Philosophy of
Logics
Week 10: Theories of Truth 1
- Traditional Theories
Brief Sketch: Traditional Theories
- Coherence theories take truth to consist in relations of coherence among a set of beliefs. - Correspondence theories take the truth of a proposition to consist in its relation to the world, its correspondence to the facts.
- The pragmatist theory has affinities both
coherence and correspondence theories. Such a theory says that a proposition is true exactly when accepting it serves a purpose.
Brief Sketch: Semantic Theories
- In Tarski's account, truth is defined in terms of satisfaction, a relation between open sentence and non-linguistic object.
- The redundancy theory of truth claims that
"true" is redundant, for to say that it is true that
p is equivalent to saying that p.
* Proponents of these theories take different views about what kinds of entities are
truth-bearers (e.g., beliefs, sentences, propositions, etc.)
Definitions vs. Criteria of Truth
But exactly what are these theories meant to be?
● Definitions: They are meant to be theories of
what truth is.
● Criteria: They are meant to be guidelines about how to judge whether the given
Definitions vs. Criteria of Truth (ct.)
● Bradley seems to allow that an account of the meaning of truth may require appeal to something like correspondence, while
coherence is rather a mark, a test, of truth. ● Blanshard, by contrast, insists that truth
consists in coherence, which is a definition
as well as a criterion. For there must be some intimate connection between a
dependable criterion and what it is a criterion
Definitions vs. Criteria of Truth (ct.)
Here is Blanshard's argument against Bradley's view that correspondence offers a definition
and coherence provides a criterion of truth:
P1. If Bradley is right, coherence will not be a guaranteeing criterion of truth.
P2. If coherence is not a guaranteeing criterion, we will never know any truth. P3. But we do know some truth.
C. Therefore, Bradley is wrong. Rescher rejects P2. (How?)
Definitions vs. Criteria of Truth (ct.)
Rescher proposes to deflect this argument by disinguishing two kinds of criteria:
● Guaranteeing criterion: C is a guaranteeing criterion of x if necessarily (C iff x obtains). ● Authorizing criterion: C is said to be an
authorizing criterion of x when C is good evidence of x but it is not necessarily the case that (C iff x obtains)
According to him, an authorizing criterion can be useful judging whether x obtains even
Correspondence Theory of Truth
This is perhaps the best known, and arguably the most intuitive theory of truth:
[a is F] is true IFF a corresponding fact, a's being F, holds in the world,
where [a is F] is an atomic proposition consisting of individual a and universal
F(-ness).
Q1. How do we define correspondence? Q2. How about non-atomic propositions?
Correspondence Th. of Truth (cont.)
By the way, here is some history about logical
atomism:
● According to Wittgenstein, the world is the totality of atomic facts, not of things.
● Russell augments this idea with his
epistemological view that individuals and universals constituting such facts, or
simples, are the target of direct acquaintance.
(He also thought that only names referring to such simples are genuine names, all others being reducible to definite descriptions.)
Correspondence Th. of Truth (cont.)
Numerous critics have observed that the trouble with the correspondence theory is that its key
idea, correspondence, is not adequately clear. [The cat is to the left of the man]
Above, the proposition consists of roughly three elements (the cat, being to the left, and the
Correspondence Th. of Truth (cont.)
This example raises several worries:
1. To make this isomorphism perfect, you will have to admit the existence of [being to the left of] as a universal. Seems to be no
problem for a universal realist, but you may fall into the trap of infinite regress. (Bradley!) 2. It might be difficult to apply this theory to
sentences. For you will need atomic
sentences which stand in the relation of isomorphism to atomic facts. Might be no problem when applied to an ideal language.
Coherence Theory of Truth
According to the coherence theory of truth,
Belief B is true IFF B coheres with a set of other truth-bearers.
Blanshard's argument for this theory is that, if B's truth consists in the correspondendence between B and a fact, the latter being entirely independent from our mind, then we will never be able to know S's truth. (Why?) So, in order to avoid skepticism, we should adopt the
Coherence Theory of Truth (cont.)
Some history: Logical positivists originally subscribed to the correspondence theory of truth, but they faced with two problems:
(i) That theory seems to be incompatible with their main tenet, the verification principle,
according to which all truths are verifiable.
(ii) It requires an ideal language (protokolsatze, as they called it) whose sentences stand in a perfectly isomorphic relation to facts.
Recognizing these problems, Otto Neurath suggested changing to the coherence theory.
Coherence Theory of Truth (cont.)
So Neurath's motivation for coherence theory was essentially epistemological.
By contrast, Bradley supported a similar theory based on his metaphysical view. According to him, the reality is an organically connected
whole, any correspondence to a part of which gives only partial truth. Hence, he thought that coherence within the entire system of beliefs, which resembles the entirety of reality, is the mark of truth.
Coherence Theory of Truth (cont.)
So the proponents of the coherence theory have adopted it (mainly) for epistemological
reasons, but this did not rule out that coherence plays an important role in our metaphysics.
