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Truth

In one classical formulation, truth is defined as the good of logic, where logic is a normative science, that is, an inquiry into a good or a value that seeks knowledge of it and the means to achieve it. In this view, truth cannot be discussed to much effect outside the context of inquiry, knowledge, and logic, all very broadly considered.

Theories of truth

Most inquiries into the character of truth begin with a notion of an informative, meaningful, or signficant element, the truth of whose information, meaning, or significance may be put into question and needs to be evaluated. Depending on the context, this element might be called an artefact, expression, image, impression, lyric, mark, performance, picture, sentence, sign, string, symbol, text, thought, token, utterance, word, work, and so on. Whatver the case, one has the task of judging whether the bearers of information, meaning, or signficance are indeed truth-bearers. This judgment is typically expressed in the form of a specific truth predicate, whose positive application to a sign, or so on, asserts that the sign is true.

Considered within the broadest horizon, there is little reason to imagine that the process of judging a work, that leads to a predication of false or true, is necessarily amenable to formalization, and it may always remain what is commonly called a judgment call. But there are indeed many well-circumscribed domains where it is useful to consider disciplined forms of evaluation, and the observation of these limits allows for the institution of what is called a method of judging truth and falsity.

One of the first questions that can be asked in this setting is about the relationship between the significant performance and its reflective critique. If one expresses oneself in a particular fashion, and someone says "that's true", is there anything useful at all that can be said in general terms about the relationship between these two acts? For instance, does the critique add value to the expression criticized, does it say something signficant in its own right, or is it just an insubstantial echo of the original sign?

Theories of truth may be described according to several dimensions of description that affect the character of the predicate "true". The truth predicates that are used in different theories may be classified by the number of things that have to be mentioned in order to assess the truth of a sign, counting the sign itself as the first thing. In formal logic, this number is called the arity of the predicate. The kinds of truth predicates may then be subdivided according to any number of more specific characters that various theorists recognize as important.

  1. A monadic truth predicate is one that applies to its main subject — typically a concrete representation or its abstract content — independently of reference to anything else. In this case one can say that a truth bearer is true in and of itself.
  2. A dyadic truth predicate is one that applies to its main subject only in reference to something else, a second subject. Most commonly, the auxiliary subject is either an object, an interpreter, or a language to which the representation bears some relation.
  3. A triadic truth predicate is one that applies to its main subject only in reference to a second and a third subject. For example, in a pragmatic theory of truth, one has to specify both the object of the sign, and either its interpreter or another sign called the interpretant before one can say that the sign is true of its object to its interpreting agent or sign.

Several qualifications must be kept in mind with respect to any such radically simple scheme of classification, as real practice seldom presents any pure types, and there are settings in which it is useful to speak of a theory of truth that is "almost" k-adic, or that "would be" k-adic if certain details can be abstracted away and neglected in a particular context of discussion. That said, given the generic division of truth predicates according to their arity, further species can be differentiated within each genus according to a number of more refined features.

Correspondence theories

The truth predicate of interest in a typical correspondence theory of truth tells of a relation between representations and objective states of affairs, and is therefore expressed, for the most part, by a dyadic predicate. In general terms, one says that a representation is true of an objective situation, more briefly, that a sign is true of an object.

The nature of the correspondence may vary from theory to theory in this family. The correspondence can be fairly arbitrary or it can take on the character of an analogy, an icon, or a morphism, whereby a representation is rendered true of its object by the existence of corresponding elements and a similar structure.

"A correspondence theory of truth represents a rejection of any sort of relativism about truth that extends further than the dyadic relation of interest, maintaining that the truth or the falsity of a representation is determined in prinicple solely by how it relates to objective reality, namely, by whether it accurately describes (that is, corresponds with) that reality. The correspondence theory can be said to see truth as correspondence with objective reality." (This paragraph mostly by previous contributors).

In practice, however, this ideal cannot be achieved ab initio, but has to be arrived at by beginning with predicates and relations that are higher than dyadic, and only gradually abstracting away from them. For example, analyses of correspondence that are cast within particular languages are forced to admit the particular language in question as an additional parameter at the outset of theoretical work, and only gradually construct a language independent truth predicate by means of a careful theory of translation among different languages. There are strong theoretical limitations on the extent to which this can be done.

