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Verificationism is the view that a statement or question is only legitimate if there is some way to determine whether the statement is true or false, or what the answer to the question is. It is a view mostly closely associated with the logical positivists of the early twentieth century, who established and applied this doctrine to distinguish between meaningful and meaningless assertive sentences. However, the core idea of verificationism is much older, dating back at least to Hume and the empiricists, who believed that observation was the only way we can acquire knowledge.
Historically, the verificationist criterion has been used to render meaningless, false, unscientific, or in some other way illegitimate many philosophical debates, due to their positing of unverifiable statements or concepts. Notoriously, verificationism was used by the logical positivists to rule out as meaningless religious, metaphysical, aesthetic, and ethical sentences. However, not all verificationists have found all sentences of these types to be unverifiable. The classical pragmatists, for example, saw verificationism as a guide for doing good work in religion, metaphysics, and ethics.
Early Verificationists 
All of the empiricists back to Locke could be treated as verificationists. The basic tenet of empiricism is that experience is our only source of knowledge and verificationism might be seen as simply a consequence of this tenet. Empiricists held that our ideas are either simple sense-perceptions or compilations and mixtures of these basic sense-perceptions. Reading this empiricist account, there does not seem to be any way for an idea to get into our heads without being connected to our perceptions and, thus, being connected to a means of verification.
The empiricists did not directly put forth a criterion of meaningfulness, but one could be seen as equivalent to the empiricists' claim that ideas not connected to experience are "empty". It is worth noting, however, that verificationism need not be a position about meaning. It could simply be the position that unverifiable sentences are defective in some way that is similar to how false sentences and meaningless sentences are defective. Empiricists could therefore be read as asserting that unverifiable sentences are defective not because they are meaningless, but because they contain terms standing for ideas/concepts that we cannot possibly possess. Or, the empiricist could be read as asserting the semantic position that unverifiable sentences are meaningless precisely because they contain terms standing for ideas/concepts that we cannot possibly acquire.
Auguste Comte put forth a semantic position not about the meaninglessness of unverifiable sentences, but rather about the pointlessness of considering them since they cannot be verified. This sort of rejection of unverifiable sentences as useless rather than meaningless would reoccur in the work of the classical pragmatists alongside their semantic verificationism. Comte was a rather extreme verificationist, rejecting everything we cannot have direct experience of. This included statements about the past, universal generalizations, as well as abstract objects like universals.
Logical Positivism 
While verificationism is not credited to A.J. Ayer, his work Language, Truth and Logic (1936) is one of the most widely known and read defenses of the verification principle and logical positivism generally. In that work, Ayer explains that the verificationist principle puts forth a criterion for meaningfulness that requires a non-analytic, meaningful sentence to be empirically verifiable.
It was hotly disputed amongst the logical positivists whether the empirical verification itself must be possible in practice or merely in principle. A statement about the core of the sun might one day be possible to confirm through observations using a technology that hasn't been invented yet, but until then it may be unverifiable in all practical senses. Ayer also distinguished between strong and weak verification.
Strong verification refers to statements which are directly verifiable, that is, a statement can be shown to be correct by way of empirical observation. For example, 'There are human beings on Earth.'
Weak verification refers to statements which are not directly verifiable, for example 'Yesterday was a Monday'. The statement could be said to be weakly verified if empirical observation can render it highly probable.
That is, strong statements are those that can be verified independently of context, while weak statements depend on context.
Despite slightly pre-dating logical positivism, pragmatism had very little influence on the logical positivists and most attention paid to verificationism has been directed to the positivists. This is mostly because logical positivism, unlike pragmatism, held the possibility of dismissing whole disciplines like metaphysics, morality, and ethics. The pragmatists differed from the logical positivists in their hospitality to areas of knowledge that the positivists hoped their principle would undermine. The pragmatists did not want to rule out metaphysics, religion, or ethics with the verification principle; they wanted to provide a standard for conducting good metaphysics, religion, and ethics.
It is commonly believed that Karl Popper rejected the requirement that meaningful sentences be verifiable, demanding instead that they be falsifiable. However, Popper later claimed that his demand for falsifiability was not meant as a theory of meaning, but rather as a methodological norm for the sciences. Often, and to Popper's dismay, he is grouped together with the verificationists rather than as a critic of verificationism.
Post-Positivist Verificationists 
Quine and the Dogmas of Empiricism (1951) 
Verificationists need not be logical positivists. Willard Van Orman Quine is a famous example of a verificationist who does not accept logical positivism, on grounds of semantic holism. He suggests that, for theoretical sentences as opposed to observation sentences, meaning is "infected by theory". That theoretical sentences are reducible to observation sentences is one of the ‘dogmas of empiricism’ he rejects as incompatible with semantic holism.
Wittgenstein and the Private Language Argument (1953) 
Some interpretations of the Private Language argument see it as a form of verificationism. So for example, Misak claims that:
To say that P is a sentence in a private language is to say that there does not have to be any public consequences if P is true [....] But then 'P seems right to me' will always be a sufficient condition for 'P is right'. There is nothing that would count as evidence for or against the private linguist's claim that she is using a term in the same way or that she is picking out the same property by the term. Nothing would count as evidence to an observer and nothing would count as evidence to the speaker herself.
