Subjunctive possibilitySubjunctive possibility (also called alethic possibility) is a form of modality studied in modal logic. Subjunctive possibilities are the sorts of possibilities considered when conceiving counterfactual situations; subjunctive modalities are modalities that bear on whether a statement might have been or could be true—such as might, could, must, possibly, necessarily, contingently, essentially, accidentally, and so on. Subjunctive possibilities include logical possibility, metaphysical possibility, nomological possibility, and temporal possibility.
DialecticDialectic (διαλεκτική, dialektikḗ; Dialektik), also known as the dialectical method, refers originally to dialogue between people holding different points of view about a subject, but wishing to arrive at the truth through reasoned argumentation. Dialectic resembles debate, but the concept excludes subjective elements such as emotional appeal and rhetoric. It has its origins in ancient philosophy and continued to be developed in the Middle Ages. In the modern period, Hegelianism refigured "dialectic" to no longer refer to a literal dialogue.
Neutral monismNeutral monism is an umbrella term for a class of metaphysical theories in the philosophy of mind, concerning the relation of mind to matter. These theories take the fundamental nature of reality to be neither mental nor physical; in other words it is "neutral". Neutral monism has gained prominence as a potential solution to theoretical issues within the philosophy of mind, specifically the mind–body problem and the hard problem of consciousness. The mind–body problem is the problem of explaining how mind relates to matter.
PragmatismPragmatism is a philosophical tradition that considers words and thought as tools and instruments for prediction, problem solving, and action, and rejects the idea that the function of thought is to describe, represent, or mirror reality. Pragmatists contend that most philosophical topics—such as the nature of knowledge, language, concepts, meaning, belief, and science—are all best viewed in terms of their practical uses and successes. Pragmatism began in the United States in the 1870s.
Syntax (logic)In logic, syntax is anything having to do with formal languages or formal systems without regard to any interpretation or meaning given to them. Syntax is concerned with the rules used for constructing, or transforming the symbols and words of a language, as contrasted with the semantics of a language which is concerned with its meaning. The symbols, formulas, systems, theorems, proofs, and interpretations expressed in formal languages are syntactic entities whose properties may be studied without regard to any meaning they may be given, and, in fact, need not be given any.
Cantor's theoremIn mathematical set theory, Cantor's theorem is a fundamental result which states that, for any set , the set of all subsets of the power set of has a strictly greater cardinality than itself. For finite sets, Cantor's theorem can be seen to be true by simple enumeration of the number of subsets. Counting the empty set as a subset, a set with elements has a total of subsets, and the theorem holds because for all non-negative integers. Much more significant is Cantor's discovery of an argument that is applicable to any set, and shows that the theorem holds for infinite sets also.
