Logical Positivism

Answer : Ayer’s being one of the chief proponents of logical positivism linguistic explanation of the a-priori Analyticity as truth is based on the fact that he says necessary propositions as analytical statement. By definition Ayer defines analyticity as follows: a proposition is analytic when its validity depends solely on the definitions of the symbols it contains, and synthetic when its validity is determined by the facts of experience. Immediately after this, though, Ayer seems to deny analyticity in terms of a priority; he says \the proposition ‘Either some ants are parasitic or none are’ is an analytic proposition. For, one need not resort to observation to discover that there are or are not ants which are parasitic. We should regard logical positivism account of analyticity as truth by definition as the fundamental one. How the analyticity of a proposition can explain it a priority Suppose that Ayer is right, and that all truths of mathematics are true by definition. How could this explain their a priority? The idea is that to understand a proposition which is true by definition, one must know the definitions of the relevant terms. And, in the case of analytic sentences which are true by definition, this knowledge of the definitions of terms is enough to show that they are true. Ayer seems to give this kind of explanation when he says: If one knows what is the function of the words ‘either,’ ‘or,’ and ‘not,’ then one can see that any proposition of the form ‘Either p is true or p is not true’ is valid. The basic idea here seems to be that knowing the function of words, in particular, knowing their definitions can, in the case of analytic propositions, be enough to know the truth of a sentence. How can analytic truths be surprising? One of the intuitive facts which stand in the way of a treatment of all mathematical and logical propositions as having no factual content is the fact that these propositions can often be surprising. How can we account for this, if to learn the truth of a mathematical proposition is not to learn about some new and surprising fact? Ayer says: \When we say that analytic propositions are devoid of factual content, and consequently that they say nothing, we are not suggesting that they are senseless in the way that metaphysical utterances are senseless. For, although they give us no information about any empirical situation, they do enlighten us by illustrating the way in which we use certain symbols. There is a sense in which analytic propositions do give us new knowledge. They call attention to linguistic usages, of which we might not otherwise be conscious, and they reveal unsuspected implications in our assertions and beliefs. Ayer is suggesting that, since analytic truths are true in virtue of certain linguistic facts (the definitions of expressions in analytic sentences) coming to know an analytic truth can bring us to awareness of these linguistic facts.

Answer : Ayer explains that the principle of verifiability may be used as a criterion to determine whether a statement is meaningful. To be meaningful, a statement must be either analytic (i.e. a tautology) or capable of being verified. According to Ayer, analytic statements are tautologies. A tautology is a statement that is necessarily true, true by definition, and true under any conditions. A tautology is a repetition of the meaning of a statement, using different words or symbols. According to Ayer, the statements of logic and mathematics are tautologies. Tautologies are true by definition, and thus their validity does not depend on empirical testing. Synthetic statements, or empirical propositions, assert or deny something about the real world. The validity of synthetic statements is not established merely by the definition of the words or symbols they contain. According to Ayer, if a statement expresses an empirical proposition, then the validity of the proposition is established by its empirical verifiability.

Propositions are statements that have conditions under which they can be verified. By the verification principle, meaningful statements have conditions under which their validity can be affirmed or denied. Statements that are not meaningful cannot be expressed as propositions. Every verifiable proposition is meaningful, although it may be either true or false. Every proposition asserts or denies something, and thus is either true or false. Ayer rejects the metaphysical thesis that philosophy can give us knowledge of a transcendent reality. He dismisses metaphysical arguments, calling them nonsense, and saying that they cannot be empirically verified. He argues that metaphysical statements have no literal meaning, and that they cannot be subjected to criteria of truth or falsehood.