As we have seen, a crucial part is played in the private-language argument by Wittgenstein's advice 'Always get rid of the idea of the private object in this way: assume that it constantly changes, but that you do not notice the change because your memory constantly deceives you.' This advice has a verificationist ring, and some philosophers have thought that the private-language argument depends, in the last analysis, on verificationist premises. But Wittgenstein's advice is not meant to be followed by the question 'How would you ever find out?' but by the question 'What possible difference would it make?' The private-language argument does indeed depend on premises carried forward from Wittgenstein's earlier philosophy; but they are not peculiar to the verificationist period of the 1930s but date back to the time of the picture theory of the proposition in the 1910s[.] 
Bas van Fraassen and Constructive Empiricism (1980) 
After the fall of logical positivism, verificationism and empiricism more generally lost many adherents. This trend was stopped and in large part reversed in 1980 with the publication of van Fraassen's The Scientific Image. Constructive empiricism states that (1) scientific theories do not aim at truth, but at empirical adequacy; and (2) that their acceptance involves a belief only that they are empirically adequate. A theory is empirically adequate if and only if everything that it says about observable entities is "true" (or well-established). Constructive empiricism therefore rejects unverifiable positions not because they lack truth or meaning, but because they go beyond what is needed to be empirically adequate.
Arthur Fine and the Natural Ontological Attitude (1986) 
In 1986, Arthur Fine offered an important alternative to van Fraassen's constructive empiricism with what he decided to playfully entitle the Natural Ontological Attitude (NOA). Fine holds that scientific anti-realists like van Fraassen beg the question against scientific realists when they assume that in theory selection there do not exist reasons to select theories that go beyond what is needed to be empirically adequate. Fine argues that we can avoid this mistake by taking note of what antirealists and realists will both agree to: the reliability of our scientific theories. This recognition of common ground brings Fine to argue that instead of aiming at true scientific theories (as the realist does) or empirically adequate theories (as the constructive empiricist does), we should aim for scientific theories that are reliable for our purposes. Fine's position has an advantage over van Fraassen's constructive empiricism in that a NOAer has a ready-made explanation for why there is no reason to select theories that go beyond what is reliable for our purposes; namely, that such theories are irrelevant to our purposes. For this reason Fine is similar to the classical pragmatists from whom he takes inspiration.
It is frequently argued that the verification principle is self-refuting, in that it is neither empirically verifiable nor tautologous. However, broader criticisms of verificationism are normally based on the impossibility of verifying specific instances of entities. The first problem faced is vagueness—in trying to verify that something is a tree, the term tree is too vague to present any conclusive answer in some cases. The second is that of open texture—even if it appears to be conclusively verified that something is not made of gold, the definition of "gold" could change as to allow said object into the category. These criticisms were first presented by Friedrich Waismann.
A shortcoming of verificationism is the inability to verify one time events in the past. Many people make claims about one time events which occurred in the past and their truthfulness or falsity are unable to be verified in the present by observations of conditions in nature or under experiment. Claims about events in the past being evidence of the true nature of reality are by their nature unverifiable. Current observations can only be used to make probability guesses based on deductive reasoning. This applies to many claims including the beginning of time and existence of matter (one of which is the Big Bang Theory), the age of the Universe, the age of the Earth, the origin of the Moon, and the occurrence of magical events in the past. The verifiability of claims, or more precisely observations increasing the probability of a claim being true or false, often differentiates different schools of thought based on the methods that are defined as legitimate forms of deductive reasoning utilized in the verification process. For instance magical thinking is unacceptable to rationalists, while it is the foundational basis of many theists whose belief systems are based on miracles occurring in the past.
See also 
|Early Verificationists||Pragmatists||Logical Positivists||Logical Atomists||Post-Positivist Verificationists|
|George Berkeley (1685–1753)||C.S. Peirce (1839–1914)||Moritz Schlick (1882–1936)||Bertrand Russell (1872–1970)||Arthur Fine (1937–Present)|
|David Hume (1711–1776)||William James (1842–1910)||Rudolf Carnap (1891–1970)||Early Ludwig Wittgenstein (1889–1951)||Michael Dummett (1925–2011)|
|Auguste Comte (1798–1857)||F.C.S. Schiller (1864–1937)||Otto Neurath (1882–1945)||Willard Van Orman Quine (1908–2000)|
|Ernst Mach (1838–1916)||John Dewey (1859–1952)||A.J. Ayer (1910–1989)||Bas van Fraassen (1941–Present)|
|Pierre Duhem (1861–1916)||Hans Reichenbach (1891–1953)||Karl Popper (1902–1994)||David Wiggins (1933–Present)|
|Carl Hempel (1905–1997)||Christopher Peacocke (1950–Present)|
- James's exact words, in the essay "What Pragmatism Means" in his book Pragmatism (1907) are "There can be no difference anywhere that doesn't make a difference elsewhere — no difference in abstract truth that doesn't express itself in a difference in concrete fact and in conduct consequent upon that fact, imposed on somebody, somehow, somewhere and somewhen."
- See, for example, the last paragraph of section 2 in ``Science: Conjectures and Refutations
- Misak 1995, p.54; cf. pp.53-55, 133
- Anthony Kenny, Wittgenstein, p. 195