A fundamental statement of Tarski's Theory of Truth is that truth is a property of sentences. What does this statement mean?

  1. What kind of Truth is it referring to?
  2. What is the formal definition of 'property'?
  3. Can we formalise process of learning? When I read about a concept, can I apply this theory to understand it better?
  • See Tarski’s theory of truth. In a nutshell, when we use in our everyday language the expression "...it is true" what we put in the place-holder (...) is the name of a sentence. – Mauro ALLEGRANZA Jan 11 at 20:23
  • And see Properties : "Properties are those entities that can be predicated of things or, in other words, attributed to them." In the sentence "the apple is red" we are predicating the property "to be red" (or redness) of the thing apple. – Mauro ALLEGRANZA Jan 11 at 20:26
  • What does it mean : "When I read about a concept, can I apply this theory to understand it better?" ... When you read a scientific textbook, we usually assume that what is writetn in it is true; when we are reading a novel, we don't. – Mauro ALLEGRANZA Jan 11 at 20:39
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    Tarski's intention was to formulate minimal conditions that any reasonable theory of truth would meet (there are non-Tarskian ones, but most of them do). No, you can not use it to formalize learning, for that you need a substantive theory of truth, a theory of meaning, and a lot more. There is no formal definition of "property", it is an informal notion, which is notoriously vague. In formal languages properties are represented by one-place predicates. – Conifold Jan 12 at 4:39
  • Davidson developed a theory of meaning inspired by Tarskian semantics that he does use to reconstruct how a linguist could learn ("interpret") a completely unfamiliar language, see Radical Interpretation on IEP – Conifold Jan 13 at 11:25

I don't think it is the fundamental statement of Tarski's theory, but nevertheless an important one.

  1. The kind of truth that applies to sentences, but not the truth as in "he is a true friend".

  2. In this context there is no formal definition of property and there doesn't need to be. The emphasis is "...is a property of sentences". There are other possible choices, for example truth could be a property of beliefs, or propositions, or thoughts, or ideas, or... In Tarski's theory sentences are the truthbearers.

  3. You can learn how to do something, and also that something is true/false. Are you referring to this second kind of learning? Belief Revision is a model of how to update a set of sentences that are believed by a rational agent, if a new sentence "is learned". But this only formalises learning insofar it says what is learned, but not how and when and why. Regarding your last question, no, a theory of truth won't help you in understanding difficult concepts better. Understanding a concept is very different from knowing its truth condition.

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