Philosophy of language is concerned with four central problems: the nature of meaning, language use, language cognition, and the relationship between language and reality. For continental philosophers, however, the philosophy of language tends to be dealt with, not as a separate topic, but as a part of logic.

First and foremost, philosophers of language prioritize their inquiry on the nature of meaning. They seek to explain what it means to "mean" something. Topics in that vein include the nature of synonymy, the origins of meaning itself, and how any meaning can ever really be known. Another project under this heading of special interest to analytic philosophers of language is the investigation into the manner in which sentences are composed into a meaningful whole out of their meaningful parts; and how or if the meanings of such complexes are derived from the meanings of parts thereof.

Secondly, they seek to better understand what speakers and listeners do with language in communication, and how it is used socially. Specific interests may include the topics of language learning, language creation, and speech acts.

Thirdly, they would like to know how language relates to the minds of both the speaker and the interpreter. Of specific interest is the grounds for successful translation of words into other words.

Finally, philosophers of language investigate how language and meaning relate to truth and the world. They tend to be less concerned with which sentences are actually true, and more with what kinds of meanings can be true or false. A truth-oriented philosopher of language might wonder whether or not a meaningless sentence can be true or false, or whether or not sentences can express propositions about things that do not exist, rather than the way sentences are used.

Nature of meaning
Generally speaking, there have been at least seven distinctive explanations of what a linguistic "meaning" is. Each has been associated with its own body of literature.

1. Idea theories of meaning, most commonly associated with the British empiricist tradition of Locke, Berkeley and Hume, claim that meanings are purely mental contents provoked by signs. Although this view of meaning has been beset by a number of problems from the beginning, interest in it has been renewed by some contemporary theorists under the guise of semantic internalism.
2. Truth-conditional theories hold meaning to be the conditions under which an expression may be true or false. This tradition goes back at least to Frege and is associated with a rich body of modern work, spearheaded by philosophers like Alfred Tarski and Donald Davidson.
3. Theories of language use, for example theories by the later Wittgenstein, helped inaugurate the idea of "meaning as use", and a communitarian view of language. Wittgenstein was interested in the way in which the communities use language, and how far it can be taken. It is also associated with P. F. Strawson, John Searle, Robert Brandom, and others.
4. Constructivist theories of language are connected to the revolutionary idea claiming that speech is not only passively describing a given reality, but it can change the (social) reality it is describing through speech acts, which for linguistics was as revolutionary a discovery as for physics was the discovery that measurement itself can change the measured reality itself. Speech act theory was developed by J. L. Austin, although other previous thinkers have had similar ideas.
5. Reference theories of meaning, also known collectively as semantic externalism, view meaning to be equivalent to those things in the world that are actually connected to signs. There are two broad subspecies of externalism: social and environmental. The first is most closely associated with Tyler Burge and the second with Hilary Putnam, Saul Kripke and others.
6. Verificationist theories of meaning are generally associated with the early 20th century movement of logical positivism. The traditional formulation of such a theory is that the meaning of a sentence is its method of verification or falsification. In this form, the thesis was abandoned after the acceptance by most philosophers of the Duhem–Quine thesis of confirmation holism after the publication of Quine's Two Dogmas of Empiricism. However, Michael Dummett has advocated a modified form of verificationism since the 1970s. In this version, the comprehension (and hence meaning) of a sentence consists in the hearer's ability to recognize the demonstration (mathematical, empirical or other) of the truth of the sentence.
7. A pragmatist theory of meaning is any theory in which the meaning (or understanding) of a sentence is determined by the consequences of its application. Dummett attributes such a theory of meaning to Charles Sanders Peirce and other early 20th century American pragmatists.
(Wikipedia)

Some Questions About Language

Within the tradition of analytic and linguistic philosophy, as developed in the twentieth century, it was Wittgenstein’s “Tractatus Logico-Philosophicus” that spelled out most clearly the ontological framework, presupposed by Russell’s program, following Leibniz. It makes the structure of language isomorphic with the structure of reality by employing a series of logical devices. It was also Wittgenstein who was the first to realize the incompatibility of the ideal language game with the actual functions which language performs in daily life and in ordinary discourse.

In his later work, “Philosophical Investigations”, Wittgenstein returned to a much broader conception of meaning by detailed analysis of ordinary speech. This gave rise, within the tradition of analytic and linguistic philosophy, to the movement or school which is devoted to the analysis of ordinary language or everyday speech. Although it is a move in the right direction, this approach to language shares one feature in common with the program of logical reconstruction it seeks to replace, namely, that it provides no account of meaning in the broad sense adopted by Wittgenstein, no solution of the basic problem of how meaningless notations become the meaningful words which are recorded in the lexicon of any language; and consequently, no account of how ordinary language is successfully used for the purposes of communication. In short, it fails to provide us with the essential rudiments of an adequate philosophy of language.

I can sum up by stating the three questions to be answered by a philosophy of language, and characterize three approaches to the consideration of language.