A significant consequence of abandoning metaphysics as a concern of philosophy is a rejection of the view that the function of philosophy is to propose basic principles of meaning and to construct a deductive system by offering the consequences of these principles of meaning as a complete picture of reality. But this is, in fact, what Ayer does, in presenting the principle of verifiability as a criterion of meaningfulness for any empirical proposition. According to Ayer, no proposition concerning ‘matters of fact’ can ever be shown to be necessarily true, because there is always a possibility that it may be refuted by further empirical testing. Logical certainty is possible only for analytic observations, which are tautologies, and not for empirical observations concerning ‘matters of fact.’ Ayer explains that his radical empiricism is opposed to rationalism. Rationalism asserts that there are truths about the world that can be known by a priori reasoning, or independently of experience.

According to the principle of verifiability, propositions about ‘matters of fact’ can be meaningful only if they are capable of being empirically verified. Ayer agrees with, and elaborates on, Kant’s explanation of the distinction between analytic and synthetic judgments. According to Ayer, a proposition is analytic if its validity depends only on the definitions of the symbols it contains. A proposition is synthetic if its validity is determined by the facts of experience. Analytic observations give us new knowledge, because they reveal unsuspected implications of our statements and beliefs. But analytic observations also do not give us new knowledge, because they only tell us what is already known. Ayer defines truth as the criterion by which empirical propositions are validated. To say that a proposition is true is simply to assert it, and to say that a proposition is false is simply to assert a contradictory proposition.

Thus, truth and falsehood are simply signs of assertion or denial of empirical propositions. For Ayer, metaphysical statements, such as statements about transcendent reality, have no objective validity, and therefore are meaningless. According to Ayer, such statements can be neither proven nor disproven, and cannot be validated or invalidated by empirical testing.

Answer : Bertrand Russell described several different definitions and philosophical analyses as treating certain entities and expressions as “logical constructions”. Examples he cited were the Frege/Russell definition of numbers as classes of equinumerous classes, the theory of definite descriptions, the construction of matter from sense data, and several others.

Generally expressions for such entities are called “incomplete symbols” and the entities themselves “logical fictions”. The notion originates with Russell’s logicist program of reducing mathematics to logic, was widely used by Russell, and led to the later Logical Positivist notion of construction and ultimately the widespread use of set theoretic models in philosophy.

Russell’s most specific formulation of logical construction as a method in Philosophy comes from his essay “Logical Atomism”. One very important heuristic maxim to be applicable in mathematical logic, and have since applied to various other fields, is a form of Occam’s razor. When some set of supposed entities has neat logical properties, it turns out, in a great many instances, that the supposed entities can be replaced by purely logical structures composed of entities which have not such neat properties. In that case, in interpreting a body of propositions hitherto believed to be about the supposed entities, we can substitute the logical structures without altering any of the detail of the body of propositions in question. This is an economy, because entities with neat logical properties are always inferred, and if the propositions in which they occur can be interpreted without making this inference, the ground for the inference fails, and our body of propositions is secured against the need of a doubtful step. The principle may be stated in the form: ‘whenever possible, substitute constructions out of known entities for inferences to unknown entities’.

Russell was speaking of logical constructions in this memorable passage from his Introduction to Mathematical Philosophy: “The method of ‘postulating’ what we want has many advantages; they are the same as the advantages of theft over honest toil. Let us leave them to others and proceed with our honest toil.”

The notion of logical construction appears frequently with the ideas that what are defined are a “logical fiction”, and an “incomplete symbol”. The latter term derives from the use of contextual definitions, providing an analysis of each sentence in which a defined symbol may occur without, however, giving an explicit definition, an equation or universal statement giving necessary and sufficient conditions for the application of the term in isolation. The terms “fiction” and “incomplete symbol” apply with differing aptness to different constructions. Russell’s first use of construction, and the model for later constructions, is the Frege/Russell definition of numbers as classes. This follows the kind of definitions used in the arithmetic analysis of the preceding century, in particular, Dedekind’s earlier construction of real numbers as bounded classes of rational numbers.

