Braun Defended
... ignores the distinction between the proposition expressed by a sentence, its assertoric content, and what contribution a sentence makes to complex sentences of which it is a part, its ingredient sense. If we distinguish the two, then sentences which express the same proposition can embed within the ...
... ignores the distinction between the proposition expressed by a sentence, its assertoric content, and what contribution a sentence makes to complex sentences of which it is a part, its ingredient sense. If we distinguish the two, then sentences which express the same proposition can embed within the ...
IS IT EASY TO LEARN THE LOGIC
... primarily applied to the logical handling of natural language, because this is the language used in academic work and future research. 5. Decision and demonstration procedure In everyday life, we often solve logical and mathematical problems, but what happens with the logic and mathematics as scienc ...
... primarily applied to the logical handling of natural language, because this is the language used in academic work and future research. 5. Decision and demonstration procedure In everyday life, we often solve logical and mathematical problems, but what happens with the logic and mathematics as scienc ...
Discrete Structure
... equivalences instead. They provide a pattern or template that can be used to match all or part of a much more complicated proposition and to find an equivalence for it. ...
... equivalences instead. They provide a pattern or template that can be used to match all or part of a much more complicated proposition and to find an equivalence for it. ...
To What Type of Logic Does the "Tetralemma" Belong?
... anhomomorphic logic opens up another interpretation, perhaps consistent with the mystical one, but not really requiring it. Namely one can imagine that Nagarjuna’s blanket denial represents a kind of “second order” application of anhomomorphic logic, one that reasons anhomomorphically, not just abou ...
... anhomomorphic logic opens up another interpretation, perhaps consistent with the mystical one, but not really requiring it. Namely one can imagine that Nagarjuna’s blanket denial represents a kind of “second order” application of anhomomorphic logic, one that reasons anhomomorphically, not just abou ...
Chapter 1 - National Taiwan University
... we should be able to assign truth values to propositions such that all requirements are satisfied. In Example 2, we are lucky to have simple requirements where there are only 2 propositions p and q. In real world, there may be hundreds, even thousands of propositions in the requirements. How to find p ...
... we should be able to assign truth values to propositions such that all requirements are satisfied. In Example 2, we are lucky to have simple requirements where there are only 2 propositions p and q. In real world, there may be hundreds, even thousands of propositions in the requirements. How to find p ...
verseny11 "In nature there cannot be two or more substances with
... mathematics makes frequent use of this concept, but we don't get a single answer about what it really is.This is because, paradoxically, there is not one concept of identity in mathematics, but many. We all claim to understand what A=B means: we can just read it out as A equals B. But we can formula ...
... mathematics makes frequent use of this concept, but we don't get a single answer about what it really is.This is because, paradoxically, there is not one concept of identity in mathematics, but many. We all claim to understand what A=B means: we can just read it out as A equals B. But we can formula ...
Document
... p ↔q denotes “I am at home if and only if it is raining.” If p denotes “You can take the flight.” and q denotes “You buy a ticket.” then p ↔q denotes “You can take the flight if and only ...
... p ↔q denotes “I am at home if and only if it is raining.” If p denotes “You can take the flight.” and q denotes “You buy a ticket.” then p ↔q denotes “You can take the flight if and only ...
The Foundations: Logic and Proofs
... raining.” then p →q denotes “If I am at home then it is raining.” In p →q , p is the hypothesis (antecedent or premise) and q is the conclusion (or consequence). ...
... raining.” then p →q denotes “If I am at home then it is raining.” In p →q , p is the hypothesis (antecedent or premise) and q is the conclusion (or consequence). ...
Document
... one is a notorious liar one is a pokerface, sometimes liar sometimes honest They make the following statements: A says: "I love mathematics." B says: "C always tells the truth." C says: "A hates math." Who is most likely the honest one? ...
... one is a notorious liar one is a pokerface, sometimes liar sometimes honest They make the following statements: A says: "I love mathematics." B says: "C always tells the truth." C says: "A hates math." Who is most likely the honest one? ...
(draft)
... In 1968, Mathematician William Howard, building on work by Haskel Curry, identified a one-to-one relationship between propositional formulas and logical proofs to types and programs respectively. More genreally, it was noticed that logical ideas have computational significance. This idea became known, ...
... In 1968, Mathematician William Howard, building on work by Haskel Curry, identified a one-to-one relationship between propositional formulas and logical proofs to types and programs respectively. More genreally, it was noticed that logical ideas have computational significance. This idea became known, ...
Overview of proposition and predicate logic Introduction
... “married-to”. Note that the first two examples are about one person, the others about two. An example of an operation on human beings is “father-of”. Applying this operation to an individual delivers the father of that individual1 . Distinguishing separate objects in the world gives the possibility ...
