In defence of an argument against truthmaker maximalism
... not. In the first case, S ′ becomes logically inconsistent exactly as in the previous example of ‘consisting of no more than 10 words’ and as in the case of the Liar Sentence, which would mean again its outright inconsistency. But if S ′ is not F , S ′ is again simply true (exactly as in the previou ...
... not. In the first case, S ′ becomes logically inconsistent exactly as in the previous example of ‘consisting of no more than 10 words’ and as in the case of the Liar Sentence, which would mean again its outright inconsistency. But if S ′ is not F , S ′ is again simply true (exactly as in the previou ...
Chapter 1: The Foundations: Logic and Proofs
... Tautology: A compound proposition that is always true. Contradiction: A compound proposition that is always false. Contingency: A compound proposition that is neither a tautology nor a contradiction. ...
... Tautology: A compound proposition that is always true. Contradiction: A compound proposition that is always false. Contingency: A compound proposition that is neither a tautology nor a contradiction. ...
![arXiv:1410.5037v2 [cs.LO] 18 Jun 2016](http://s1.studyres.com/store/data/007883898_2-29c425582568c0e0d15c3d815896c9cf-300x300.png)
Second-order Logic
... First-order logic has a number of nice properties. We know it is not decidable, but at least it is axiomatizable. That is, there are proof systems for first-order logic which are sound and complete, i.e., they give rise to a derivability relation ` with the property that for any set of sentences Γ a ...
... First-order logic has a number of nice properties. We know it is not decidable, but at least it is axiomatizable. That is, there are proof systems for first-order logic which are sound and complete, i.e., they give rise to a derivability relation ` with the property that for any set of sentences Γ a ...
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 ...
Section 1
... Contrapositives, converses, and inverses Definition Consider the implication p q 1. The converse of the implication is 2. The inverse of the implication is 3. The contrapositive of the implication is Proposition 3 1. An implication and its contrapositive are logically equivalent 2. The converse a ...
... Contrapositives, converses, and inverses Definition Consider the implication p q 1. The converse of the implication is 2. The inverse of the implication is 3. The contrapositive of the implication is Proposition 3 1. An implication and its contrapositive are logically equivalent 2. The converse a ...
Chapter 4. Logical Notions This chapter introduces various logical
... seen to be deductive in nature. But these are not questions that we shall explore. The intuitive notion of valid (deductive) argument is sometimes defined in modal terms: a valid argument is said to be one for which it is impossible that the premisses should be true and the conclusion false. This is ...
... seen to be deductive in nature. But these are not questions that we shall explore. The intuitive notion of valid (deductive) argument is sometimes defined in modal terms: a valid argument is said to be one for which it is impossible that the premisses should be true and the conclusion false. This is ...
