, and, like pragmatism, it permeates Peirce’s work. Peirce had three methods for arriving at his list of categories. The first and earliest one is found in the 1867 ‘On a New List of Categories’. The project is a Kantian one—to find out what ‘is’ or ‘has being’ by ‘reducing the manifold of sense impressions to unity’ via an analysis of the proposition. The second method is an argument from phenomenology, which ‘ascertains and studies the kinds of elements universally present in the phenomenon’ or ‘whatever is present at any time to the mind in any way’. ([12.1], 1:186). Both of these methods aim to show that everything that we experience or identify, i.e. anything that ‘is’, has an element of each of the three categories in it, and that we do not experience anything that goes beyond the three categories. Both the Kantian and the phenomenological derivations of the categories rest on the Aristotelian/Scholastic method of analysis of prescission. This method separates or distinguishes different elements of a concept so that, although we cannot imagine a situation in which one of them is actually isolated, we can tell that the elements are distinct. We can ‘suppose’ one without the other, for we can, by attending to one feature and neglecting others, isolate features of phenomena which are not in fact separable. We can, for instance, suppose space without colour even though colourless space is not imaginable. Prescission, however, is not reciprocal, as it is a matter of discerning a logical priority of notions. Hence, we cannot prescind colour from space—we cannot suppose colour without spatial extension. With respect to the categories, Peirce argues that we can abstract or prescind certain notions from experience and classify them as belonging to one or another of the categories. We can prescind firstness from secondness and we can prescind both from thirdness, but we cannot prescind in the other direction. So the categories are designed to describe the general features of each of the classes of elements that come before the mind or are experienced. Each class is distinct, but its members cannot stand in isolation. Each of the categories is present in everything we experience, but there are many cases in which one or the other of the categories is emphasized or predominant: ‘although they are so inextricably mixed together that no one can be isolated, yet it is manifest that their characters are quite disparate’ ([12.1], 1:284). And the list of three is all that is needed. Perhaps the easiest way to set out Peirce’s doctrine of categories is to concentrate on his third derivation, that which rests on the logic of relations. (This method, however, is discussed by Peirce as being part of phenomenology.) Here the categories are represented by n-place relations. Peirce argued that all relations fall into one of three fundamental classes: monadic, dyadic and triadic. Each is irreducible to the others, and all predicates with more than three places are reducible to triadic ones. For instance, ‘a is red’ is monadic, ‘a hit b’ is dyadic and ‘a gives b to c’ is triadic. A four-place predicate such as ‘a put b between c and d’ is reducible to two three-place ones: ‘a put b in spot e’; ‘spot e is between c and d’. ‘Gives’, on the other hand, is not reducible to ‘a put b down’ and ‘c picked b up’, as the latter set fails to express the intention of a that c should have b. The results of each of the three ways of inquiring into the ultimate categories merge. Here is a brief description of those results, one which does not undertake the intimidating task of sorting out the relationships between all of the things that supposedly manifest each category. The third category involves a medium or connecting link between two things; irreducibly triadic action is such that an event A produces an event B as a means to the production of an event C. Thirdness is characteristically manifested in psychological concepts. For instance, Peirce argues that representation is such that an interpreting thought mediates between sign and object. (One route to Peirce’s claim that all experience is a matter of thirdness is via his argument that everything that we experience is of the nature of a sign or representation. There is no experience independent of our representation of it.) Similarly, we cannot grasp what it is for a to give b to c without the notion of intention mediating between a putting b down and c picking up b. There must be an intention to give on a’s part and a realization of that intention on b’s part. Peirce also says that law and