Pragmatic theories

Peirce defines truth in the following way:

Truth is that concordance of an abstract statement with the ideal limit towards which endless investigation would tend to bring scientific belief, which concordance the abstract statement may possess by virtue of the confession of its inaccuracy and one-sidedness, and this confession is an essential ingredient of truth. (Peirce 1901, CP 5.565).

This says that ideas of approximation, incompleteness, and partiality, what Peirce describes elsewhere as fallibilism and "reference to the future", are of the essence for a proper conception of truth. Although Peirce uses words like concordance and correspondence to describe one aspect of the pragmatic sign relation, he is also quite explicit in saying that definitions of truth based on mere correspondence are no more than nominal definitions, which he relegates to a lower status than real definitions.

Now thought is of the nature of a sign. In that case, then, if we can find out the right method of thinking and can follow it out — the right method of transforming signs — then truth can be nothing more nor less than the last result to which the following out of this method would ultimately carry us. In that case, that to which the representation should conform, is itself something in the nature of a representation, or sign — something noumenal, intelligible, conceivable, and utterly unlike a thing-in-itself. (Peirce, CP 5.553, 1906)

Peirce's theory of truth depends on his theory of sign relations and his theory of inquiry. Inquiry is seen as a process that transforms signs in regard to an object, and it includes all forms of belief revision and logical inference, including scientific method. A sign-to-sign transaction in respect of an object is a relationship that involves three roles. In logic, this is called a ternary or triadic relation. In sum, pragmatism involves a triadic theory of truth.

Philosophy of truth (23 April 2006)

Philosophical discussions of truth can be sorted according to what they take as their subject matter and what they regard as legitimate to say about their subject matter. The two kinds of terms involved in this may be called the subjects and the predicates of the discussion, respectively. It is conventional to refer to a distinctive philosophical treatment of a particular subject matter as a theory, whether or not it ever becomes a theory in the logical sense. The body of this article bows to that convention, right up until the point where it becomes necessary to take up more precisely logical treatments of truth.

JA: Yes, it was deliberately written to be as logically generic as possible. But it did introduce the general idea of a "subject matter", allowing for later speciation according to each theory's taste, and it did sneak in, with an informal definition in passing, the dread word "predicate", in a way that is natural enough in everyday discourse. Maybe that seems trivial, but we've been stuck on that kind of trivial for quite some time, and this move at least hops past it a step. Jon Awbrey 14:42, 23 April 2006 (UTC)

JA: Another serious problem with the article, for those that have been trying to read past the introduction, is the two ways that the word "theory" is used: (1) its informal use to indicate any distinctive philosophical attitude, doctrine, perspective, or position, (2) its more sacrosanct usage by log, math, and model theory communities. It's not worth the bother right now, but I'll eventually have to differ with Kenosis about how many theorists post-Tarski really are theorists in the more holy sense of the word. At any rate, it's a good idea to try and forestall the eventual confusion that is bound to arise. Jon Awbrey 15:00, 23 April 2006 (UTC)

Onward and upward and back again

I'm glad to see the article moving forward. Does anyone know what to do about Kripke? He seems to be a major philosopher, but if his work is based on Russell and Whitehead, that should be mentioned, and his theory of truth (basically hierarchical) should be together with similar theories (Robust? Or have we abandoned that word?). Rick Norwood 14:12, 23 April 2006 (UTC)

JA: Here's the section intro as I last left it:

Philosophy of truth

Philosophical discussions of truth can be sorted according to what they take as their subject matter and what they regard as legitimate to say about their subject matter. The two kinds of terms involved in this may be called the subjects and the predicates of the discussion, respectively. It is conventional to refer to a distinctive philosophical treatment of a particular subject matter as a theory, whether or not it ever becomes a theory in the logical sense. The body of this article bows to that convention, right up until the point where it becomes necessary to take up more precisely logical treatments of truth.

JA: I know that it's probably a waste of time and energy working on a weekend, as sheer novelty impacting on Monday-morning-moodiness is likely to get 3 days' work reverted without a second's consideration, but let me try to explain anyway some of the outstanding problems in the article that the above wedge is intended to ease the way toward alleviating.