... “married-to”. Note that the first two examples are about one person, the others about two. An example of an operation on human beings is “father-of”. Applying this operation to an individual delivers the father of that individual1 . Distinguishing separate objects in the world gives the possibility ...
coppin chapter 07e
... If a statement A is contingent then we say that A is possibly true, which is written: ◊A If A is non-contingent, then it is necessarily true, which is written: A ...
... If a statement A is contingent then we say that A is possibly true, which is written: ◊A If A is non-contingent, then it is necessarily true, which is written: A ...
Programming and Problem Solving with Java: Chapter 14
... If a statement A is contingent then we say that A is possibly true, which is written: ◊A If A is non-contingent, then it is necessarily true, which is written: A ...
... If a statement A is contingent then we say that A is possibly true, which is written: ◊A If A is non-contingent, then it is necessarily true, which is written: A ...
Truth-tables .1in | University of Edinburgh | PHIL08004 | .3in [width
... “We all learned in school how to compute the probabilities of various events. . . Now in doing these school exercises in probability, we were in fact introduced at a tender age to a set of (miniature) ‘possible worlds’. The thirty-six possible states of the dice are literally thirty-six ‘possible w ...
... “We all learned in school how to compute the probabilities of various events. . . Now in doing these school exercises in probability, we were in fact introduced at a tender age to a set of (miniature) ‘possible worlds’. The thirty-six possible states of the dice are literally thirty-six ‘possible w ...
T - UTH e
... raining.” then p →q denotes “If I am at home then it is raining.” In p →q , p is the hypothesis (antecedent or premise) and q is the conclusion (or consequence). ...
... raining.” then p →q denotes “If I am at home then it is raining.” In p →q , p is the hypothesis (antecedent or premise) and q is the conclusion (or consequence). ...
Radical Enactivism, Wittgenstein and the cognitive gap
... to (or ever having had to) interact with it in a first hand manner” (ibid, p41). ...
... to (or ever having had to) interact with it in a first hand manner” (ibid, p41). ...
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. ...
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 15 Logic Name Date Objective: Students will use
... If p and q are propositions, then p V q stands for their inclusive disjunction and p V q stand for their exclusive disjunction. The inclusive disjunction is true when one or both propositions are true, since in this case p or q means p or q, or both p and q. i.e. p V q = p or q or both p and q The e ...
... If p and q are propositions, then p V q stands for their inclusive disjunction and p V q stand for their exclusive disjunction. The inclusive disjunction is true when one or both propositions are true, since in this case p or q means p or q, or both p and q. i.e. p V q = p or q or both p and q The e ...
January 12
... task of proving that arithmetic is analytic. The problem with ordinary language is that there is no clear way of determining whether one proposition follows logically from another. Aristotelian logic helps to remedy this problem with the introduction of a logical symbolism for expressing proposition ...
... task of proving that arithmetic is analytic. The problem with ordinary language is that there is no clear way of determining whether one proposition follows logically from another. Aristotelian logic helps to remedy this problem with the introduction of a logical symbolism for expressing proposition ...
Tractatus Logico-Philosophicus
The Tractatus Logico-Philosophicus (Latin for ""Logico-Philosophical Treatise"") is the only book-length philosophical work published by the German-Austrian philosopher Ludwig Wittgenstein in his lifetime. The project had a broad aim – to identify the relationship between language and reality and to define the limits of science – and is recognized as a significant philosophical work of the twentieth century. G. E. Moore originally suggested the work's Latin title as homage to the Tractatus Theologico-Politicus by Baruch Spinoza.Wittgenstein wrote the notes for the Tractatus while he was a soldier during World War I and completed it when a prisoner of war at Como and later Cassino in August 1918. It was first published in German in 1921 as Logisch-Philosophische Abhandlung. The Tractatus was influential chiefly amongst the logical positivists of the Vienna Circle, such as Rudolf Carnap and Friedrich Waismann. Bertrand Russell's article ""The Philosophy of Logical Atomism"" is presented as a working out of ideas that he had learned from Wittgenstein.The Tractatus employs a notoriously austere and succinct literary style. The work contains almost no arguments as such, but rather consists of declarative statements that are meant to be self-evident. The statements are hierarchically numbered, with seven basic propositions at the primary level (numbered 1–7), with each sub-level being a comment on or elaboration of the statement at the next higher level (e.g., 1, 1.1, 1.11, 1.12).Wittgenstein's later works, notably the posthumously published Philosophical Investigations, criticised many of the ideas in the Tractatus.