Russell’s logicist program could not rest content with postulates for the fundamental objects of mathematics such as the Peano Axioms for the natural numbers. Instead numbers were to be defined as classes of equinumerous classes. Russell also refers to this method as “abstraction”, now known as the abstraction of an equivalence class. The definition of equinumerosity, or of the existence of a one to one mapping between two classes, also called “similarity”, is solely in terms of logical notions of quantifiers and identity. With the numbers defined, for example, two as the class of all two member sets, or pairs, the properties of numbers could be derived by logical means alone.

The most influential of Russell’s constructions was the theory of descriptions from his paper “On Denoting” in 1905. Russell’s theory provides an analysis of sentences of the form ‘The F is G’ where ‘The F’ is called a definite description. The analysis proposes that ‘The F is G’ is equivalent to ‘There is one and only one F and it is G’. With this analysis, the logical properties of descriptions can now be deduced using just the logic of quantifiers and identity. Among the theorems in of Principia Mathematica are those showing that,

If there is just one F, then ‘The F is F’ is true, and if there is not, then ‘The F is G’ is always false and, crucially for the logical manipulation of descriptions,

If the F = the G, and the F is H, then the G is H.

In other words, proper (uniquely referring) descriptions behave like singular terms. Some of these results are contentious. Strawson noted that ‘The present king of France is bald’ should be truth valueless since there is no present king of France, rather than “plainly false”, as Russell’s theory predicts. The theory of descriptions introduces Russell’s notion of incomplete symbol. Definite descriptions ‘The F’ do not show up in the formal analysis of sentences in which they occur, thus ‘The F is H’ becomes.

The theory of descriptions is often described as a model for avoiding ontological commitment to objects and so logical constructions in general are often seen as being chiefly aimed at ontological goals. In fact, that goal is at most peripheral to most constructions. The principal goal is to allow the proof of propositions that would otherwise have to be assumed as axioms or hypotheses. Nor need the ontological goal be always elimination of problematic entities. Other constructions should be seen more as reductions of one class of entity to another, or replacements of one notion by a more precise, mathematical, substitute.

Answer : The attitude of logical positivism towards metaphysics is well expressed by Carnap. Carnap says that language consists of a vocabulary, i.e. a set of meaningful words, and a syntax, i.e. a set of rules governing the formation of sentences from the words of the vocabulary. Pseudo-statements, i.e. sequences of words that at first sight resemble statements but in reality have no meaning, are formed in two ways: either meaningless words occur in them, or they are formed in an invalid syntactical way. According to Carnap, pseudo-statements of both kinds occur in metaphysics. A word W has a meaning if two conditions are satisfied. First, the mode of the occurrence of W in its elementary sentence form (i.e. the simplest sentence form in which W is capable of occurring) must be fixed. Second, if W occurs is an elementary sentence S, it is necessary to give an answer to the following questions (that are - according to Carnap - equivalent formulation of the same question):

What sentence is S deducible from, and what sentences are deducible from S?

Under what a condition is S supposed to be true, and under what conditions false?

How S is to be verified?

What is the me.

There are also pseudo-statements that consist of meaningful words. An example is the word sequence “Caesar is a prime number” that has the same form of “Caesar is a general”. These two sentences are well formed in English, because there is not a grammatical distinction between predicates which can be affirmed of human beings (such as “general”) and predicates which can be affirmed of numbers (such as “prime number”). Although every word occurring in “Caesar is a prime number” has a definite meaning, the sequence evidently has no meaning. In a logically constructed language - says Carnap - a distinction between the different kinds of predicates is specified, and pseudo-statements as “Caesar is a prime number” could not arise. Metaphysical statements which do not contain meaningless words are indeed meaningless because they are formed in a way which is admissible in natural languages but not admissible in logically constructed languages.What is the role of metaphysics? According to Carnap, although metaphysics has not theoretical content, it has content indeed: metaphysical pseudo-statements express the attitude of a person towards life. The metaphysician, instead of using the medium of art, works with the medium of the theoretical; he confuses art with science, attitude towards life with knowledge, and thus produces an unsatisfactory and inadequate work.