necessity manifest thirdness. A law, or a necessary connection, mediates between the action of one thing upon another, making it more than an accident that they behaved in the way in which they did. Continuity and generality are other instances of thirdness. We can cognitively isolate secondness as the duality of action and reaction without any mediating force. It is brute existence and hence is the modality of actuality. It is found (by prescission) most clearly in the notions of struggle, action/reaction, cause/effect, and brute force. The second category is one ‘which the rough and tumble of life renders most familiarly prominent. We are continually bumping up against hard fact’ ([12.1], 1:324). For We can make no effort where we experience no resistance, no reaction. The sense of effort is a two-sided sense, revealing at once a something within and another something without. There is binarity in the idea of brute force; it is its principal ingredient. ([12.1], 2:84) A First is a simple monadic element. Peirce says that it suggests spontaneity, and it is real ‘regardless of anything else’. In virtue of its very nature, it is indescribable; it can only be grasped by prescission: It cannot be articulately thought: assert it, and it has already lost its characteristic innocence; for assertion always implies a denial of something else. Stop to think of it, and it has flown!…that is first, present, immediate, fresh, new, initiative, original, spontaneous, free, vivid, conscious, and evanescent. Only, remember that every description of it must be false to it. ([12.1], 1:357) These ‘qualities of feeling’ are mere possibilities: I do not mean the sense of actually experiencing these feelings… that is something that involves these qualities as an element of it. But I mean the qualities themselves which, in themselves, are mere may-bes, not necessarily realized. ([12.1], 1:287) So the first category is that of possibility. One upshot of Peirce’s doctrine of categories is that he thinks that reality comes in three grades. He is a ‘realist’ with respect to all of the categories—possibility, actuality and generality are real. He insists that ‘the will he’s, the actually is’s, and the have beens are not the sum of the reals—they only cover actuality. There are besides would be’s and can be’s that are real’ ([12.1], 8:216). And his ‘Scholastic realism’ has it that laws or thirds are real; they are not mere mental constructions. Peirce takes nominalism—the doctrine that ‘laws and general types are figments of the mind’ ([12.1], 1:16)—to be pernicious. He says, ‘the property, the character, the predicate, hardness, is not invented by men, as the word is, but is really and truly in the hard things and is one in them all, as a description of habit, disposition, or behavior’ ([12.1], 1:27 n.1). Peirce thinks that the fact that we can predict things ought to convince us of realism about generals. Realism explains prediction, for, on that theory, laws and dispositions have causal efficacy: ‘if there is any would be at all, there is more or less causation; for that is all that I mean by causation’ ([12.1], 8:225 n.10). If a prediction has a tendency to be fulfilled, it must be the case that future events have a tendency to conform to a general rule. Peirce concludes that some laws or generals are real. Laws and dispositions mediate between possibility (Firstness) and actuality (Secondness)—it is the law that makes the possible actual, for laws or general patterns cause their instances. But Peirce does not think that possibilities and generals actually exist; universals or generals are not ‘things’. The realm of existence is the second category, and so possibilities and generals are real but not existent. METAPHYSICS The doctrine of categories is not Peirce’s only metaphysical venture. But the briefest sketch of these metaphysical positions, which seem to be in a different spirit from the inquiry-directed pragmatic epistemology described in the first six sections, is all that space allows. Peirce was set against determinism or necessitarianism, which he took to be the position that ‘every single fact in the universe is precisely determined by law’ ([12.1], 6:36). His ‘Tychism’, on the other hand, had it that there is absolute chance in the universe—there is spontaneous deviation from the laws of nature. Peirce took a corollory of Tychism to be that physical laws are statistical, something which physics now takes for granted. Tychism is tied to Peirce’s view of evolutionary cosmology, for Tychism has it that there is a tendency toward