In philosophy of mind: Thoughts and propositions It was noted above that understanding is a relation that someone can bear to a thought. But what sort of thing is a thought? This is a topic of enormous controversy, but one can begin to get a grasp of it by noticing that… Read More
epistemological distinctions
In epistemology: A priori and a posteriori knowledge …of as applying to “propositions,” which may be thought of as the contents, or meanings, of sentences that can be either true or false. For example, the English sentence “Snow is white” and the German sentence “Schnee ist weiß” have the same meaning, which is the proposition “Snow is… Read More
predication
In predication …subject to produce a meaningful statement combining verbal and nominal elements. Thus, a characteristic such as “warm” (conventionally symbolized by a capital letter W) may be predicated of some singular subject, for example, a dish—symbolized by a small letter d, often called the “argument.” The resulting statement is “This dish… Read More
logic
In logic: Scope and basic concepts …step from one or more propositions, called premises, to a new proposition, usually called the conclusion. A rule of inference is said to be truth-preserving if the conclusion derived from the application of the rule is true whenever the premises are true. Inferences based on truth-preserving rules are called deductive,… Read More
Aristotle’s syllogisms
In Aristotle: Syllogistic …which deal respectively with words, propositions, and syllogisms. These works, along with the Topics, the Sophistical Refutations, and a treatise on scientific method, the Posterior Analytics, were grouped together in a collection known as the Organon, or “tool” of thought. Read More
In history of logic: Categorical forms …concerned with certain kinds of propositions that can be analyzed as consisting of (1) usually a quantifier (“every,” “some,” or the universal negative quantifier “no”), (2) a subject, (3) a copula, (4) perhaps a negation (“not”), (5) a predicate. Propositions analyzable in this way were later called categorical propositions Read More
formal logic
In formal logic …logic, the abstract study of propositions, statements, or assertively used sentences and of deductive arguments. The discipline abstracts from the content of these elements the structures or logical forms that they embody. The logician customarily uses a symbolic notation to express such structures clearly and unambiguously and to enable manipulations… Read More
modal logic
In formal logic: Modal logic True propositions can be divided into those—like “2 + 2 = 4”—that are true by logical necessity (necessary propositions), and those—like “France is a republic”—that are not (contingently true propositions). Similarly, false propositions can be divided into those—like “2 + 2 = 5”—that are false by… Read More
predicate calculus
In formal logic: The predicate calculus Propositions may also be built up, not out of other propositions but out of elements that are not themselves propositions. The simplest kind to be considered here are propositions in which a certain object or individual (in a wide sense) is said to possess a… Read More
propositional calculus
In formal logic: Basic features of PC …branch of logic is the propositional calculus, hereafter called PC, so named because it deals only with complete, unanalyzed propositions and certain combinations into which they enter. Various notations for PC are used in the literature. In that used here the symbols employed in PC first comprise variables (for which… Read More
Stoic logic
In history of logic: The Megarians and the Stoics …words used to combine simpler propositions into more complex ones. In addition to the conditional, which had already been explored by the Megarians, they investigated disjunction (or) and conjunction (and), along with words such as since and because. Some of these they defined truth-functionally (i.e., solely in terms of the… Read More
syllogistic
In syllogistic …A, E, I, and O propositions. The proposition “Every b is an _a_” is now written “_Aba_”; “Some b is an _a_” is written “_Iba_”; “No b is an _a_” is written “_Eba_”; and “Some b is not an a_” is written “_Oba.” Careful examination of the relations obtaining between… Read More
philosophy of
Empiricism
In empiricism: Fundamental distinctions Propositions such as “all triangles have three sides,” “all bachelors are unmarried,” and “all red things are coloured” are necessarily true in one or both of these senses. Likewise, it was held that propositions that are contingently true, or true merely by virtue of the… Read More
Hume
Leibniz
In Gottfried Wilhelm Leibniz: The Hanoverian period of Gottfried Wilhelm Leibniz …unpublished, was his generalization concerning propositions that in every true affirmative proposition, whether necessary or contingent, the predicate is contained in the notion of the subject. This notion seemed to imply determinism and thus to undermine human freedom—as did Leibniz’s conception of monads, the soul-like individual substances that make up… Read More
logical atomism
In analytic philosophy: Logical atomism …facts, those expressible by atomic propositions. More complex propositions, called molecular propositions, are built up out of atomic propositions via the logical connectives—such as “… or …,” “… and …,” and “… not …”—and the truth-value of the molecular proposition is in each case a function of the truth-values of… Read More
In Ludwig Wittgenstein …of which is that a proposition can express a fact by virtue of sharing with it a common structure or “logical form.” This logical form, however, precisely because it is what makes “picturing” possible, cannot itself be pictured. It follows both that logic is inexpressible and that there are—pace Frege… Read More