The three fundamental questions are as follows:

1. How meaningless notations become the meaningful words?
What is it that confers referential meaning on otherwise meaningless marks or sounds, thus making them into the meaningful words of a language? This is a question about the genesis of meaning.

2. What is it that meaningful words refer to when they have referential significance?
This is a question about the referents of name-words, not of all words, for particles do not have referential significance.

3. How ordinary language is successfully used for the purposes of communication?
Can ordinary language be used satisfactorily for the purpose of communication and for the expression of knowledge; or must it be replaced by a much better instrument logically devised to do what ordinary language cannot do?

The three different approaches to the philosophical consideration of language are as follows. only the third of which I regard as sound and fruitful.

A. “The syntactical approach,” of which Russell’s program of logical syntax is an example. This approach answers the third of the foregoing questions by rejecting ordinary language and by replacing it with a logically constructed or syntaxed language. It, therefore, sees no need at all to answer Question 1; and its answer to Question 2 is as follows: the referent is always a real existent.

B. “The ‘ordinary language’ approach,” exemplified by the later Wittgenstein and his followers.
This approach answers Question 3 to the extent that it favors the retention of ordinary language for philosophical as well as for ordinary discourse. However, it fails to explain why and how ordinary language can be used successfully for these purposes because it totally sidesteps Question 1, and because its inadequate answer to Question 2 consists merely in the observation that some words have referential meaning and some do not, with the additional observation that it is better to treat all words as if they did not have referential meaning and so, instead of looking for their referents, pay attention to how they are used.

C. “The semantic and lexical approach,” exemplified by the philosophy of language set forth in my book. This approach also commits itself to ordinary language as a satisfactory instrument of both philosophical and everyday discourse. It answers Question 3 by showing that human discourse, using ordinary language, really does what it appears to be doing, and it is able to show this by the way in which it answers Questions 1 and 2: Question 1 by explaining the genesis of referential meaning by the voluntary imposition of meaningless notations on the objects of our apprehension; Question 2 by seeing that apprehended objects are the referents of the name-words we use. And although the answers it gives to Questions 1 and 2 involve presuppositions and certain ontological and psychological posits, none of these is a prior commitment; all are posterior to the consideration of language itself.

The third approach has its roots in an earlier philosophical tradition which originated with Aristotle, was elaborated by Aquinas, and was applied to the consideration of language by Jean Poinsot, a contemporary of Thomas Hobbes. Poinsot wrote a systematic treatise on signs that dealt with the fundamental problems of meaning and laid down the basis for the answers which the third approach gives to Questions 1 and 2. If Poinsot’s influence had prevailed in modern times, instead of that of Hobbes and Leibniz, modern thought might have been spared many of the little errors which have had such serious consequences not only for philosophy in general, but for the philosophy of language in particular. In addition to Poinsot, Edmund Husserl and his followers are modern authors who approach the consideration of language without prior ontological commitments and with insights that contribute to the solution of the basic questions about meaning. The rudiments of a sound and adequate approach to the philosophy of language can be found in modern thought, but not within the orbit of what, in the twentieth century, has come to be called “linguistic philosophy”.

Words and Meanings

Mistaken view about Words and Meanings: The failure to recognize that ideas are meanings.
The correct view consists in seeing that our ideas are the formal signs we can never apprehend. They enable us to apprehend all the objects we do apprehend. These are also the objects that our ideas, functioning as formal signs, refer to - the objects to which we give names and to which we refer when we use the words that signify them. This holds true just as much for the intelligible objects of conceptual thought as it does for the sensible objects of perception, memory, and imagination.

When a baby learns to speak and later to read, or when we learn a foreign language, marks and sounds (let us use the word “notations” to cover both) that were at first meaningless become meaningful. A meaningful notation is a word.

How that which at first was a meaningless notation acquired the meaning that turned it into a meaningful word?

We often learn the meaning of a word that is new and strange by being told in other words that we do understand. It is like a dictionary definition – a verbal description of the object signified by the word in question. This holds for some words, but it cannot hold for all. The other way for meaningless notations to acquire meaning and become words is by direct acquaintance with the object that the meaningless notation is used to signify.

The simplest example of this is to be found in our learning the meaning of proper names. We can learn the meaning of “George Washington” only by verbal descriptions. None of us has ever been introduced to George Washington. We can have no direct acquaintance with him. We know what his proper name means by being told that it signifies the first President of the United States.

The situation is quite different with other proper names – the names of persons in our families or persons we have been introduced to. The verbal introduction may be as brief as “Let me introduce you to John Smith”. But it accompanies your direct acquaintance with the object named. That is how “John Smith” becomes for you the proper name of the person to whom you have been introduced.

It is very much in the same way that meaningless notations become significant common names. The baby is told that the animal in his playroom is a dog or a cat. This may be repeated a number of times. Soon the baby, pointing at the animal, utters “dog” or “cat” or something that sounds similar. A significant common name has been added to the baby’s vocabulary.

