YABLO WITHOUT GODEL
... or syntactic techniques – such as recursion theorem or Gödel’s diagonal lemma – that are often seen as involving self-reference. The axioms used here are to weak to prove such sophisticated lemmata. Thirdly, in Visser’s paradox the satisfaction predicate of level y is applied only to lower levels, ...
... or syntactic techniques – such as recursion theorem or Gödel’s diagonal lemma – that are often seen as involving self-reference. The axioms used here are to weak to prove such sophisticated lemmata. Thirdly, in Visser’s paradox the satisfaction predicate of level y is applied only to lower levels, ...
Weak MSO+U over infinite trees
... a subtree with b-factors of unbounded size. It follows that all the nodes with label a form a connected set, call it X, which contains the root. There must be b-factors of unbounded size below every node from X, however every such b-factor must be finite, and have bounded size b-factors in its subtr ...
... a subtree with b-factors of unbounded size. It follows that all the nodes with label a form a connected set, call it X, which contains the root. There must be b-factors of unbounded size below every node from X, however every such b-factor must be finite, and have bounded size b-factors in its subtr ...
Logic - Disclaimer
... • Obviously, this holds true in general. Hence, showing one possible scenario cannot demonstrate validity! • Of course, we could try and generate all relevant possible worlds, but this method is either impractical (there are too many), or simply impossible (there are infinitely many). ...
... • Obviously, this holds true in general. Hence, showing one possible scenario cannot demonstrate validity! • Of course, we could try and generate all relevant possible worlds, but this method is either impractical (there are too many), or simply impossible (there are infinitely many). ...
Basic Concepts of Formal Logic
... is false. The negation of a proposition, in turn, can be shown to be false if, from it, another proposition that is known to be false can be validly derived. If the conclusion of a valid argument is a false proposition, then at least one of the premises from which that conclusion has been derived mu ...
... is false. The negation of a proposition, in turn, can be shown to be false if, from it, another proposition that is known to be false can be validly derived. If the conclusion of a valid argument is a false proposition, then at least one of the premises from which that conclusion has been derived mu ...
Proofs - Arizona State University
... • Write in complete sentences. While “1+2=3” is a complete sentence it is not possible in a proof since we never start a sentence with a mathematical expression or symbol. Moreover, writing too many equations without words looks more like scratch work. • Only use the (subjective) pronoun we - no oth ...
... • Write in complete sentences. While “1+2=3” is a complete sentence it is not possible in a proof since we never start a sentence with a mathematical expression or symbol. Moreover, writing too many equations without words looks more like scratch work. • Only use the (subjective) pronoun we - no oth ...
Chapter 4. Logical Notions This chapter introduces various logical
... representing the form of m-formulas. Thus (p1Zp2) (viewed now as a metaformula) represents a form whose only instance is the formula (p1Zp2) itself, while (AZB) represents a form whose instances are all the disjunctive formulas. Of course, these formula instances will themselves have 'ordinary' sen ...
... representing the form of m-formulas. Thus (p1Zp2) (viewed now as a metaformula) represents a form whose only instance is the formula (p1Zp2) itself, while (AZB) represents a form whose instances are all the disjunctive formulas. Of course, these formula instances will themselves have 'ordinary' sen ...
Proofs by Contradiction and Contraposition
... statement and make one deduction after another until you reach the conclusion. • Indirect proofs are more roundabout. One kind of indirect proof, argument by contradiction, is based on the fact that either a statement is true or it is false but not both. • So if you can show that the assumption that ...
... statement and make one deduction after another until you reach the conclusion. • Indirect proofs are more roundabout. One kind of indirect proof, argument by contradiction, is based on the fact that either a statement is true or it is false but not both. • So if you can show that the assumption that ...
Internal Inconsistency and the Reform of Naïve Set Comprehension
... excluded from RSC comprehension by the Russell exclusion. It is contended that all set descriptions implicated in the known logical antinomies can be shown intuitively to “contain” their own contradictions since the contradiction is inferred by the set description of an invalid description alone; su ...