diversification in the universe. Laws, Peirce argued, evolved from nothing or from ‘pure possibility’. The starting point ‘was not a state of pure abstract being. On the contrary it was a state of just nothing at all, not even a state of emptiness, for even emptiness is something’ ([12.1], 6:215). He usually says that it was pure Firstness. Recall that spontaneity is paradigmatic of Firstness. It is a state which has no existing things (Secondness), compulsion (Secondness), or law (Thirdness): it is a state of pure chance or possibility. From this state of possibility came accidental ‘flashes’ ([12.1], 1:412) which, again accidentally, reacted with one another. That is, Secondness emerged. And from these reactions arose a habit-taking tendency or Thirdness. Peirce says that it is the nature of habit ever to strengthen itself and, thus, laws came into being. Evolution is the process of growth; the world becomes more and more rational and law-bound. This view is connected to Peirce’s claims that our ultimate aim or summum bonum is the perfection of ‘concrete reasonableness’ (see [12.1], 5:3). He was fond of saying that ethics is prior to science and that logic is normative. These claims cover a variety of theses, most of which are compatible with the work on logic canvassed above. For instance, sometimes he means the following: ‘Logic is a normative science; that is to say, it is a science of what is requisite in order to attain a certain aim’ ([12.3], 432:1)—the aim of getting doubt-resistant beliefs. And sometimes he means that logic is critical and involves self-controlled thought, just as morals involves self-controlled conduct (see [12.3], 453). But sometimes, especially towards the end of his life, he means that logic must rest on an inquiry into the ultimate good. It seems to him ‘that the logician ought to recognize what our ultimate aim is. It would seem to be the business of the moralist to find this out, and that the logician has to accept the teaching of ethics in this regard’ ([12.1], 1:611). As commentators have long noted, the attempt to base logic on an ultimate aim of something like perfect rationality seems to be in contradiction to the bulk of his work on logic. That work attempts to offer a naturalistic, non-psychological account of logic. Logic, on that naturalistic view, is intimately tied to the scientific method and to getting beliefs which would not be overturned by recalcitrant experience. Another of Peirce’s metaphysical doctrines is ‘Synechism’, which has it that the notion of continuity is the key to philosophy. Sometimes he says that ‘Synechism is not an ultimate and absolute metaphysical doctrine; it is a regulative principle of logic prescribing what sort of hypothesis is fit to be entertained and examined’ ([12.1, 6:173). But at other times he presents it as highly metaphysical. Like Aristotle, Peirce holds that a continuous series is not a collection of discrete points. A continuous series is rather a possibility of endless further determination. A continuum has no existing parts but only a potential for being divided into parts. The infinite number of points on a continuous line are really places at which a point could be located, they are merely possibles or Firsts rather than actuals or Seconds. Continuity itself is an instance of Thirdness; it is a kind of ultimate mediation. For a continuous series is a path where we can always find one thing between two others. Peirce characteristically tries to link up this example of Thirdness with others, most particularly laws and generality. Another metaphysical debate which Peirce joined is the debate about reality. Sometimes he writes of reality not in the way described above, where reality is the object of perfectly stable beliefs. Instead, he places his view of reality within the idealismmaterialism debate and sides for a kind of idealism. Reality, he says, is nothing but ‘effete mind’—‘what we call matter is not completely dead, but is merely mind hidebound with habits’ ([12.1], 6:158). It is unclear whether this idealism can be reconciled with the view of reality elucidated within Peirce’s account of truth. And it is unclear whether idealism, along with the other metaphysical doctrines touched upon here, can pass the pragmatic test, which requires metaphysical theories to have consequences for practice.4 INFLUENCE The pragmatic theory of truth is very popular these days. Some of the current brands are not the one Peirce himself offered but closer to those of William James and John Dewey, both of whom acknowledged their debt to