Truth has been, and still is, one of the most important topics in the history of philosophical thought. How to get truth from falsity, how to approach the truth, or the connection between truth, wisdom and the sense of life, all that has been the object of never-ending debates which anyone familiar with philosophy will recall without problems. The nature of truth itself is one of the most central philosophical problems: what kind of property it is, and what types of objects or entities can have it or not have it. For the one looking for deep answers to those questions, this article will perhaps be a little bit disappointing, for I shall introduce what is surely the most ‘minimalist’ (and recent) account of truth: the so-called ‘prosentential’ theory of truth.
Before explaining the notion of ‘prosentences’ on which the theory is based, it is interesting to begin by putting an apparently simple question, not directly regarding to the concept of truth, but to the terms ‘truth’ or ‘true’: what do we gain by having those terms in our language? I.e., what things can we say, or express, thanks to those terms, that we could not express, or refer to, without them. This seems a weird question. “If our language hadn’t the term ‘true’, we could not say that such and such things are true; it’s simple, isn’t it?” Well, not so. One might acknowledge that, ‘true’, as almost any other word in the language, could be thought to be a little bit redundant because one might substitute each use of a particular word with its definition or by means of a periphrasis (e.g., English does not have a word for each single variety of each species of rodents existing in the world, but we can refer to those varieties with more complex expressions when we need it). Nevertheless, the problem with the word ‘true’ is that it seems to be redundant not just in this general and uncontroversial sense, but in a much deeper way. After all, what we mean when we say that ‘Euclides theorem is true’ is exactly what Euclides theorem says, that there are infinite prime numbers. We express exactly the same fact about numbers in saying ‘there are infinite prime numbers’ as in saying ‘it is true that there are infinite prime numbers’. This property of the term ‘true’ is so important that it is taken to be (at least according to the polish logician and mathematician Alfred Tarski1, and to most philosophers after him) as a requisite any adequate definition of ‘true’ must fulfil:
The sentence ‘X’ is true if and only if X
The sentence ‘there are infinite prime numbers’ is true if and only if there are infinite prime numbers
Actually, the prosentential theory of truth shares with other modern views on the topic the assumption that this is not only a requisite of any acceptable definition of ‘true’, but the thesis that it is the only thing that has to be contained in such a definition. These modern theories are called ‘disquotational’ (because what ‘true’ makes is something to ‘transform’ the ‘X’ with inverted commas into something equivalent to the X without them) or ‘deflationary’ (because they say that anything else –in particular, anything metaphysical or epistemological– is superfluous for our understanding the concept of truth) (See David, 19962; Hill, 20023, and McGrath, 20004).
So, it is not that the meaning of the term ‘true’ could be expressed by using a periphrasis instead of that word; the curious thing is that the term ‘true’ seems not to add absolutely anything to those objects (sentences or propositions) it is applied to. Hence our initial question: if by saying that the sentence ‘there are infinite prime numbers’ is true we express exactly the same as by saying that there are infinite prime numbers… why we bother in having the word ‘true’ at all?
Of course, a little reflection shows that there are cases in which the use of that term is not so redundant, or at least, not so idle. For example, imagine that teenager Rose has narrated to her mother Louise what she was doing in the past evening’s party; not believing too much her daughter, Louise asks Rose’s friend Mary, and the latter answers:
It (i.e., what Rose has told) is true
Mary could have repeated all that Rose had said, but this would be cumbersome, at least; it is simpler just to say that all was true. More importantly, there are cases in which it would be much more difficult to say all the relevant things. For example, Rose might say something like
Everything Rose will tell you is true,
even if Rose still does not know what Rose will tell her mother, perhaps in the following days. (Note: it is irrelevant for our discussion whether what Rose tells is true or false –of course, most of it, and probably the most relevant things, will be false in a case like this–, for we are only thinking about what Mary means in using the word ‘true’ in connection to what Rose says, not about whether Mary thinks this is true or not).
In even more interesting cases, it can even be impossible to know in advance all the propositions or sentences to which we are applying the term, as in the following examples:
All logical consequences of true axioms are true
If the prediction of a theory is not true, then we have to reject the theory.
We cannot just substitute the word ‘true’ in propositions like these ones with the sentences to which that word is referring… because we don’t know what sentences they are, and, more importantly, because those propositions are meaning to be universal, applicable to an infinitude of cases, nor just to something we can list. So, the word ‘true’ is in the end not so redundant as it seemed. Actually, it is even less redundant as many other terms, since it is difficult even to imagine with what other word or periphrasis we could substitute the occurrence of ‘true’ in our two last propositions.
I shall leave you thinking about this question till the next chapter of this series. Hope this can serve to make more sense of the problem ‘what is the word ‘true’ good for’.
- Tarski, A. 1983, Logic, Semantics, Metamathematics, papers from 1923 to 1938, ed. John Corcoran, Indianapolis: Hackett Publishing Company. ↩
- David, M., 1996. Correspondence and Disquotation: An Essay on the Nature of Truth, New York: Oxford University Press. ↩
- Hill, C., 2002. Thought and World: An Austere Portrayal of Truth, Reference, and Semantic Correspondence, Cambridge: Cambridge University Press. ↩
- McGrath, M., 2000. Between Deflationism and Correspondence, New York: Garland Publishing. ↩