JA: Yes, it was deliberately written to be as logically generic as possible. But it did introduce the general idea of a "subject matter", allowing for later speciation according to each theory's taste, and it did sneak in, with an informal definition in passing, the dread word "predicate", in a way that is natural enough in everyday discourse. Maybe that seems trivial, but we've been stuck on that kind of trivial for quite some time, and this move at least hops past it a step. Jon Awbrey 14:42, 23 April 2006 (UTC)

JA: Another serious problem with the article, for those that have been trying to read past the introduction, is the two ways that the word "theory" is used: (1) its informal use to indicate any distinctive philosophical attitude, doctrine, perspective, or position, (2) its more sacrosanct usage by log, math, and model theory communities. It's not worth the bother right now, but I'll eventually have to differ with Kenosis about how many theorists post-Tarski really are theorists in the more holy sense of the word. At any rate, it's a good idea to try and forestall the eventual confusion that is bound to arise. Jon Awbrey 15:00, 23 April 2006 (UTC)

RN: Let's see if we can spend the weekend finding a compromise, then, since I assume most people only Wiki while goofing off from work. : )

JA: On another note, my section introduction is not intended as a mere segue to the flationary dispute, as that is hardly the only thing worth talking about when it comes to truth, but is when viewed in a broader perspective but a mere sideshow of late 20th century linguistic-analytic approaches to a certain sector of the subject. It reflects an extremely parochial and peculiar POV to suggest that this quidditch-quibble is the only game in town. Jon Awbrey 15:45, 23 April 2006 (UTC)

RN: I think quidditch-quibble is a good description of the whole flationary argument. My change in the paragraph in question was based on style, not substance. Do you think it is worth working toward a compromise? Rick Norwood 16:09, 23 April 2006 (UTC)

JA: My efforts here are precisely directed toward working out a compromise with the large number of established stakeholders to the same territory. If you are interested in that sort of compromise, then we already have a common charge. My first try at a compromise generated an inclusive list of subject matter terms that I know various stakeholders to use. That was quite understandably judged unwieldy, so my next attempt at conciliating the various participants, living and dead, was to introduce the generic term "subject matter" to cover them all. Given that start, it will now be easier to add more specific terms in their proper contexts, with the benefit of a covering generalization. Likewise for the variety of truth predicates. So that's my plan for a compromise. Jon Awbrey 16:22, 23 April 2006 (UTC)

Good. We still need a reference to at least one authority who uses the phrase "truth bearer". Do you know one? Rick Norwood 17:58, 23 April 2006 (UTC)

Pragmatic theory of truth (18 Apr 2006)

Pragmatic theory of truth refers to those accounts, definitions, and theories of the concept truth that distinguish the philosophies of pragmatism and pragmaticism. The conception of truth in question varies along lines that reflect the influence of several thinkers, initially and notably, Charles Sanders Peirce, William James, and John Dewey, but a number of common features can be identified. The most characteristic features are (1) a reliance on the pragmatic maxim as a means of clarifying the meanings of difficult concepts, truth in particular, and (2) an emphasis on the fact that the product variously branded as belief, certainty, knowledge, or truth is the result of a process, to wit, inquiry.

Peirce

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Very little in Peirce's thought can be understood in its proper light without understanding that he thinks all thoughts are signs, and thus, according to his theory of thought, no thought is understandable outside the context of a sign relation. Sign relations taken collectively are the subject matter of a theory of signs. So Peirce's semeiotic, his theory of sign relations, is key to understanding his entire philosophy of pragmatic thinking.

That truth is the correspondence of a representation with its object is, as Kant says, merely the nominal definition of it. Truth belongs exclusively to propositions. A proposition has a subject (or set of subjects) and a predicate. The subject is a sign; the predicate is a sign; and the proposition is a sign that the predicate is a sign of that of which the subject is a sign. If it be so, it is true. But what does this correspondence or reference of the sign, to its object, consist in? (Peirce, CP 5.553, 1906).