... excluded from RSC comprehension by the Russell exclusion. It is contended that all set descriptions implicated in the known logical antinomies can be shown intuitively to “contain” their own contradictions since the contradiction is inferred by the set description of an invalid description alone; su ...
Translating the Hypergame Paradox - UvA-DARE
... The structure of the hypergame paradox may be adapted and proposed in several contexts. Some earlier statements of the paradox (even if not completely clear) can be found in non-technical papers, as Gardner (1984), Smullyan (1983). A more interesting earlier version is due to Shen-Yuting and dates b ...
... The structure of the hypergame paradox may be adapted and proposed in several contexts. Some earlier statements of the paradox (even if not completely clear) can be found in non-technical papers, as Gardner (1984), Smullyan (1983). A more interesting earlier version is due to Shen-Yuting and dates b ...
Section 2.4: Arguments with Quantified Statements
... y = 2m2 is an integer and n = 2 ∗ y, it follows that n2 is an even integer. Note that there we actually excluded a number of steps in this argument (because they were similar to the ones we already stated coming from the elementary rules of arithmetic). In order to make a completely formal argument, ...
... y = 2m2 is an integer and n = 2 ∗ y, it follows that n2 is an even integer. Note that there we actually excluded a number of steps in this argument (because they were similar to the ones we already stated coming from the elementary rules of arithmetic). In order to make a completely formal argument, ...
Logic and Existential Commitment
... elements) may be used in relation to one another and how the truth or falsity of the sentence depends upon such a coordinated use of elements. A possible use will be any coordinated use of the elements of a sentence consistent with its structure. For example, taking ‘and’ to be the logical constant ...
... elements) may be used in relation to one another and how the truth or falsity of the sentence depends upon such a coordinated use of elements. A possible use will be any coordinated use of the elements of a sentence consistent with its structure. For example, taking ‘and’ to be the logical constant ...
Definition: A proof is a system of reasoning or argument to convince
... Fallacies Common to Mathematical Proofs: 1. Hasty generalizations – jumping to conclusions based on insufficient evidence 2. Circular Argument – when you assume what you are trying to prove 3. Accident – misapplying a general principle for a situation for which is was not intended. (e.g. applying m ...
... Fallacies Common to Mathematical Proofs: 1. Hasty generalizations – jumping to conclusions based on insufficient evidence 2. Circular Argument – when you assume what you are trying to prove 3. Accident – misapplying a general principle for a situation for which is was not intended. (e.g. applying m ...
In defence of an argument against truthmaker maximalism
... cannot be used against Milne’s argument since they either lead to contradiction or simply are true sentences. The first result in not surprising, because the sentences of the type of S confuse object-language and metalanguage assigning truth-value to themselves, which results in similar consequences ...
... cannot be used against Milne’s argument since they either lead to contradiction or simply are true sentences. The first result in not surprising, because the sentences of the type of S confuse object-language and metalanguage assigning truth-value to themselves, which results in similar consequences ...
Critical Terminology for Theory of Knowledge
... Typically, what is meant by necessary and sufficient conditions is something stronger: that the conditions are logically necessary or logically sufficient. S is logically sufficient for N if and only if, necessarily, if S, then N; N is logically necessary for S under the same condition. States of a ...
... Typically, what is meant by necessary and sufficient conditions is something stronger: that the conditions are logically necessary or logically sufficient. S is logically sufficient for N if and only if, necessarily, if S, then N; N is logically necessary for S under the same condition. States of a ...
![[Ch 3, 4] Logic and Proofs (2) 1. Valid and Invalid Arguments (§2.3](http://s1.studyres.com/store/data/014954007_1-d36c768aba23f0b4aa633cb9a2a27ee2-300x300.png)
[Ch 3, 4] Logic and Proofs (2) 1. Valid and Invalid Arguments (§2.3
... To say that an argument form is valid means the following: No matter what particular predicates are substituted for the predicate symbols in its premises, if the resulting premise statements are all true, then the conclusion is also true. An argument is called valid if, and only if, its form is vali ...
