The Logical Foundations of Induction information

The Logical Foundations of Induction (Arabic: الأسس المنطقية للاستقراء) is a philosophical book by the Shia jurisprudent and philosopher Sayyid Muhammad...

enumerative induction to have no rational, let alone logical, basis; instead, induction was the product of instinct rather than reason, a custom of the mind...

to the next one (the step). — Concrete Mathematics, page 3 margins. A proof by induction consists of two cases. The first, the base case, proves the statement...

inference, or retroduction) is a form of logical inference that seeks the simplest and most likely conclusion from a set of observations. It was formulated...

disjunct of a logical disjunction must be false because the other disjunct is true; A or B; A, therefore not B. Affirming the consequent – the antecedent...

Transfinite induction is an extension of mathematical induction to well-ordered sets, for example to sets of ordinal numbers or cardinal numbers. Its correctness...

the same logical form is also valid, no matter how different it is on the level of its contents. Logical consequence is knowable a priori in the sense that...

valid logical argument is one in which the conclusion is entailed by the premises, because the conclusion is the consequence of the premises. The philosophical...

In a narrow sense, foundations of mathematics is the logical and mathematical framework that allows developing mathematics without generating self-contradictory...

establish foundations of mathematics. Since its inception, mathematical logic has both contributed to and been motivated by the study of foundations of mathematics...

Europe before 1935 and in the United States thereafter. He was a major member of the Vienna Circle and an advocate of logical positivism. Carnap's father...

deduction and induction, a distinction that in Europe dates at least to Aristotle (300s BCE). Deduction is inference deriving logical conclusions from...

"principle of induction" to be par with the various "logical principles" that include the "Laws of Thought". In his Part I "The Indefinables of Mathematics"...

philosophers of the 20th century. His two most important contributions to philosophy are his books "Our Philosophy" and "The Logical Foundations of Induction." He...

Logical positivism, later called logical empiricism, and both of which together are also known as neopositivism, is a movement whose central thesis is...

undefined values in a logical system. strong mathematical induction A form of mathematical induction that allows one to assume the proposition for all smaller...

This logical perspective on argument is relevant for scientific fields such as mathematics and computer science. Logic is the study of the forms of reasoning...

Logical truth is one of the most fundamental concepts in logic. Broadly speaking, a logical truth is a statement which is true regardless of the truth...

is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths...

The problem of induction is a philosophical problem that questions the rationality of predictions about unobserved things based on previous observations...

logic, the logical form of a statement is a precisely-specified semantic version of that statement in a formal system. Informally, the logical form attempts...

axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning which establish logical certainty, to be distinguished...

(1948). The theory of probability, an inquiry into the logical and mathematical foundations of the calculus of probability. University of California Press...

prove—and I do not think the proof can be controverted—is that the induction is an independent logical principle, incapable of being inferred either from...

Carnap's Logical Foundations of Probability and E.T. Jaynes Probability Theory: The Logic of Science. Keynes's conception of this generalised notion of probability...

or other symbols instead of logic symbols. In logic, a set of symbols is commonly used to express logical representation. The following table lists many...

resolved by making foundational changes in a logical system. Examples outside logic include the ship of Theseus from philosophy, a paradox that questions...

[citation needed] The logical notation in PM was not widely adopted, possibly because its foundations are often considered a form of Zermelo–Fraenkel set...