Answer : Ayer’s stated aim in Language, Truth & Logic is one which many philosophers have pursued: “to establish beyond question what should be the purpose and method of a philosophical inquiry”. Central to this aim, as Ayer conceived of it, was the demolition of traditional metaphysics, where this was thought of as the attempt to say something about “a reality transcending the world of science and common sense.” Ayer thought that this metaphysical project was an impossible one. The reason why he thought this was a kind of empiricism: the view that all of our knowledge must be based in sense experience. In Ayer’s view, scientific knowledge was the paradigm of knowledge that conformed to this empiricist restriction. According to Ayer the criterion of verifiability says that a sentence is meaningful if and only if it has some relation to observation. Historically, the form that formulations of this criterion took was to settle on a class of observation sentences, and then to claim that all and only sentences which bear a certain specified relation to these sentences will count as meaningful. There were then two tasks to be accomplished:

• saying what an observation sentence is, and
• spelling out the required relationship between meaningful sentences and observation sentences.

One main issue regarding the first task is whether the observation sentences are thought of as claims about sense data, or as claims about material objects. Intuitively, it is hard to see how material object statements could count as observation sentences if one buys a sense datum theory of perception (as Ayer and the other logical positivists did); but if one takes sense datum statements as the observation statements, then one runs the danger of making the material object statements of, e.g., science come out meaningless.

This is not a result that Ayer and the other logical positivists were prepared to accept; in their view, scientific and commonsense claims made on the basis of sensory experience were the paradigm cases of meaningful utterances, and the question was whether other claims of philosophy should also be categorized as meaningful. The moral of this is that if we are trying to establish the meaningfulness of some sentence by relating it to some set of observation sentences, we need not require that we have actually made the observations corresponding to those observation sentences; all that is required is that we could, in principle, make those observations.

Ayer attempts to define meaningfulness in terms of what he calls strong verifiability. Ayer attempts to define meaningfulness in terms of strong verification to include attempts to define meaningfulness in terms of either conclusive verification or conclusive falsification. The first attempt at defining meaningfulness in terms of strong verification is to say that a sentence is meaningful if and only if it is conclusively verifiable. As Ayer notes, there is a problem with this view: Ayer’s point here is a general one, and shows that universally quantified claims are not conclusively verifiable. Because these claims are nonetheless meaningful, the suggested criterion of meaning is not a good one. A second attempt is to say that a sentence is meaningful if it is conclusively falsifiable. Ayer claims that no generalization can either be conclusively verified or falsified by experience, since an observation statement can only contradict a generalization with the help of other supporting propositions.

But this is not obvious; any anyway there is a simpler argument against the equation of meaningfulness with conclusive falsifiability. Just as universal generalizations are not conclusively verifiable, existential generalizations are not conclusively falsifiable. e.g., ‘There is at least one red swan.” It seems that no finite set of observation sentences can entail that this is false, for just the same reason that no finite set of observation sentences can entail that the universal generalization “All swans are non-red” is true. This result suggests an obvious way of extending first two attempts to define meaningfulness in terms of strong verification: we can claim that a sentence is meaningful if and only if it is either conclusively verifiable or conclusively falsifiable. This seems to deal with simple universal generalizations, since they are conclusively falsifiable, and with simple existential generalizations, since they are conclusively verifiable.

This problem suggests that an entirely new approach is in order, and this is in fact what Ayer says: “Accordingly, we fall back on the weaker sense of verification. We say that the question that must be asked about any putative statement of fact is not; would any observations make its truth or falsehood logically certain? But simply, would any observations be relevant to the determination of its truth or falsehood? And it is only if a negative answer is given to this second question that we conclude that the statement under consideration is nonsensical.” This move from focusing on what can be derived from observation claims to focus on what observation claims might be relevant to marks an important. Thus Ayer is of opinion that metaphysical sentences can neither be verified nor falsified. They are just meaningless sentences Later Ayer himself accepted that his theory is not flawless and on the basis of this theory his own proposition can not be verified.