ASSIGNMENT 3
... example, in modern Euclidean geometry the terms ‘point and ‘line’ are typically left undefined. 2. Axioms (or Postulates): An axiom (or postulate) is a logical statement about terms that is accepted without proof. For example, the statement “A straight line can be drawn from any point to any point” ...
... example, in modern Euclidean geometry the terms ‘point and ‘line’ are typically left undefined. 2. Axioms (or Postulates): An axiom (or postulate) is a logical statement about terms that is accepted without proof. For example, the statement “A straight line can be drawn from any point to any point” ...
Proof
... • “If n is odd and m ≡ 3 (mod 4), then (n2 + m) is divisible by 4.” (More complicated than midterm.) ...
... • “If n is odd and m ≡ 3 (mod 4), then (n2 + m) is divisible by 4.” (More complicated than midterm.) ...
HISTORY OF LOGIC
... Gottlob Frege (1848 – 1925): – Considered to be the father of Analytic Philosophy. – His Objective was demonstrating that arithmetic is identical with logic. – He invented axiomatic predicate logic and quantified variables, which solved the problem of multiple generality. ...
... Gottlob Frege (1848 – 1925): – Considered to be the father of Analytic Philosophy. – His Objective was demonstrating that arithmetic is identical with logic. – He invented axiomatic predicate logic and quantified variables, which solved the problem of multiple generality. ...
PPT
... is both consistent and complete. Suppose Q were provable. Then, P(G(Q)) would be provable, because a proof definitely exists. But Q is true iff G(Q) is not provable. This is a contradiction. Now suppose Q were not provable. Then, P(G(Q)) would not be provable, because a proof definitely doesn’t exis ...
... is both consistent and complete. Suppose Q were provable. Then, P(G(Q)) would be provable, because a proof definitely exists. But Q is true iff G(Q) is not provable. This is a contradiction. Now suppose Q were not provable. Then, P(G(Q)) would not be provable, because a proof definitely doesn’t exis ...
mathematical logic: constructive and non
... Ì [every system S which makes B0, Bv B2,... true) is provable as a theorem. This confirms that the predicate calculus fully accomplishes (for 'elementary theories') what we started out by considering as the role of logic. But what is combined with this in Gödel's completeness theorem (including Löwe ...
... Ì [every system S which makes B0, Bv B2,... true) is provable as a theorem. This confirms that the predicate calculus fully accomplishes (for 'elementary theories') what we started out by considering as the role of logic. But what is combined with this in Gödel's completeness theorem (including Löwe ...