In

*logic*, as in

*gramma*r, 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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