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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 meaning of our life is truth.
Perhaps the most intuitive theory of truth is 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 is 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 compared two things that are different in nature, like 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. And so forth. 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.
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 staments 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 like "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 can't define truth in a language through the language itself and avoid contradictions. So he defined only "truth in a language". One must use 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. Alfred Tarski's theory of truth does not work well with ordinary languages, although it works wonders with the formal languages of mathematical logic. The problem with Tarski's theory is that it is not clear what he defined. He did not defined 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 about the linguistic feature, and does not seem to even address the metaphysical question.
The correspondence theory of truth assumes that the definition of truth is in the world. However, one can object that everything is ultimately in the mind and therefore the definition of truth is inside us. It is pointless to look for a definition in the world. Idealists (as opposed to materialists) believe this. This leads to a difference theory of truth: truth can no longer be defined as the correspondence to the facts of the worlds, but has to be defined as the correspondence with the facts of the mind. The "coherence theory of truth" defines truth as coherence with the system of beliefs in one's mind: the statement "snow is white" is true if the fact asserted by this statement this is coherent with all the other facts that are believed to be true. Truth is defined by the set of coherent statements that make up a whole system of beliefs. Any theory of Cosmology, for example, is of this kind: the truth of a statement about black holes cannot verified (because we can't travel into a black hole and not even close to one) and therefore it only depends on whether it is coherent with the other "truths" of Cosmology. Idealists believe that this is the definition of truth in general: we can never be sure of the world, therefore we can only assess whether a statement is coherent or not with our beliefs. The idea of "coherence" is extended by phenomenology to mean a state of balance with the environment. Martin Heidegger, one of the most confusing and cryptic (not to mention boring) of philosophers, claimed that truth is "freedom". What he calls freedom is an "attunement" with the world (or "letting beings be"). You attune to the world and truth is revealed to you.
Charles Peirce enunciated the "pragmatist" motto, that amounts to: the meaning of an idea consists in its practical effects on our daily lives. If two ideas have the same practical effects on us, they have the same meaning. The idea of truth is defined accordingly: truth is the effect is has on us, and that effect is "consensus". Truth is not agreement with reality, it is agreement among humans. That agreement is reached after a process of scientific investigation. At the end of each such process, humans reach a consensus about what is "true" (e.g., that the Earth is not the center of the universe, that water is made of hydrogen and oxygen, that the Everest is the tallest mountain on the Earth). This set the foundations for relating truth to "verifications": something is true if and only if its truth can be practically verified. For Michael Dummett, the truth of a statement must be provable in a finite amount of time, otherwise the statement is not true. The statement "I will never win the Nobel prize" is provable (just wait until I die), but the statement "I am a genius" or "there will never be another like me" are not provable, and thereforetheir truth value cannot be determined. When we say that a statement is true, we mean that it can be verified. Dummett applies to the world at large the same rules that "intuitionists" applied to logic: to decide the truth of a statement is to prove a theorem. The proof determines truth. If no proof can be constructed, then there is no truth. Verification is not just a means to achieve truth: it is truth. The two concepts are virtually impossible to separate.
In 1927 Frank Ramsey inaugurated "deflationary" thinking about truth by claiming that the word "true" is simply redundant: "it is true that the snow is white" does not say anything more than "the snow is white". By adding "it is true that" we are not adding anything, we are merely making it sound nicer. Quine's "disquotationalism" follows from this claim: to ascribe truth to a statement merely means to remove the quotation marks. For example, the statement "snow is white" is true if and only if it is a fact that snow is white. Now remove the inessential words and what you have is: "snow is white" is true if and only if snow is white. The truth predicate "is true" simply removes the quotation marks. "Truth is disquotation". Quine concedes that the truth predicate (the expression "is true") has at least one useful function: it allows us to generalize, like when I state "everything I told you is true". By using the truth predicate, I can simplify what would otherwise be an infinite list of statements. But this is the only usefulness of the truth predicate: there is no need for a theory of truth, there is no nature of truth. The truth predicate is merely a linguistic expedient to generalize statements. The problem remains, of course, that ordinary humans can easily grasp the concept of "true", whether Quine believes it to be a mere "disquotation" or not. There is something that we call "truth" in our minds. Donald Davidson advocates that truth is a primitive concept that cannot be defined via any other concept. In fact, no other concept would exist without the concept of truth.
Inspired by Ludwig Wittgenstein's common-sense theory of truth, that different statements can be all true without being true in the same way (that led him to "alethic pluralism", i.e. to accept that truth is a multi-faceted concept), Lynch takes issue with the idea that there is "one" theory of truth. Lynch argues that there is a plurality of "truths", rather than a single all-encompassing theory of truth. For example, truth in ethics and truth in justice and truth in mathematics obey different laws. The nature of truth is difficult to find because there isn't only one nature of truth. One needs a different theory of truth for each domain, and that is precisely what ordinary humans employ in their daily lives. Just like functionalism believes in "multiple realizations" of the same mental phenomenon, i.e. that the same mental state can be "realized" by different physical states (what matters being the function, not the "stuff"), Lynch believes that "truth" (a uniform concept across domains) can be realized by different theories in different domains. For example, pain is a mental state that is causually related to some inputs (e.g., a sore finger), outputs (e.g., facial expression and sounds), and other mental states (e.g., unhappiness). Any state that realizes this causal role is called "pain", even if the pain due to a blister and the pain due to a cold are very different in nature. Lynch claims that "truth" names a functional role, and that we all understand what that role is, regardless of what realizes it. Lynch compares this with the concept of "head of state": both the president of the United States, the king of Jordan, Fidel Castro and the chancellor of Germany are heads of state, although they way they got the job and the way they administer it vary greatly. The "function" of head of state, though, is understood the same way in the US, France and Cuba. (A possible objection is that equality is sometimes merely a form of fuzziness: the closer you look, the less similar Castro and the king of Jordan are, and the less clear the term "head of state" is. One can suspect that "functional role" is a synonym for "vague definition". Relax the definition and just about anything in this universe will have the same "functional role" as anything else). If truth is merely a functional role, if "to be true" is to play the alethic role, what is exactly that role? Lynch thinks that truth is defined by an "alethic network", a set of interdependent definitions that, jointly, define each other: a proposition is whatever is true or false, a fact is what makes a proposition true or false, etc. Lynch claims that each "alethic concept" in the alethic network is defined by the role it plays in the network. One can't grasp an alethic concept (truth, proposition, fact) without grasping them all. Each alethic concept depends on all of the others. Truth cannot be defined as "stand alone", but only as part of the broader definition of all alethic entities. Truth is the property of playing the truth role in an alethic network. There is one and only one concept of truth, but it can be realized in multiple ways.

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