Predicate Premise Propositions

In logic, as in grammar, a subject is that about which we make an assertion, and a predicate is that which we assert about the subject.

In grammar, the predicate of a sentence makes the assertion about the subject, and comprises a finite verb (required), with or without other related words. Thus, the predicate comprises any part of the sentence that is not a part of the subject, but that provides information about the subject.

First order logic applies when the subject of the sentence is an individual object, such as Socrates in "Socrates is mortal". Second order logic applies when the subject is another predicate, for example "being mortal" in "Being mortal is tragic".

Prior to development of predicate logic* in the late 19th c., the logical tradition that originated with Aristotle used traditional logic ("term logic"):
The term is a part of speech representing something, but which is not true or false in its own right, for example "man" or "mortal".
The proposition is capable of truth or falsity, and comprises two terms, in which the predicate is affirmed or denied of the subject.
The syllogism is a logical argument in which one proposition (the conclusion) is inferred from two others (the premises).

The modality of a statement or proposition P is the manner in which P's truth holds.

Propositions may be universal or particular, and affirmative or negative. Thus there are just four kinds of propositions:
A-type: Universal and affirmative or ("All men are mortal")
I-type: Particular and affirmative ("Some men are scientists")
E-type: Universal and negative ("No philosophers are rich")
O-type: Particular and negative ("Some men are not philosophers").

*In informal usage, the term "predicate logic" typically refers to first-order logic. In mathematical logic, predicate logic is the generic term for symbolic formal systems involving formulae with quantifiable variables: examples are first-order logic; second-order logic; many-sorted logic; and infinitary logic. Common quantifiers include existential and universal quantifiers.

In logic, a premise is a statement or assertion that forms the basis for a rationale, approach, or position. Thus, a premise is a proposition that is offered in support of the truth of the conclusion (another proposition) in an argument. A premise of an argument is assumed to be true, though it may in practice be false in arguments that lack validity. The argument proceeds from the premise or premises to the conclusion, and a cogent argument proceeds logically from premise/s to conclusion. Critical thinking aims to discern the cogency and validity of arguments by assessing the acceptability of premises, the logic by which the arguments moves from premise/s to conclusion, and the validity of the conclusion.

In logic, a proposition is a statement, couched as a declarative sentence, that affirms or denies the predicate, and that is either true or false. An analytic proposition can variously be described as a proposition whose predicate concept is contained within its subject concept, a proposition that is true by definition, whose truth depends solely on the meaning of its terms, or a proposition that is made true solely by the conventions of language. Analytic propositions, because truth is built in by virtue of terminology, are all a priori in that they do not require experience. Conversely, a synthetic proposition is a proposition whose predicate concept is not contained in its subject concept. Thus, synthetic propositions are not true simply in virtue of their meaning, so their truth must be assessed on the basis of experience.

Kant, in Critique of Pure Reason, discussed the possible combinations of analytic vs synthetic with a priori vs a posteriori propositions, which yield four possible types of propositions:
1. analytic a priori – according to Kant, all analytic propositions are a priori.
2. synthetic a priori – Kant maintains that all important metaphysical knowledge is of synthetic a priori propositions
3. analytic a posteriori – Kant argues that there are none, because analytic indicates a priori.
4. synthetic a posteriori – knowledge of the truth value of such propositions depends on experience.

Contingent propositions describe conditions that could have been otherwise, and so can be rationally denied without resulting in any self-contradiction. A proposition that describes a necessary truth could not have been otherwise, and so cannot be denied without generating a contradiction.

In logical positivism, propositions are often related to closed sentences, distinguishing them from the content of an open sentence (predicate). Propositions comprise the content of assertions, and are sometimes expressed as non-linguistic abstractions derived from the linguistic sentence that constitutes an assertion. Because propositions can have different functions (names, predicates and logical constants), the nature of propositions is a subject of debate amongst philosophers. Many logicians prefer to use sentences and to avoid use of the term proposition.

"We say that a sentence is factually significant to any given person, if and only if, he knows how to verify the proposition which it purports to express-that is, if he knows what observations would lead him, under certain conditions, to accept the proposition as being true, or reject is as being false." ~ A. J. Ayer
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