In the course of the child’s growth, with his education and with all the learning in a wide variety of experiences, his vocabulary of common names will be greatly expanded. Those same two objects that he called dog and cat, he will be able to use other common names for, such as “canine”, “feline”, “mammal”, “pet” “domesticated animal”, and so on.

A meaning word, a notation with significance, is a sign. A sign functions by presenting to the mind for its attention an object other than itself. Thus, when I utter the word “dog”, you not only hear the word itself, but hearing the word serves to bring before your mind the object thus named.

Not all signs function in this way, especially signs that are not words. We say that clouds signify rain; that smoke signifies fire; that the ringing of the dinner bell signifies the meal is ready. Such signs, unlike words are signals, whereas words are usually as designators – signs that refer to the objects they name.

Words can function as signals as well. “Fire” cried out in a crowded theatre not only designates the object thus named, but also signifies an imminent danger that calls for action. So, too, the word “dinner” shouted from the farmhouse steps to workers in the field functions exactly like the ringing of the dinner bell.

What is common to the signs, either designators or signals or both, is that they are themselves objects of which we are perceptually aware as well as instruments that function to bring to mind the objects the signify. Let us call all such designators and signals instrumental signs. Their whole being does not consist in signifying. They have perceptible existence in themselves as well.

There is another kind of designative sign, one the whole existence of which consists in signifying. Like other signs, signs of this special kind present to the mind objects other than themselves. But unlike other signs, they themselves are entities of which we have no awareness whatsoever. They are thus distinct from instrumental signs. Let us call them pure or formal signs. A formal sign is never an object we apprehend. Its whole existence or being consists in the function it performs as a sign, referring to something we do apprehend.

The philosophical mistake to which we now turn consists in the neglect of pure or formal signs in the attempt to explain how meaningless notations get their designative significance and become words.

John Locke, in his Essay Concerning Human Understanding, devotes the whole of the third book to words and their meanings. He was correct in thinking that meaningless notations become meaningful words by our voluntarily imposing them on objects as the names of objects that we apprehend. This holds for some words but not for those the meaning of which for us depends upon verbal descriptions of the kind we find in dictionaries. Locke neglected to observe this distinction between meanings acquired by direct acquaintance and meanings acquired by verbal description. Nevertheless, he was correct in thinking that our voluntary imposing of a meaningless notation upon an object apprehended is the way in which at least some words must acquire their meaning.

His mistake consisted in thinking that ideas are the objects to which all meaningful words directly refer. To say this is to say that when an individual uses words referentially, he is always referring to his own ideas and nothing else.

Locke explicitly denied that individuals can use words to refer to the ideas in the minds of others or to signify the things that exist in reality, their qualities or other attributes, or the events that occur in the world. We do not have any direct awareness of such things. The only objects that we directly apprehend are our own ideas.

Locke nevertheless realized that this account of how words get meaning and have referential significance completely defeats the purpose that makes language so important in human life – communication. How can two individuals talk to one another if the words each of them uses refer only to his or her own ideas? Even more perplexing is the fact that two individuals cannot talk to one another about the things or events that really exist or occur in the world in which they both live,

Locke’s efforts to explain what for him should be inexplicable involves a second step in his account of the significance of words. Our ideas being representations of the things that exist in reality, they themselves signify the things they represent. Our ideas, in other words, are signs that refer to things, things we ourselves cannot directly apprehend. Locke’s second step permits him to say that words, directly signifying our own ideas, indirectly refer to the real things that our ides signify. Hence we can use words to talk to one another not about our own ideas, but about the real world in which we live.

If, as was argued in previous section (“What is an idea?” and “Consciousness and its objects.”), the ideas in our minds are not that which we directly apprehend but rather that by which we apprehend whatever we do apprehend, all of Locke’s contradictions can be avoided. The objects to which we give names and to which we refer when we use the words that signify them are the objects that we directly apprehend. This holds true just as much for the intelligible objects of conceptual thought as it does for the sensible objects of perception, memory, and imagination.

This basic truth provides us with a satisfactory explanation of the meaning of words, that the ideas in our minds are formal signs. Another way of saying this is that our ideas are meanings.

Our ideas do not have meaning. Each of our ideas is a meaning and that is all it is. Mind is the realm in which meanings exist and through which everything else that has meaning acquires meaning, changes meaning, or loses meaning.

The correct view consists in seeing that our ideas are the formal signs we can never apprehend. They enable us to apprehend all the objects we do apprehend. Those words that do not acquire meaning by verbal description acquire it by our direct acquaintance with objects that we apprehend. These are also the objects that our ideas, functioning as formal signs, refer to.

Because the words we use have referential meaning, we can use words to refer to the objects that we directly apprehend by means of our ideas. And since our ideas function as formal signs, we can communicate with one another about objects that are public in the sense that they are objects apprehended by and so are common to two or more individuals.

