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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.
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.
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 ...
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.
Mathematics is the classification and study of all possible patterns. [ 14 ] Walter Warwick Sawyer, 1955. Yet another approach makes abstraction the defining criterion: Mathematics is a broad-ranging field of study in which the properties and interactions of idealized objects are examined. [ 15 ]
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