... To say that an argument form is valid means the following: No matter what particular predicates are substituted for the predicate symbols in its premises, if the resulting premise statements are all true, then the conclusion is also true. An argument is called valid if, and only if, its form is vali ...
Power Point Slides
... • Kant's point, then, is that one cannot define things into existence because existence is not a real property or predicate in the explained sense. If this is what he means, he's certainly right. But is it relevant to the ontological argument? Couldn't Anselm thank Kant for this interesting point an ...
... • Kant's point, then, is that one cannot define things into existence because existence is not a real property or predicate in the explained sense. If this is what he means, he's certainly right. But is it relevant to the ontological argument? Couldn't Anselm thank Kant for this interesting point an ...
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 ...
Truth-tables .1in | University of Edinburgh | PHIL08004 | .3in [width
... 5.123 If a god creates a world in which certain propositions are true, then by that very act he also creates a world in which all the propositions that follow from them come true. And similarly he could not create a world in which the proposition ‘p’ was true without creating all its objects. ...
... 5.123 If a god creates a world in which certain propositions are true, then by that very act he also creates a world in which all the propositions that follow from them come true. And similarly he could not create a world in which the proposition ‘p’ was true without creating all its objects. ...
PROOFS BY INDUCTION AND CONTRADICTION, AND WELL
... n ∈ T for all 1 ≤ n ≤ k. In other words, none of the numbers 1, . . . , k lie in S. Now if k + 1 was in S, it would be a least element, so we must have k + 1 ∈ T instead, which completes the inductive step. We conclude, based on strong induction, that T = N, which contradicts the assumption that S i ...
... n ∈ T for all 1 ≤ n ≤ k. In other words, none of the numbers 1, . . . , k lie in S. Now if k + 1 was in S, it would be a least element, so we must have k + 1 ∈ T instead, which completes the inductive step. We conclude, based on strong induction, that T = N, which contradicts the assumption that S i ...
PROOFS BY INDUCTION AND CONTRADICTION, AND WELL
... n ∈ T for all 0 ≤ n ≤ k. In other words, none of the numbers 0, 1, . . . , k lie in S. Now if k+1 was in S, it would be a least element, so we must have k+1 ∈ T instead, which completes the inductive step. We conclude, based on strong induction, that T = N, which contradicts the assumption that S is ...
... n ∈ T for all 0 ≤ n ≤ k. In other words, none of the numbers 0, 1, . . . , k lie in S. Now if k+1 was in S, it would be a least element, so we must have k+1 ∈ T instead, which completes the inductive step. We conclude, based on strong induction, that T = N, which contradicts the assumption that S is ...
Chapter 1: The Foundations: Logic and Proofs
... that is neither a tautology nor a contradiction. ...
... that is neither a tautology nor a contradiction. ...
Chapter 5: Methods of Proof for Boolean Logic
... it. You repeat this process for each disjunct. So it doesn’t matter which disjunct is true—you get the same conclusion in any case. Hence you may infer that it follows from the entire disjunction. In practice, this method of proof requires the use of “subproofs”—we will take these up in the next cha ...
... it. You repeat this process for each disjunct. So it doesn’t matter which disjunct is true—you get the same conclusion in any case. Hence you may infer that it follows from the entire disjunction. In practice, this method of proof requires the use of “subproofs”—we will take these up in the next cha ...
Conditional and Indirect Proofs
... • A tautology will follow from any premises whatever. • This is because the negation of a tautology is a contradiction, so if we use IP by assuming the negation of a tautology, we can derive a contradiction independently of other premises. This is why this process is called a zeropremise deduction. ...
... • A tautology will follow from any premises whatever. • This is because the negation of a tautology is a contradiction, so if we use IP by assuming the negation of a tautology, we can derive a contradiction independently of other premises. This is why this process is called a zeropremise deduction. ...