With regard to our using names to signify imaginary objects that never have existed in reality, we can communicate descriptively.

What about such common names as “liberty”, “equality”, “justice”, “electron”, “thought”, “mind”, “spirit”, “inflation”, "credit”? None of these is a perceptual object with which we can have direct acquaintance. How in these cases did what must have been at first meaningless notations get meaning and become useful words for us?

These are totally non-perceptible objects, yet objects we are able to think about by means of intellectual activity and conceptual thought , as was argued in previous section (“What is an idea?” and “The Intellect”). These are the ideas through the functioning of which the common names in our vocabulary signify and refer to the kinds or classes that they enable us to apprehend as objects of thought.

Another mistake about language that follows as a consequence of the failure to distinguish the human intellect from the senses is one of which animal psychologists and behavioral scientists are for the most part guilty, though many contemporary philosophers agree with them.

In their study of the evidence of animal communication, they seldom if ever note the difference between signs that function merely as signals and signs that function as designators – as names that refer to objects. Almost all of the cries, sounds, gestures, that animals in the wild and domesticated animals as well, use to express their emotions and desires, serve as signals, not as designators. It is only in the laboratory and under experimental condition, often with very ingeniously contrived special apparatus, that such higher mammals as chimpanzees and dolphins appear to be communicating by using words as if they were names, and even to be making sentences by putting them together with some vestige of syntax.

The appearance is then misinterpreted by the scientists as a basis for asserting that the only difference between animal and human language is one od degree, not of kind. This misinterpretation arises from the neglect or ignorance of the difference between perceptual and conceptual thought. That, in turn, stems from the failure to acknowledge the difference between the senses and the intellect.

While there is evidence that chimpanzees under experimental conditions do use artificially contrived signs to designate or name things, the things they name are all perceptual objects. There is no evidence showing their ability to use signs to designate what lies totally beyond the sensible realm.

Therein lies the difference between the animal’s power of perceptual thought and the human power of conceptual thought.

The animal’s behavior manifests different reactions to objects that are different in kind. But the kinds of things that animals appear to differentiate are all kinds of which there are perceptual instance in the animal’s experience. Human differentiate kinds or classes of which there are no perceptual instances in their experience. This is the distinguishing characteristic of conceptual thought and the irrefutable evidence of the presence of intellect in man and of its absence in brutes.

One further observation involves the distinction between a word acquiring its designative meaning through direct perceptual acquaintance with the object named and the acquirement of meaning by means of a verbal description. There is no instance where a sign that an animal uses gets its meaning from a collocation of other signs that purport to express its meaning.

Finally, we come to one more philosophical mistake that had very serious consequences for the contemporary philosophy of language. This mistake is introduced into modern thought by Thomas Hobbes in his Leviathan (1651), Chapter 4 of which is concerned with speech. Before Hobbes, the term meaningless had a purely descriptive significance. It signified that a sound or mark simply lacked meaning; that it was like the nonsense syllables “glub” and “trish”.

Hobbes introduced a dyslogistic use of the term meaningless. For him a word like “angel” or its equivalent phrase “incorporeal substance” is a meaningless expression because of his espousal of materialism as a metaphysical doctrine, according to which only bodies or material things exist in reality. Since angels or incorporeal substances do not exist, the words “angel” or “incorporeal substance” must be meaningless. They designate nothing; they refer to nothing.

The main point is that Hobbes reduced the designative reference of name words to the one mode of reference which involves a reference to some really existent thing or to a class of things of which there are really existent instances. “If a man should speak to me about immaterial substances, or about a free subject, a free will, Hobbes writes, “I should not say he were in error, but that his words were without meaning; that is to say, absurd”. He goes on to say that statements about things that never have been, “nor can be incident to sense”, are absurd speeches, “taken upon credit, without any signification at all”.

The focal point of Hobbes’ error is the elimination of all designative references that are not also existentially denotative (i.e., references to the really existent). As we observed earlier, except for special proper names and the common names for objects perceived, all other common names have designative references that are not also existentially denotative.

All the words that name the objects of thought do have referential significance. Their designative meaning consists in their reference to such objects, whether or not they actually exist and can be perceived. They have as much referential significance as any correctly used proper name or definite description.

The reductionist error of reducing referential significance to the one mode of significance that involves a reference to something really existent, lies at the heart of Bertrand Russell’s famous theory of descriptions. And what lies at the heart of that error is the mistake of supposing that naming is asserting – that we cannot name something without also asserting that the thing named really exists.

Naming is not asserting, any more than apprehending an object of thought is identical with making the judgment that the object has existence in reality. Apprehending an object and making the judgment that it really exists are inseparable only in the case of veridical (cognitive) perceptions. In every other case, the acts of apprehension and judgment are not only distinct but also quite separate. One act can occur without the other occurring. Hence we can use words to refer to apprehended objects about the existence of which we suspend judgment or ask questions.