Peirce. (In the 1900s Peirce renamed his doctrine ‘pragmaticism’ to distinguish it from the positions of James, Schiller, etc. He thought that this new name was ‘ugly enough to be safe from kidnappers’ ([12.1], 5:414).) Richard Rorty’s pragmatism, for instance, while having affinities with Peirce’s, has it that the notion of truth is metaphysical and ought to be abandoned. Peirce, on the other hand, thinks that truth is not only a sensible notion, but, given that it is what inquirers aim for, it is essential for inquiry. W.V.O.Quine (in some moods), Hilary Putnam and Jürgen Habermas are more clearly the inheritors of Peircean pragmatism. Another area where Peirce’s influence is still felt is in the field of semiotics, where many of his distinctions, classifications and terminology still reign. He had influence in the field of logic, but he was a Boolean and that school was eventually edged out of the mainstream by the Fregeans. Schröder adopted Peirce’s notation, and some well known results are written in it.5 And Whitehead seems to have learnt quantification from Peirce. But despite the quantity and quality of his work in formal logic and statistical inference, he is probably best remembered in logic for introducing abductive inference, something which by its very nature cannot be formalized. Unfortunately, Peirce’s lack of success in securing an academic position, his rather abrasive personality and his penchant for cumbersome terminology combined to render his views pretty much inaccessible during his own lifetime. He died penniless and unappreciated. It has been only recently that his work has found the interest it deserves and the excavation it requires. NOTES BIBLIOGRAPHY Works by Peirce 12.1 Peirce, C.S. Collected Papers of Charles Sanders Peirce, ed. C.Hartshorne and P.Weiss (1–6) and A.Burks (7 and 8), Cambridge, Mass.: Belknap Press, 1931–58. 12.2 Peirce, C.S. Writings of Charles S.Peirce: A Chronological Edition, ed. M. Fisch, Bloomington: Indiana University Press, 1982–. 12.3 Peirce, C.S. The Charles S. Peirce Papers, microfilm, Cambridge, Mass.: Harvard University. 12.4 Peirce, C.S. The New Elements of Mathematics, ed. C.Eisle, The Hague: Mouton, 1976. Other works 12.5 Ayer, A.J. The Origins of Pragmatism, London: Macmillan, 1968. 12.6 Dauben, J.W. ‘Peirce’s Place in Mathematics’, Historia Mathematica, 9 (1982):311– 25. 12.7 Dipert, R.R. ‘Peirce’s Prepositional Logic’, Review of Metaphysics, 34 (March 1981):569–95. 12.8 Hacking, I. ‘The Theory of Probable Inference: Neyman, Peirce and Braithwaite’, in D.H.Mellor, ed., Science, Belief and Behavior: Essays in Honour of R.B.Braithwaite, 1 References to Peirce’s Collected Papers, are by volume and paragraph number; to the new Chronological Edition and to The New Elements of Mathematics, by volume and page number. 2 Some of the material in this and other sections is taken from my Truth and the End of Inquiry: A Peircean Account of Truth [12.11]. It is reproduced here by kind permission of Oxford University Press. 3 The psychological hypothesis, however, seems to be false. My suggestion as to how to resolve the difficulty is that Peirce is best read as holding that being responsive to evidence is one of the ‘essentials of belief, without which it would not be belief’ ([12.3], 673:11). Thus, the aim of inquiry is to get beliefs which are not merely fixed, but which are fixed in such a way that they fit with and respond to the evidence. See [12.11]. 4 Peirce did argue against some kinds of idealism on pragmatic grounds: ‘Very well; an idealist…is lounging down Regent Street…when some drunken fellow unexpectedly…lets fly his fist and knocks him in the eye. What has become of his philosophical reflections now?’ ([12.1], 5:539). 5 For instance, Löwenheim’s theorem and Zermelo’s axioms: see Putnam [12.13]. Cambridge: Cambridge University Press, 1980. 12.9 Lenz, J. ‘Induction as Self-Corrective’, in E.C.Moore and R.Robin, eds, Studies in the Philosophy of Charles Sanders Peirce, 2nd series, Amherst: University of Massachusetts Press, 1964. 12.10 Levi, I. ‘Induction as Self-Correcting According to Peirce’, in D.H.Mellor, ed., Science, Belief and Behavior: Essays in Honour of R.B.Braithwaite, Cambridge: Cambridge University Press, 1980. 12.11 Misak, C.J. Truth and the End of Inquiry: A Peircean Account of Truth, Oxford: Clarendon Press, 1991. 12.12 Perry, R.B. The Thought and Character of William James, Boston: Little, Brown, 1936. 12.13 Putnam, H. ‘Peirce the Logician’, Historia Mathematica, 9 (1982):290–301.

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