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Deductive reasoning is the reasoning of proof, or logical implication. It is the logic used in mathematics and other axiomatic systems such as formal logic. In a deductive system, there will be axioms (postulates) which are not proven. Indeed, they cannot be proven without circularity.
This theory of deductive reasoning – also known as term logic – was developed by Aristotle, but was superseded by propositional (sentential) logic and predicate logic. [citation needed] Deductive reasoning can be contrasted with inductive reasoning, in regards to validity and soundness. In cases of inductive reasoning, even though the ...
As theory of knowledge, epistemology differs from ontology, which is a subbranch of metaphysics, theory of reality. [46] Ontology proposes categories of being—what sorts of things exist—and so, although a scientific theory's ontological commitment can be modified in light of experience, an ontological commitment inevitably precedes ...
[1] [2] [3] It is one of the most famous tasks in the study of deductive reasoning. [4] An example of the puzzle is: You are shown a set of four cards placed on a table, each of which has a number on one side and a color on the other. The visible faces of the cards show 3, 8, blue and red.
Predictions (inductive and deductive reasoning from the hypothesis or theory) Experiments (tests of all of the above) Each element of the scientific method is subject to peer review for possible mistakes. These activities do not describe all that scientists do but apply mostly to experimental sciences (e.g., physics, chemistry, biology, and ...
Non-deductive reasoning is an important form of logical reasoning besides deductive reasoning. It happens in the form of inferences drawn from premises to reach and support a conclusion, just like its deductive counterpart. The hallmark of non-deductive reasoning is that this support is fallible.
A syllogism (Ancient 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.
Set theory originated in the study of the infinite by Georg Cantor, and it has been the source of many of the most challenging and important issues in mathematical logic. They include Cantor's theorem, the status of the Axiom of Choice, the question of the independence of the continuum hypothesis, and the modern debate on large cardinal axioms ...