Still, there is a difficult question:
Q. How do we define coherence? (Compare with "How to define correspondence?")
Rescher suggests that maximally consistent set of beliefs (in short: MCS) provides a reliable
test of truth. But there will be a multiple # of MCS.
Pragmatic Theory of Truth
These views are often associated with two early American philosophers, Peirce, James, and Dewey. It is very hard to tell exactly what they wanted to say about truth. But they seem to have been, at least, committed to this
slogan;
Truth is satisfactory to believe.
Unfortunately, this does not look like a definition of truth. I take it that they meant something like:
Pragmatic Theory of Truth (cont.)
But even that biconditional seems to be incomplete as a definition of truth. For
satsifaction is a purpose-relative concept. (It might be satisfactory to be with Tom for the purpose of business, but not for that of
romance.) So we have to fill out the blank in:
p is true IFF it is satsifactory to believe p for
the ____ purpose.
Peirce takes this purpose to be purely
epistemic, while James arguably allows it to be practical.
Pragmatic Theory of Truth (cont.)
This leads to the following theories:
(Pragmaticism) p is true IFF it is satsifactory to believe p for the epistemic purpose.
(Pragmatism) p is true IFF it is satisfactory to believe p for the practical purpose.
Each theory faces with difficulties. If the epistemic purpose is understood as the
purpose of acquiring truth beliefs and avoiding false beliefs, then it becomes circular. Russell criticizes pragmatism as "identification of truth with congenial beliefs."
Pragmatic Theory of Truth (cont.)
So, to defend pragmaticism, it is necessary to
explain the notion of "epistemic purpose" without any of use of truth/falsity. Peirce suggests:
Truth is the end of inquiry.
More elaborately, truth is a stable belief at which we come to arrive as a result of a (usually long) inquiry based on a scientific method. Since the reality
restricts what beliefs you come to arrive, Peirce's theory of truth is taken to be compatible with the correspondence theory of truth.
Pragmatic Theory of Truth (cont.)
James's view is distinguished from Peirce's in two aspects:
First, James tends to take a less realistic
stance to the notions of truth and inquiry. So he does not share Peirce's view that reality
restricts, based on scientific methods, how an inquiry can proceed.
Second, James sometimes speaks of the true as "being good," the "expedient," the "useful." Russell criticizes James exactly in this aspect.
Pragmatic Theory of Truth (cont.)
Dewey adopts Peirce's definition as "the best definition of truth." But he prefers the
expression "warranted assertability" to "truth, and adds the thesis that it is precisely
warranted assertability that characterizes those beliefs to which we give the honorific title,
Realism vs. Anti-Realism
In comparison with the correspondence theory of truth, the coherence and pragmatic theories do not so much emphasize the role of reality in determining what is true and what is false. So the correspondence theorists are often realists:
(Realism) There exists reality independent from mind and language, and this reality determines the truth, but in general, not
vice-versa.
(Anti-Realism) Everything that determines the truth is dependent on mind or language.
Realism vs. Anti-Realism (continued)
The coherence and pragamtic theorists often accept this principle:
(Verification Principle) For any p, If there is no way to determine whether p is true, then p
cannot be true.
So, if one cannot decide whether p coheres with other belief or not, or if it is impossible to decide if
p is true or false based on a scientific method, then p is neither true nor false. So those theories allow
Correspondence & The Classic
Notion of Logical Consequence
Now, why is the debate on truth so important in the philosophy of logic? It is because logical
consequence, the main topic of phil. of logic, is defined in terms of truth. Furthermore, the
correspondence theory states that p is true exactly when the corresponding fact f exists. Arguably, existence is not a matter of degree, but a matter of all-or-nothing. So there is no case in which a premise or conclusion is, for example, half-true and half-false at the same time.
The Fuzzy Notion of Logical
Consequence
By contrast, p might cohere with one's other beliefs better than q does, so that p is truer than q
according to the coherence theory. Similarly, it might be more satisfactory to believe p than to
believe q, so that p is truer than q accoridng to the pragmatic theories. Now suppose that, in some
case, A is almost true and B almost false, but in no possible case, A is perfectly true and B perfectly false. Should we say that A//B is valid? Perhaps, the fuzzy notion of logical consequence can solve this kind of problem.
Summary
● Traditional theories of truth include the
correspondence, coherence, and pragmatic theories.
● The correspondence theory is arguably the most important, but it requires (i) the
introduction of facts to our ontology and (ii) the definiton of correspodence between facts and propositions/sentences.
● The cohrence theories say that truth consists in coherence within a set of beliefs, but it is not so easy to tell what coherence is.
Summary (continued)
● Pramatic theorists think that a proposition is true if it is satisfactory to believe it, but for what purpose? It might be either an
epistemic purpose or a pragmatic one. In either way, they have to deal with
philosophical problems.
● The realists often favor the correspondence theory of truth, while the coherence or
pragmatic theorist are often anti-realists.
● If you are a coherence or pragmatic theorist, you will perhaps have to consider fuzzy logic more seriously.