As a result of these errors, originating with Hobbes, linguistic philosophy in the twentieth century has abandoned the effort to explain the referential significance of most words in our daily vocabulary – all words that do not have the one mode of referential significance that denotes something really existent.

This has led to the famous injunction “Don’t look for the meaning; look for the use”, as if it were possible to discover the use of a word without first ascertaining its meaning as used, a meaning that it must have had before it was used in order to be used in one certain way rather than another. Language does not control thought, as contemporary linguistic philosophers appear to believe. It is the other way around.

Tarski's Semantic theory of truth

ALFRED TARSKI
Alfred Tarski (January 14, 1901 – October 26, 1983) was a Polish logician, mathematician and philosopher. Educated at the University of Warsaw and a member of the Lwów–Warsaw school of logic and the Warsaw school of mathematics and philosophy, he immigrated to the USA in 1939 where he became a naturalized citizen in 1945, and taught and carried out research in mathematics at the University of California, Berkeley from 1942 until his death.

A prolific author best known for his work on model theory, metamathematics, and algebraic logic, he also contributed to abstract algebra, topology, geometry, measure theory, mathematical logic, set theory, and analytic philosophy.
His biographers Anita and Solomon Feferman state that, "Along with his contemporary, Kurt Gödel, he changed the face of logic in the twentieth century, especially through his work on the concept of truth and the theory of models."

SEMANTIC THEORY OF TRUTH
The "Convention T" (also T-schema) standard in his "inductive definition of truth" was an important contribution to symbolic logic, semantics, and the philosophy of language. In 1933, Tarski published a very long paper in Polish, titled "Pojęcie prawdy w językach nauk dedukcyjnych", setting out a mathematical definition of truth for formal (logical) languages. The 1935 German translation was titled "Der Wahrheitsbegriff in den formalisierten Sprachen", "The concept of truth in formalized languages", sometimes shortened to "Wahrheitsbegriff". An English translation appeared in 1956 in the first edition of the Logic, Semantics, Metamathematics.

Some recent philosophical debate examines the extent to which Tarski's theory of truth for formalized languages can be seen as a correspondence theory of truth. The debate centers on how to read Tarski's condition of material adequacy for a truth definition. That condition requires that the truth theory have the following as theorems for all sentences p of the language for which truth is being defined:

"p" is true if and only if p.
(where p is the proposition expressed by "p")

The debate amounts to whether to read sentences of this form, such as
"Snow is white" is true if and only if snow is white
as expressing merely a deflationary theory of truth or as embodying truth as a more substantial property (see Kirkham 1992). It is important to realize that Tarski's theory of truth is for formalized languages, so examples in natural language are not illustrations of the use of Tarski's theory of truth.
(Wikipedia)

In 1933, Alfred Tarski published (in Polish) his analysis of the notion of a true sentence. This long paper undertook two tasks: first to say what should count as a satisfactory definition of ‘true sentence’ for a given formal language, and second to show that there do exist satisfactory definitions of ‘true sentence’ for a range of formal languages.

We say that a language is fully interpreted if all its sentences have meanings that make them either true or false. All the languages that Tarski considered in the 1933 paper were fully interpreted.This was the main difference between the 1933 definition and the later model-theoretic definition of 1956.

Tarski described several conditions that a satisfactory definition of truth should meet.

OBJECT LANGUAGE AND METALANGUAGE
If the language under discussion (the object language) is L, then the definition should be given in another language known as the metalanguage, call it M. The metalanguage should contain a copy of the object language (so that anything one can say in L can be said in M too), and M should also be able to talk about the sentences of L and their syntax.

FORMAL CORRECTNESS
The definition of True should be ‘formally correct’. This means that it should be a sentence of the form
For all x, True(x) if and only if φ(x),
where True never occurs in φ;
or the definition should be provably equivalent to a sentence of this form. The equivalence must be provable using axioms of the metalanguage that don't contain True.

MATERIAL ADEQUACY
The definition should be ‘materially adequate’. This means that the objects satisfying φ should be exactly the objects that we would intuitively count as being true sentences of L, and that this fact should be provable from the axioms of the metalanguage.
Tarski used many sentences of M to express truth, namely all the sentences of the form
φ(s) if and only if ψ
whenever s is the name of a sentence S of L and ψ is the copy of S in the metalanguage. So the technical problem is to find a single formula φ that allows us to deduce all these sentences from the axioms of M; this formula φ will serve to give the explicit definition of True.

Tarski's own name for this criterion of material adequacy was Convention T. More generally his name for his approach to defining truth, using this criterion, was the semantic conception of truth.
(The Stanford Encyclopedia of Philosophy)

Semantic theory of truth

A semantic theory of truth is a theory of truth in the philosophy of language which holds that truth is a property of sentences.

