PROPOSITION, DEFINED

A proposition refers to any statement which is capable of being determined to be true or false, regardless of whether it is actually true or false. For example, the statements “Hawaii is an archipelago in the Pacific Ocean” and “Hawaii is an archipelago in the Atlantic Ocean” are both propositions. Even though only the former is true, both statements are propositions because both can be determined to be true or false.

On the other hand, the statement “Hawaii is beautiful,” while most people would probably agree with it, is not a proposition because whether Hawaii is beautiful is a matter of opinion and cannot be determined to be true or false.

Nonsensical statements such as “Hawaii is almost” are also not propositions because they cannot be determined to be true or false. All propositions are expressed in language, which means that they must conform to the laws of thought to be coherent.

ANALYTIC VS. SYNTHETIC PROPOSITIONS

Analytic propositions are those whose truth or untruth is determined exclusively by the meaning of their terms. The statement “all bachelors are unmarried” is an example of an analytic proposition that happens to be true, as a bachelor is, by definition, an unmarried man. However, a proposition need not be true to be analytic.  For example, the statement “all bachelors are married” is an analytic proposition even though it is, by definition, untrue.   

Synthetic propositions are those whose truth or untruth is determined by whether their terms accurately correlate to a state of the world of experience. The statement, “Hawaii is an archipelago in the Pacific Ocean” is an example of a synthetic proposition that happens to be true. A synthetic proposition need not be supported by evidence or even plausible. For example, the outlandish proposition “there are sharks living on top of Mount Everest,” is just as synthetic as the proposition that “Hawaii is an archipelago in the Pacific Ocean.” 

POSSIBLE OBJECTIONS TO THE TENABILITY OF ANALYTIC-SYNTHETIC DISTINCTION

The American philosopher Willard Van Orman Quine called the tenability of the distinction between analytic and synthetic propositions into question (see “Two Dogmas of Empiricism”).[1] As I understand him, he called this distinction into question on three grounds.

First, it is not possible in practice to formally distinguish between statements that are true by definition, such as “all bachelors are unmarried,” and statements that depend on information about a state of the world for their truth but which are nonetheless true in all circumstances, such as “some men are bachelors.”

Second, the terms of purely analytic statements are not interchangeable or perfectly synonymous in all circumstances. For example, the terms “bachelor” and “unmarried man” are interchangeable in the statement “all bachelors are unmarried” so that the statement “all unmarried men are unmarried” is perfectly synonymous with it, but these terms are not interchangeable in the statement “bachelor is a single word” because “unmarried men” is not a single word.

Third, all explanations for analyticity are circular because they always require an additional qualifier that is synonymous with analyticity to justify the given explanation for analyticity. For example, to assert that “all bachelors are unmarried” is true by definition, one must assert that “bachelor” and “unmarried man” are synonyms because they are interchangeable, but to adequately express the view that interchangeability is a sufficient condition of synonymy, one must add a qualifier such as the modal adverb “necessarily” and assert, e.g., that “it is necessarily the case that all bachelors, and only bachelors, are unmarried men.”

All of Quine’s objections to the analytic-synthetic distinction have merit. Another objection is that the meaning of terms of analytic propositions depend on factors external to the terms of such propositions in all or nearly all cases. For example, in order to understand the statement “all bachelors are unmarried,” even supposing these terms are necessarily synonymous, one must still understand that a bachelor is a type of person, and one must further understand what it means for a person to be “unmarried” in order for this statement to make sense. One’s understanding of these terms will depend on one’s encounters with those terms in prior contexts and, even more fundamentally, on one’s experience of the states of the world represented by those terms. It is not possible to understand what it means for a man to be a “bachelor” or a person to be “unmarried” if one has never encountered examples of people who are married or unmarried in one’s prior experiences of the world. It is possible to have such an understanding based on imaginary examples, such as characters who are married in a work of fiction, but these are still examples from the world.

ANALYTIC PROPOSITIONS CAN BE OBJECTS OF TRULY JUSTIFIED TRUE BELIEF

None of the foregoing objections to the analytic-synthetic distinction render the statement “all bachelors are unmarried” untrue. This statement is still true in all contexts, as are statements such as “2+2=4” and “all triangles are either equilateral, isosceles, or scalene.” Even if such statements were ultimately synthetic rather than analytic, they would still function as analytic statements in practice and they would remain true in all cases so long as the meanings of the terms that constitute them remain consistent.

