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A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems ; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms ...
Logical reasoning is a mental activity that aims to arrive at a conclusion in a rigorous way. It happens in the form of inferences or arguments by starting from a set of premises and reasoning to a conclusion supported by these premises.
Each premise and the conclusion can be of type A, E, I or O, and the syllogism can be any of the four figures. A syllogism can be described briefly by giving the letters for the premises and conclusion followed by the number for the figure. For example, the syllogism BARBARA below is AAA-1, or "A-A-A in the first figure".
Critical thinking is the process of analyzing available facts, evidence, observations, and arguments to make sound conclusions or informed choices. It involves recognizing underlying assumptions, providing justifications for ideas and actions, evaluating these justifications through comparisons with varying perspectives, and assessing their rationality and potential consequences. [1]
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Circumstantial ad hominem – stating that the arguer's personal situation or perceived benefit from advancing a conclusion means that their conclusion is wrong. [ 73 ] Poisoning the well – a subtype of ad hominem presenting adverse information about a target person with the intention of discrediting everything that the target person says.
Inductive reasoning is any of various methods of reasoning in which broad generalizations or principles are derived from a body of observations. [1] [2] This article is concerned with the inductive reasoning other than deductive reasoning (such as mathematical induction), where the conclusion of a deductive argument is certain given the premises are correct; in contrast, the truth of the ...
The conclusion is rephrased to look different and is then placed in the premises. — Paul Herrick [ 2 ] For example, one can obscure the fallacy by first making a statement in concrete terms, then attempting to pass off an identical statement, delivered in abstract terms, as evidence for the original. [ 13 ]
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