ORIGIN
The semantic conception of truth, which is related in different ways to both the correspondence and deflationary conceptions, is due to work published by Polish logician Alfred Tarski in the 1930s. Tarski, in "On the Concept of Truth in Formal Languages", attempted to formulate a new theory of truth in order to resolve the liar paradox. In the course of this he made several metamathematical discoveries, most notably Tarski's undefinability theorem using the same formal technique as Kurt Gödel used in his incompleteness theorems. Roughly, this states that a truth-predicate satisfying convention-T for the sentences of a given language cannot be defined within that language.

TARSKI'S THEORY
To formulate linguistic theories without semantic paradoxes like the liar paradox, it is generally necessary to distinguish the language that one is talking about (the object language) from the language that one is using to do the talking (the metalanguage). In the following, quoted text is use of the object language, while unquoted text is use of the metalanguage; a quoted sentence (such as "P") is always the metalanguage's name for a sentence, such that this name is simply the sentence P rendered in the object language. In this way, the metalanguage can be used to talk about the object language; Tarski demanded that the object language be contained in the metalanguage.

Tarski's material adequacy condition, also known as Convention T, holds that any viable theory of truth must entail, for every sentence "P", a sentence of the following form (known as "form (T)"):

(1) "P" is true if, and only if, P.

For example,

(2) 'snow is white' is true if and only if snow is white.

These sentences (1 and 2, etc.) have come to be called the "T-sentences". The reason they look trivial is that the object language and the metalanguage are both English; here is an example where the object language is German and the metalanguage is English:

(3) 'Schnee ist weiß' is true if and only if snow is white.

It is important to note that as Tarski originally formulated it, this theory applies only to formal languages. He gave a number of reasons for not extending his theory to natural languages, including the problem that there is no systematic way of deciding whether a given sentence of a natural language is well-formed, and that a natural language is closed (that is, it can describe the semantic characteristics of its own elements). But Tarski's approach was extended by Davidson into an approach to theories of meaning for natural languages, which involves treating "truth" as a primitive, rather than a defined concept. (See truth-conditional semantics.)

Tarski developed the theory to give an inductive definition of truth as follows.

For a language L containing ¬ ("not"), ∧ ("and"), ∨ ("or"), ∀ ("for all"), and ∃ ("there exists"), Tarski's inductive definition of truth looks like this:
(1) "A" is true if, and only if, A.
(2) "¬A" is true if, and only if, "A" is not true.
(3) "A∧B" is true if, and only if, A and B.
(4) "A∨B" is true if, and only if, A or B or (A and B).
(5) "∀x(Fx)" is true if, and only if, every object x satisfies the sentential function F.
(6) "∃x(Fx)" is true if, and only if, there is an object x which satisfies the sentential function F.

These explain how the truth conditions of complex sentences (built up from connectives and quantifiers) can be reduced to the truth conditions of their constituents. The simplest constituents are atomic sentences. A contemporary semantic definition of truth would define truth for the atomic sentences as follows:
An atomic sentence F(x1,...,xn) is true (relative to an assignment of values to the variables x1, ..., xn)) if the corresponding values of variables bear the relation expressed by the predicate F.

Tarski himself defined truth for atomic sentences in a variant way that does not use any technical terms from semantics, such as the "expressed by" above. This is because he wanted to define these semantic terms in terms of truth, so it would be circular were he to use one of them in the definition of truth itself. Tarski's semantic conception of truth plays an important role in modern logic and also in much contemporary philosophy of language. It is a rather controversial matter whether Tarski's semantic theory should be counted either as a correspondence theory or as a deflationary theory.

Donald Davidson

Donald Herbert Davidson (March 6, 1917 – August 30, 2003) was an American philosopher. He served as Slusser Professor of Philosophy at the University of California, Berkeley from 1981 to 2003 after having also held teaching appointments at Stanford University, Rockefeller University, Princeton University, and the University of Chicago. Davidson was known for his charismatic personality and the depth and difficulty of his thought. His work exerted considerable influence in many areas of philosophy from the 1960s onward, particularly in philosophy of mind, philosophy of language, and action theory. While Davidson was an analytic philosopher, and most of his influence lies in that tradition, his work has attracted attention in continental philosophy as well, particularly in literary theory and related areas. (Wikipedia)

TRUTH AND MEANING
In 1967 Davidson published "Truth and Meaning," in which he argued that any learnable language must be statable in a finite form even if it is capable of a theoretically infinite number of expressions, as may be assumed that natural human languages are.
If it could not be stated in a finite way, it could not be learned through a finite, empirical method such as the way humans learn their languages.
It follows that it must be possible to give a theoretical semantics for any natural language that could give the meanings of an infinite number of sentences on the basis of a finite system of axioms.
Following, among others, Rudolf Carnap (Introduction to Semantics, Harvard 1942, 22) Davidson also argued that "giving the meaning of a sentence" was equivalent to stating its truth conditions, so stimulating the modern work on truth-conditional semantics.