Now, if in 200 years the word “bachelor” somehow changes to become synonymous with “husband” rather than “unmarried man,” the statement “all bachelors are unmarried” will no longer be true. Similarly, if the symbol “2” somehow comes to refer to the amount we now refer to with the symbol “3,” while the symbol “4” still refers to the same amount it does now, then the statement “2+2=4” will no longer be true. But unless such improbable changes of meaning occur, it will not be possible to be mistaken about the truth of these statements. It is thus possible to have truly justified true belief in the correctness of such statements.

SYNTHETIC PROPOSITIONS ARE ONLY EVER OBJECTS OF APPARENTLY JUSTIFIED APPARENTLY TRUE BELIEF

In contrast, it is always possible to be mistaken about the truth of clearly synthetic statements like “Hawaii is an archipelago in the Pacific Ocean” or “no sharks live on top of Mount Everest” even if their truth has been repeatedly confirmed by observable evidence. Such statements, even if their truth seems to be fully established, can only be said to be apparently true. And because the justifications upon which belief in them is based can also be mistaken, such justifications are likewise only apparent.

For all synthetic propositions it is only possible to have, at most, apparently justified apparently true belief. This is an awkward turn of phrase, but it must suffice because no more elegant way of expressing the concept is available. This phrasing makes it clear that no synthetic beliefs, no matter how robust and verifiable they seem, and no matter how certain those who hold them claim to be, can ever be known to be true with absolute certainty. Put another way, it is never possible to be certain that any synthetic proposition is true and never possible to be certain that one is justified in believing that any synthetic proposition is true. Thus, it is never possible to be certain that one has truly justified true belief in any synthetic proposition.

However, it is possible to have near-certainty in the truth of some synthetic propositions and thus to treat them as established facts, even if there is a distant possibility that they are false. For example, the statement “all giant pandas in the wild live in China” seems to be true based on repeated observations. Nonetheless, it is possible that some giant pandas in the wild live in, say, Myanmar or Laos. Though unlikely, absolute certainty that no wild pandas live outside China is impossible.

To use an even more extreme example, it is possible to assert with great confidence bordering on absolute certainty that “no sharks live on top of Mount Everest.” To question such a proposition would be ludicrous, but however remote the possibility, it is still possible it is incorrect. If a species of shark were found that can somehow breathe outside of water, maintain its body temperature in frigid environments, and survive the frigid cold of the high Himalaya, it would falsify the proposition. Again, the possibility of finding such a species of shark is so remote as to not warrant serious consideration, but because it is not literally impossible, even the belief that “no sharks live on top of Mount Everest” can only be said to be apparently justified and apparently true.

Another way of making the same point without resorting to absurd examples is to state that it is possible that any belief in any synthetic proposition, no matter how seemingly obvious, could be wrong. Indeed, many seemingly obvious beliefs have been shown to be wrong by later observations and discoveries. For example, it was once widely believed and held to be common knowledge in Europe that there were no black swans in the world, but this changed when the Dutch explorer Willem de Vlamingh discovered black swans in Australia in the late seventeenth century.

ON POSSIBLY JUSTIFIED POSSIBLY TRUE BELIEF

In addition to apparently justified apparently true belief, it is possible to have mere possibly justified possibly true belief in a synthetic proposition. But to say a proposition is possibly true is also to say it is possibly false, and to say one is possibly justified in believing a proposition is also to say one is possibly not justified in believing it. Thus, if a proposition is possibly justified and possibly true, this simply means that there is insufficient evidence to determine its apparent truth or its apparent falsehood, either way. However, this does not necessarily mean that one who cares about truth and the search for truth must adopt an agnostic attitude or suspend judgment with respect to possibly justified possibly true beliefs unless more evidence emerges. Indeed, I will argue that nonbelief is fully warranted in such cases.    

CITATION

[1] Quine, Willard van Orman. “Two Dogmas of Empiricism.” The Philosophical Review 60 (1951): 20-43. Available online at http://www.ditext.com/quine/quine.html (last accessed 12 Apr. 2022).