Reference - Wylie Breckenridge
... formulation of some claims in the preceding paragraph. For present purposes, these will do. ...
... formulation of some claims in the preceding paragraph. For present purposes, these will do. ...
Formal Reasoning - Institute for Computing and Information Sciences
... The sentence ‘if a and b, then a’ is true, whatever you substitute for a and b. So, we’d like to be able to say: the sentence ‘a ∧ b → a’ is true2 . But we can’t, because we haven’t formally defined what that means yet. As of yet, ‘a ∧ b → a’ is only one of the words of our formal language. Which is ...
... The sentence ‘if a and b, then a’ is true, whatever you substitute for a and b. So, we’d like to be able to say: the sentence ‘a ∧ b → a’ is true2 . But we can’t, because we haven’t formally defined what that means yet. As of yet, ‘a ∧ b → a’ is only one of the words of our formal language. Which is ...
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Logic and Existential Commitment
... non-logical elements. The structure of a sentence determines how its unstructured parts (or 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 s ...
... non-logical elements. The structure of a sentence determines how its unstructured parts (or 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 s ...
A Syntactic Characterization of Minimal Entailment
... data base, ϕ ∨ ψ cannot be derived from that data base. It has been proved (cf. [She88], thm. 32.5) that GCWA coincides with cwa in all data bases for which cwa is consistent. Another version of closed world assumption, cwaS , has been proposed in [Suc87]: A sentence ϕ is asserted if, and only if, ...
... data base, ϕ ∨ ψ cannot be derived from that data base. It has been proved (cf. [She88], thm. 32.5) that GCWA coincides with cwa in all data bases for which cwa is consistent. Another version of closed world assumption, cwaS , has been proposed in [Suc87]: A sentence ϕ is asserted if, and only if, ...
How Robust can Inconsistency Get?
... This is rather striking. For anyone at ease with excluded middle, Hewitt’s generalized proof does for consistency the sort of thing the Curry-proof did for truth.10 That is, it proves that there is massively too much of it. This we might call “the paradox of consistency.” I don’t want to overpress t ...
... This is rather striking. For anyone at ease with excluded middle, Hewitt’s generalized proof does for consistency the sort of thing the Curry-proof did for truth.10 That is, it proves that there is massively too much of it. This we might call “the paradox of consistency.” I don’t want to overpress t ...
An Introduction to Löb`s Theorem in MIRI Research
... This expository note is devoted to answering the following question: why do many MIRI research papers cite a 1955 theorem of Martin Löb [12], and indeed, why does MIRI focus so heavily on mathematical logic? The short answer is that this theorem illustrates the basic kind of self-reference involved ...
... This expository note is devoted to answering the following question: why do many MIRI research papers cite a 1955 theorem of Martin Löb [12], and indeed, why does MIRI focus so heavily on mathematical logic? The short answer is that this theorem illustrates the basic kind of self-reference involved ...
Symbolic Logic I: The Propositional Calculus
... For a random example, suppose that we are given statements L, M, P, Q in S. We may first form, say, L ∧ M and P ∨ Q, then form ¬(L ∧ M ) and P ∨ (¬(L ∧ M )), and then, finally, (P ∨ Q) ⇒ (P ∨ (¬(L ∧ M ))). We have inserted parentheses to indicate that what they enclose is to be regarded as denoting ...
... For a random example, suppose that we are given statements L, M, P, Q in S. We may first form, say, L ∧ M and P ∨ Q, then form ¬(L ∧ M ) and P ∨ (¬(L ∧ M )), and then, finally, (P ∨ Q) ⇒ (P ∨ (¬(L ∧ M ))). We have inserted parentheses to indicate that what they enclose is to be regarded as denoting ...
If…then statements If A then B The if…then statements is a
... If…then statements If A then B The if…then statements is a conditional statement. B “requires” A to happen. This establishes a conditional relationship. A proof is a formal justification of a hypothesis. A hypothesis is a possible explanation for an observation that has yet to be established as fact ...
... If…then statements If A then B The if…then statements is a conditional statement. B “requires” A to happen. This establishes a conditional relationship. A proof is a formal justification of a hypothesis. A hypothesis is a possible explanation for an observation that has yet to be established as fact ...