He proposed that it must be possible to distinguish a finite number of distinct grammatical features of a language, and for each of them explain its workings in such a way as to generate trivial (obviously correct) statements of the truth conditions of all the (infinitely many) sentences making use of that feature.
Thus, a finite theory of meaning can be given for a natural language; the test of its correctness is that it would generate (if applied to the language in which it was formulated) all the sentences of the form 'p' is true if and only if p (e.g., 'Snow is white' is true if and only if snow is white) ---They are called T-sentences: Davidson derives the idea from Alfred Tarski.

This work was originally delivered in his John Locke Lectures at Oxford and launched a large endeavor by many philosophers to develop Davidsonian semantical theories for natural language.

Davidson’s most important achievement is his theory of meaning. His view is a variant of truth-conditional theories. However, one of the merits of his approach is that unlike many truth-conditional theories, his avoids epistemological infusions. A typical truth-conditional theory employs such notions as “know”, “determine”, or “establish” – holding, for example, that one knows the meaning of a sentence if one knows under what conditions it is true or false. Davidson’s approach eliminates any epistemic or verificationist intrusions. He wishes to define meaning itself, rather than describing the conditions for knowing what a sentence means. His approach to the topic is strictly from a logic/semantical point of view.

His conception is based on Alfred Tarski’s work on the conception of truth. In his Wahreitsbegriffe (1936) – made available to English readers in a shortened form as “The Semantic Conception of Truth” (1944) – Tarski developed a definition of truth in terms of the concept of satisfaction. One of the questions he raised about any definition was whether it captured and then made more precise the ordinary person’s notion of truth. As a way of determining whether it did, he laid down a condition that any definition must satisfy. This he called a “condition of material adequacy”. The basic idea was that any definition must satisfy this condition or it could be rejected as being counterintuitive or in other ways defective. Tarski gave a semantic rendering of this condition, which he formulated as follows:
S is true in L if and only if p.
This condition, he emphasized, must not be confused with his or any other definition of truth; rather, it is a test of the merit of any definition. Davidson calls it Convention T. He agrees that any adequate definition of truth must satisfy Convention T. In English, Convention T says, for example: The sentence “Snow is white”, is true in L – for example, in English – if and only if snow is white. It will be noted that S is the name of a sentence – that is, it is a quoted expression. “L” refers to whatever language S occurs in, and p produces the sentence itself. Tarski demonstrated that his definition of truth satisfied Convention T.

Davidson, reflecting on Tarski’s procedure, notes that sentence “Snow is white” has the same meaning as p. He realizes that Tarski is thus treating the notion of meaning as a primitive in order to define the concept of truth. Davidson seized on the idea of inverting this procedure – of taking truth as primitive and defining meaning in terms of it. His theory was thus designed to construct a set of axioms that would allow for the interpretation of a speaker’s utterances in such a way that they would entail all true T-sentences for that speaker’s language. Suppose, for instance, that a speaker said in Italian, “La neve è bianca”. The axioms of Davidson’s theory then entail that the speaker’s utterance is true in Italian if and only if snow is white. In this way, the meaning of any utterance is captured by the appeal to the axioms and to convention T.

Davidson suggests that one can find empirical evidence to support his theory. If a speaker says “La strada è humida” on an occasion when it has been raing and a certain street is wet, one might infer that the speaker takes as true the Italian sentence “La strada è humida” when it is or recently has been raining. This would provide additional, nonlogical support for his theory by noting what the speaker in fact says.

There are two major criticisms of this doctrine. The first is the objection that Davidson covertly introduces epistemic considerations into his theory that render it circular. Accordingly to this objection, one must first know what a sentence means before one can determine whether it is true or false or even understand what its truth conditions might be. The objection holds, in effect, that Davidson preanalytically understand the meaning of a particular sentence and only then is able to speak about its truth conditions.

The second objection derives from the early history of the philosophy of language. In “On Denoting” (1905), Russell points out that there is a difference in meaning between the sentences, “Scott is Scott” and “Scott is the author of Waverley”, even though preanalytically both can be treated as true identity sentences. He indicated that when these are embedded into belief contexts, the difference is immediately apparent. For example, King George IV certainly believed that Scott is Scott, but he did not necessarily believe that Scott is the author of Waverley, since he might not have known that Scott wrote that novel. Similar examples are found in Frege’s and in Quine’s early logical papers. The distinction bears on Davidson’s treatment of meaning in terms of truth conditions. The two sentences “Scott is Scott” and “Scott is the author of Waverley” have truth conditions, but they clearly differ in meaning. It follows that one cannot define meaning in terms of truth conditions. Despite these difficulties, Davidson’s idea, with various modifications, continues to be widely discussed, and attempts have been made to apply it to a variety of puzzling sentences, such as indexicals, that is, such words as “I”, “here”, and “now”.