Here Peirce makes a statement that is decisive for understanding the relationship between his pragmatic definition of truth and any theory of truth that leaves it solely and simply a matter of representations corresponding with their objects. Peirce, like Kant before him, recognizes Aristotle's distinction between a nominal definition, a definition in name only, and a real definition, one that states the function of the concept, the reason for conceiving it, and so indicates the essence, the underlying substance of its object. This tells us the sense in which Peirce entertained a correspondence theory of truth, namely, a purely nominal sense. To get beneath the superficiality of the nominal definition it is necessary to analyze the notion of correspondence in greater depth.

In preparing for this task, Peirce makes use of an allegorical story, the moral of which is that there is no use seeking a conception of truth that we cannot conceive ourselves being able to capture in a humanly conceivable concept. So we might as well proceed on the assumption that we have a real hope of comprehending the answer, of being able to "handle the truth" when the time comes. Bearing that in mind, the problem of defining truth reduces to the following form:

Now thought is of the nature of a sign. In that case, then, if we can find out the right method of thinking and can follow it out — the right method of transforming signs — then truth can be nothing more nor less than the last result to which the following out of this method would ultimately carry us. In that case, that to which the representation should conform, is itself something in the nature of a representation, or sign — something noumenal, intelligible, conceivable, and utterly unlike a thing-in-itself. (Peirce, CP 5.553, 1906).

This statement tells us that Peirce's theory of truth depends essentially on two other, imtimately related subject matters, namely, his theory of sign relations and his theory of inquiry, inquiry being a species of semiosis, that is, a process that transforms signs in a specific manner. The statement tells us somthing more: Peirce, having started out in accord with Kant, is here giving notice that he's parting ways with the Kantian notion of an unknowable thing-in-itself as the ultimate object of a representation. Peirce would say that the object is known by its representation, however partially, to the extent that it is known at all.

Semiosis is a process that transforms signs into signs while maintaining a given regard to an object, which object may be lodged off the path of signs or else reside at the end of it. To consider a sign to sign transaction involving an object is thus to consider a transaction that involves three parties, or a relationship that involves three roles. In logic, this is called a ternary or triadic relation.

Putting roller skates on the horse

JA: That's not how the Automobile got invented. The way I see it, a lot of time and ingenuity is being wasted on a system of citation that experienced scholars just plain don't use anymore, and never will again, for all sorts of reasons that would be immediately obvious here if WikiPedians had a longer history of actually sourcing their contributions in any routine and systematic way. Here are some of things that normally become obvious when you do this all the time.

  1. Once you get more than a dozen or so items in your list of references and/or bibliography, then it's time to use an alphabetized list for both.
  2. The list of references needs to be in one place, not scattered throughout the text. This allows for (1) easy error correction and omission checking, by virtue of the parallel comparison of literature entries that it facilitates, (2) extracting the references whole hog from an article, as scholars already familiar with a topic often find that the literature section is the only thing of real interest, for instance, if it cites sources that they haven't seen before. Further, this practice helps to prevent the erosion of accurate citations that inevitably occurs as editors will tend to use more and more abbreviated reference entries as time goes on.

JA: I'll add some more items as they occur to me. Jon Awbrey 12:26, 20 April 2006 (UTC)

Is solipsism falsifiable? (12 May 2006)

Solipsism is sometimes said to be unfalsifiable, but this confuses a question of logic, namely, the logical contingency of the solipsistic thesis by virtue of its logical form, with a question of rhetoric, namely, the practical difficulties of persuading a particular person, with a particular psychological constitution, of the contingency thereof. But the normative science of logic is quite distinct from the descriptive science of psychology, and has nothing to do with the peculiarites of an individual person's thought process.

To say this another way, not all solipsists need be alike. Some may see the possibility that their solipsistic hypothesis is false, even if some do not, just as a person may accept any other hypothesis on a provisional basis and yet see the possibility of its being shown false. To say that solipsism is unfalsifiabile is to say that it is a necessary truth, a tautology. But such a claim cannot be supported by the existence or the possibile existence of a diverse population of solipsists. The usual run of argument for solipsism being indefeasible picks a hypothetical case from this population, one that is hypothesized to be the worst possible case. The imagination of such a case is often very diverting, but it begins as insufficient reasoning and ends the same way.

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 «Mÿšíc»  (T) 20:15, 8 May 2006 (UTC)