Every meaningful declarative sentence is either true or false
the verdict
CONTESTED
contested - evenly split
refutedsupported
the weight of evidence
2 sources for · 3 against
Logic sources are divided on whether every meaningful sentence is either true or false, with some affirming bivalence while others point to semantic paradoxes like the liar paradox as instances where sentences are neither true nor false.
meaning cannot be said to be either true or false. Sentences are not true or false. Neither are their meanings … of a declarative sentence by a particular person on a particular occasion and is either true or false … cognitively or descriptively meaningful a proposition must be either true or false. A descriptive proposition
Semantic pathologies of self-reference include the Liar ('this sentence is false'), the Truth-Teller ('this sentence is true') and the Open Pair ('the neighbouring sentence is false' 'the neighbouring sentence is false'). Although they seem like perfectly meaningful declarative sentences, truth value assignment to their uses seems either inconsistent (the Liar) or arbitrary (the Truth-Teller and the Open-Pair). These pathologies thus call for a resolution. I propose such a resolution in terms of relative-truth: the truth value of a pathological sentence use varies with the context of its assessment. It always has a determinate truth value, but this truth value is relative to the context of its assessment. I start by considering truth-tellers, that is, sentences which say of themselves that they are true. I make the case that truth value of a given truth-teller use must in general depend on the context of its assessment, and that one can indeed change its truth value at will. I then show how the notion of assessment-sensitive truth can help us provide solutions to other semantic paradoxes such as the Liar and the Open Pair and that those solutions are immune to revenge problems. I conclude by situating my proposal among the main approaches to the semantic paradoxes, and by drawing a very broad moral about pathological self-reference and intentionality.
the sense that, as above, every meaningful sentence is either true or false. In subsequent chapters, we … every identity sentence is either true or false but not both (i.e., true-in-a-case or false-in-a- case, … we assume that every (mathematical) sentence is either true or false—that is, that ei- ther A or A is true
be false, leading to a contradiction if it is either true or false. liar sentence A sentence that asserts its own falsity, such as "This sentence is false
This is a glossary of logic. Logic is the study of the principles of valid reasoning and argumentation.
first-degree entailment (FDE)
A logical system that allows for the existence of both true and false atomic propositions but does not require every proposition to be either true or false, rejecting the law of the excluded middle for certain propositions.
"neither true nor false". This response to the paradox is, in effect, the rejection of the claim that every statement has to be either true or false, also
In philosophy and logic, the classical liar paradox or liar's paradox or antinomy of the liar is the statement of a liar that they are lying: for instance, declaring that "I am lying". If the liar is indeed lying, then the liar is telling the truth, which means the liar just lied. In "this sentence is a lie", the paradox is strengthened in order to make it amenable to more rigorous logical analysi
If (A) is true, then "This statement is false" is true. Therefore, (A) must be false. The hypothesis that (A) is true leads to the conclusion that (A) is false, a contradiction.
If (A) is false, then "This statement is false" is false. Therefore, (A) must be true. The hypothesis that (A) is false leads to the conclusion that (A) is true, another contradiction. Either way, (A) is both true and false, which is a paradox.
However, that the liar sentence can be shown to be true if it is false and false if it is true has led some to conclude that it is "neither true nor false". This response to the paradox is, in effect, the rejection of the claim that every statement has to be either true or false, also known as the principle of bivalence, a concept related to the law of the excluded middle.
The proposal that the statement is neither true nor false has given rise to the following, strengthened version of the paradox:
Assume (D1) is true. Then (D2) is true. This would mean that (D1) is false. Therefore, (D1) is both true and false.
Assume (D1) is false. Then (D2) is false. This would mean that (D1) is true. Thus (D1) is both true and false. Either way, (D1) is both true and false – the same paradox as (A) above.
The multi-sentence version of the liar paradox generalizes to any circular sequence of such statements (wherein the last statement asserts the truth/falsity of the first statement), provided there are an odd number of statements asserting the falsity of their successor; the…
Assume (E1) is true. Then (E2) is false, which means (E3) is true, and hence (E1) is false, leading to a contradiction.
Assume (E1) is false. Then (E2) is true, which means (E3) is false, and hence (E1) is true. Either way, (E1) is both true and false – the same paradox as with (A) and (D1).
There are many other variants, and many complements, possible. In normal sentence construction, the simplest version of the complement is the sentence:
Everything we examined (5) — 3 independent sources
This check searched the claim as stated. It did not run a separate search for evidence against it.