RADICAL INTERPRETATION
Davidson's work is well noted for its unity, as he has brought a similar approach to a wide variety of philosophical problems. Radical interpretation is a hypothetical standpoint which Davidson regards as basic to the investigation of language, mind, action, and knowledge. Radical interpretation involves imagining that you are placed into a community which speaks a language you do not understand at all. How could you come to understand the language? One suggestion is that you know a theory that generates a theorem of the form 's means that p' for every sentence of the object language (i.e. the language of the community), where s is the name of a sentence in the object language, and p is that sentence, or a translation of it, in the metalanguage in which the theory is expressed. However, Davidson rejects that suggestion on the grounds that the sentential operator 'means that' is sensitive not only to the extensions of the terms that follow it, but also to their intensions. Hence, Davidson replaces 'means that' with a connective sensitive only to the extensions of sentences; since the extension of a sentence is its truth value, this is a truth functional connective. Davidson elects the biconditional (if and only if) as the connective needed in a theory of meaning. He concludes that a theory of meaning must be such that for each sentence of the object language it generates a theorem of the form 's is true if and only if p'. A theory of truth for a language can serve as a theory of meaning.

The significance of this conclusion is that it allows Davidson to draw on the work of Alfred Tarski in giving the nature of a theory of meaning. Tarski showed how we can give a compositional theory of truth for artificial languages. Thus, Davidson takes three questions to be central to radical interpretation. Firstly, can a theory of truth be given for a natural language? Secondly, given the evidence plausibly available for the radical interpreter, can they construct and verify a theory of truth for the language they wish to interpret? Thirdly, will having a theory of truth suffice for allowing the radical interpreter to understand the language? Davidson has shown, using the work of Tarski, that the first question can be answered affirmatively.

Davidson points out that beliefs and meanings are inseparable. A person holds a sentence true based on what he believes and what he takes the sentence to mean. If the interpreter knew what a person believed when that person held a sentence to be true, the meaning of the sentence could then be inferred. Vice versa, if the interpreter knew what a person took a sentence to mean when that person held it to be true, the belief of the speaker could be inferred. So Davidson doesn't allow the interpreter to have access to beliefs as evidence, since the interpreter would then be begging the question. Instead, Davidson allows that the interpreter can reasonably ascertain when a speaker holds a sentence true, without knowing anything about a particular belief or meaning. That will then allow the interpreter to construct hypotheses relating a speaker and an utterance to a particular state of affairs at a particular time.

Davidson argues that because the language is compositional, it is also holistic: sentences are based on the meanings of words, but the meaning of a word depends on the totality of sentences in which it appears. That holistic constraint, along with the requirement that the theory of truth is law-like, suffices to minimize indeterminacy just enough for successful communication to occur.

In summary, what radical interpretation highlights is what is necessary and sufficient for communication to occur. The conditions are to recognize speakers as speakers, their beliefs must be mostly coherent and correct; indeterminacy of meaning does not undermine communication, but it must be constrained just enough.

I conclude that there is no such thing as a language, not if a language is anything like what many philosophers and linguists have supposed. There is therefore no such thing to be learned, mastered, or born with. We must give up the idea of a clearly defined shared structure which language-users acquire and then apply to cases. And we should try again to say how convention in any important sense is involved in language; or, as I think, we should give up the attempt to illuminate how we communicate by appeal to conventions.
— "A Nice Derangement of Epitaphs," Truth and Interpretation, 446

KNOWLEDGE AND BELIEF
After the 1970s Davidson's philosophy of mind picked up influences from the work of Saul Kripke, Hilary Putnam, and Keith Donnellan, all of whom had proposed a number of troubling counterexamples to what can be generally described as "descriptivist" theories of content. The views, which roughly originate in Bertrand Russell's Theory of Descriptions, held that the referent of a name, which object or person the name refers to, is determined by the beliefs a person holds about that object. Kripke et al. argued that this was not a tenable theory, and that in fact whom or what a person's beliefs were about was in large part (or entirely) a matter of how they had acquired those beliefs, and those names, and how if at all the use of those names could be traced "causally" from their original referents to the current speaker.

Davidson picked up this theory, and his work in the 1980s dealt with the problems in relating first-person beliefs to second- and third-person beliefs. It seems that first person beliefs ("I am hungry") are acquired in very different ways from third person beliefs (someone else's belief, of me, that "He is hungry"). How can it be that they have the same content?

Davidson approached the question by connecting it with another one: how can two people have beliefs about the same external object? He offers, in answer, a picture of triangulation: beliefs about oneself, beliefs about other people, and beliefs about the world come into existence jointly.

Many philosophers throughout history had, arguably, been tempted to reduce two of these kinds of belief and knowledge to the other one: René Descartes and David Hume thought that the only knowledge that people start with is self-knowledge. Some logical positivists (and some would say Wittgenstein, or Wilfrid Sellars) held that people start with beliefs only about the external world. (Arguably, Friedrich Schelling and Emmanuel Levinas held that people start with beliefs only about other people). It is not possible, on Davidson's view, for a person to have only one of the three kinds of mental content; anyone who has beliefs of one of the kinds must have beliefs of the other two kinds.