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Aristotelian views of (cardinal or counting) numbers begin with Aristotle's observation that the number of a heap or collection is relative to the unit or measure chosen: "'number' means a measured plurality and a plurality of measures ... the measure must always be some identical thing predicable of all the things it measures, e.g. if the things are horses, the measure is 'horse'."
Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship with other human activities. Major themes that are dealt with in philosophy of mathematics include: Reality: The question is whether mathematics is a pure product of human mind or whether it has some reality by itself.
Aristotle. Aristotle[A] (Greek: Ἀριστοτέλης Aristotélēs; [B] 384–322 BC) was an Ancient Greek philosopher and polymath. His writings cover a broad range of subjects spanning the natural sciences, philosophy, linguistics, economics, politics, psychology, and the arts.
Four causes. Aristotle 's Four Causes illustrated for a table: material (wood), formal (structure), efficient (carpentry), final (dining). The four causes or four explanations are, in Aristotelian thought, four fundamental types of answer to the question "why?" in analysis of change or movement in nature: the material, the formal, the efficient ...
Syllogism. A syllogism (Greek: συλλογισμός, syllogismos, 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. "Socrates" at the Louvre. In its earliest form (defined by Aristotle in his 350 BC book Prior ...
Term logic. In logic and formal semantics, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to formal logic that began with Aristotle and was developed further in ancient history mostly by his followers, the Peripatetics.
Actual infinity is now commonly accepted in mathematics under the name "infinite set". Indeed, set theory has been formalized as the Zermelo–Fraenkel set theory (ZF). One of the axioms of ZF is the axiom of infinity, that essentially says that the natural numbers form a set. All mathematics has been rewritten in terms of ZF.
Mathematicism. Mathematicism is 'the effort to employ the formal structure and rigorous method of mathematics as a model for the conduct of philosophy', [1] or the epistemological view that reality is fundamentally mathematical. [2] The term has been applied to a number of philosophers, including Pythagoras [3] and René Descartes [4] although ...