Piero Scaruffi(Copyright © 2013 Piero Scaruffi | Legal restrictions )
These are excerpts and elaborations from my book "The Nature of Consciousness"
What is a theory of truth? Let's take an example from Physics, a science that is famous for theories. A theory of electricity is an explanation of the nature and cause of electricity and a set of laws that electrical phenomena obey. A theory of truth is essentially an explanation of the nature of truth and a set of laws that "true" things obey.
Electricity is the property that all electrical things share. What is the property that all true statements have in common?
Why is a theory of truth important? Because that is what, ultimately, our cognitive life is all about: truth. Whenever we analyze a scene, whenever we analyze a statement, whenever we recall a memory, whenever we do anything with our brain, we are on a quest for truth.
Our cognitive life is a continuous struggle for truth: is that stain in the distance a tree? Is she home tonight? Will my flight take off on time? Why did the Roman empire fall?
Our mind, ultimately, is an organ to identify truth. The meaing of our life is truth.
The most intuitive theory of truth is perhaps the "correspondence theory of truth", that relates truth to reality: a statement is true if and only if the world it describes is real. Truth corresponds to the facts. The statement "Snow is white" is true in virtue of the fact that snow is, indeed, white. The statement "My name is Piero" is true in virtue of the fact that my name is, indeed, Piero. And so forth.
There are several problems with this theory of truth. The truth predicate (the expression "is true") acts as an intermediary between words (language, mind) and the world. One problem is that this definition of truth relates two things that are very different in nature and it is not clear how we can find a correspondence between things that belong to different realms. Precisely, statements (such as "Snow is white" and "My name is Piero") are mental objects. They are in my head. The reality we compare them with is made of objects, such as snow. A statement is made of a number of words (each of which may present its own problems at close scrutiny). The reality it refers to is made of objects and properties of objects. Is there truly a correspondece between the words "Snow is white" and the fact that snow is white? How can we compare two things that are different in nature, such as a mental object and a physical fact?
This point is important because we are supposed to define truth outside us: truth must not depend on us, it must depend on the world. Something is true not because i think so, but because there is some objective truth out there in the world. If this is the case, the problem is: how can a mental object like a statement relate to an object that is outside the mind.
Second, most statements just do not accurately reflect reality: is snow white? Not really. The closer you look at snow the less white it is. Is today a "hot" day? Yes, if you don't start arguing about which temperature qualifies for hot.
The first objection can be answered by observing that, if you believe in modern science, we rarely talk about things that exist and mostly talk about things that our brain presents us with. I don't know if there exists snow. My brain shows me something that we named snow, but quantum physics tells me that there is only a clod of particles. I see white, but quantum physics tells me that there is a stream of photons. And so forth. When we say that snow is white, we are not referring to something that exists in the world (it may or it may not exist). We are referring to something that is happening in our brain: our brain received some inputs from the senses and generated the perception of snow and of white. Therefore, both statements and "reality" are mental objects, and it is perfectly legitimate to relate a mental object such as the statement "Snow is white" to a mental object such as the perception or the memory that snow is white.
We can rephrase the correspondence problem in neural terms. A statement (for example, about the snow being white) is a neural pattern in the brain. The fact that snow is white is also a neural pattern in the brain (either a pattern of recalling a memory of snow or a pattern of perceiving the snow). It is perfectly legitimate to compare two patterns of brain activity.
The Polish mathematician Alfred Tarski found his own solution to the problems of the correspondence theory.
Alfred Tarski's theory of truth has two components. First, he defines a true statement as a statement that corresponds to reality. This is only a definition of "true statement" and not of "truth" in general. Of course, if one lists all true statements, one gets a definition of truth: truth is "Snow is white" and "My name is Piero" and "The Earth is not the center of the universe" and "France won the 1998 world cup" and "..." But this is neither elegant nor practical (most languages have an infinite number of true statements).
The second component to Tarski's theory is the idea that truth can only be defined relative to another language. Most languages include the word "true", but that leads to paradoxes such as "I am lying" which is both true and false at the same time. The problem is simply that "true" is a word of the language and we are applying it to a statement of the language. Tarski realized that one could not define truth in a language through the language itself and avoid contradictions. So he introduced a "meta-language" to define truth in the "object language". Truth in the object language can then be defined recursively from the truth of elementary statements (the "sentential functions"). "For all sentences s in language L, s is true if and only if T(s) is true", where T(s) is a formula containing s and L's primitives.
Tarski based his “model-theoretic” semantics (models of the world yield interpretations of sentences in that world) on this “correspondence theory of truth” (a statement is true if it corresponds to reality), so that the meaning of a proposition is, basically, the set of situations in which it is true.
Alas, Tarski's theory of truth does not work well with ordinary languages, although it works wonders with the formal languages of Logic.
The problem with Tarski's theory is that it is not clear what he defined. He did not define truth, but "truth in a language". By this, it is not clear if he indirectly acknowledged that the nature of truth is impossible or even pointless.
A secondary problem is that his theory does not distinguish the linguistic theory from the metaphysical theory: explaining the word "true" is a linguistic matter, whereas explaining the nature of truth is a metaphysical matter.
Tarski's theory is really about the linguistic feature.
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