Chpt-3-Proof - WordPress.com
... The universal statement x P(x) is false if x D such that P(x) is false. The value x that makes P(x) false is called a counterexample to the statement x P(x). – Example: P(x) = "every x is a prime number", for every integer x. – But if x = 4 (an integer) this x is not a primer number. Then 4 is ...
... The universal statement x P(x) is false if x D such that P(x) is false. The value x that makes P(x) false is called a counterexample to the statement x P(x). – Example: P(x) = "every x is a prime number", for every integer x. – But if x = 4 (an integer) this x is not a primer number. Then 4 is ...
this PDF file - Lexicon Philosophicum
... contradictory way be only the affirmation or the negation of one thing about one thing. So it is possible to show how the principle known as of excluded middle establishes the ‘necessary duality’ of affirmation and negation. When applied to propositions, ‘necessary duality’ means that one cannot exp ...
... contradictory way be only the affirmation or the negation of one thing about one thing. So it is possible to show how the principle known as of excluded middle establishes the ‘necessary duality’ of affirmation and negation. When applied to propositions, ‘necessary duality’ means that one cannot exp ...
31-3.pdf
... with how complicated it is to describe a set in terms of how many quantifiers you need and what symbols are needed in the language. There are many connections to complexity theory in that virtually all descriptive classes are equivalent to the more standard complexity classes. 2. Theory of Computing ...
... with how complicated it is to describe a set in terms of how many quantifiers you need and what symbols are needed in the language. There are many connections to complexity theory in that virtually all descriptive classes are equivalent to the more standard complexity classes. 2. Theory of Computing ...
sophisms and insolubles
... over 60 sophisms concern respectively two specific kinds of syncategorematic words. One of these consists of words expressing exclusion or exception (such as tantum ‘only’, solus ‘alone’, and praeter ‘except’), and the other consists of words like omnis ‘every’, which signal universal ...
... over 60 sophisms concern respectively two specific kinds of syncategorematic words. One of these consists of words expressing exclusion or exception (such as tantum ‘only’, solus ‘alone’, and praeter ‘except’), and the other consists of words like omnis ‘every’, which signal universal ...
Lambda in Sentences with Designations: An Ode to
... lxiv (1990): 93–119, at p. 95n6. The basic idea is that, where a and b are exactly synonymous terms (terms having the very same semantic content), fab is a sentence containing free occurrences of both terms, and faa is the result of substituting free occurrences of a for free occurrences of b in fab ...
... lxiv (1990): 93–119, at p. 95n6. The basic idea is that, where a and b are exactly synonymous terms (terms having the very same semantic content), fab is a sentence containing free occurrences of both terms, and faa is the result of substituting free occurrences of a for free occurrences of b in fab ...
Meaning before truth
... speciWcation of what the lexical items mean; where such a speciWcation can be given disquotationally, using ‘‘axioms’’ like ‘barked means BARKED’ to report that a certain word means what it does. But this seems wrong, for reasons discussed by Higginbotham (1985) and others. To understand a complex e ...
... speciWcation of what the lexical items mean; where such a speciWcation can be given disquotationally, using ‘‘axioms’’ like ‘barked means BARKED’ to report that a certain word means what it does. But this seems wrong, for reasons discussed by Higginbotham (1985) and others. To understand a complex e ...
View PDF - CiteSeerX
... to account for someone’s a priori knowledge, regardless of the language he learns and speaks, by appeal to a metalinguistic notion like analyticity, “is analytic” must be applicable to every possible language in which mathematical and logical truths are expressible. Quine’s criticisms of Carnap’s di ...
... to account for someone’s a priori knowledge, regardless of the language he learns and speaks, by appeal to a metalinguistic notion like analyticity, “is analytic” must be applicable to every possible language in which mathematical and logical truths are expressible. Quine’s criticisms of Carnap’s di ...
The Future of Post-Human Mathematical Logic
... (and Other Mental States) ............................................................67 Table 1.11. The Theoretical Levels of Consciousness (and Other Mental States) ............................................................68 Table 1.12. The Thematic Issues of Consciousness (and Other Mental Sta ...
... (and Other Mental States) ............................................................67 Table 1.11. The Theoretical Levels of Consciousness (and Other Mental States) ............................................................68 Table 1.12. The Thematic Issues of Consciousness (and Other Mental Sta ...