Philosophy of Logic and Language
... it was widely held in the early 20th century. But it fell out of favour in and around the 1930s. ...
... it was widely held in the early 20th century. But it fell out of favour in and around the 1930s. ...
Logic and Existential Commitment
... is plagued with substantial epistemological difficulties, and at present the advantages of doing this are unclear. I conclude by highlighting why this should increase the comfort level for thinking that ordinary first-order logic depends on substantive facts about the world. The Possible Meaning Acc ...
... is plagued with substantial epistemological difficulties, and at present the advantages of doing this are unclear. I conclude by highlighting why this should increase the comfort level for thinking that ordinary first-order logic depends on substantive facts about the world. The Possible Meaning Acc ...
Chapter 1 Logic and Set Theory
... The relation between intuition and formal rigor is not a trivial matter. Intuition tells us what is important, what might be true, and what mathematical tools may be used to prove it. Rigorous proofs are used to verify that a given statement that appears intuitively true is indeed true. Ultimately, ...
... The relation between intuition and formal rigor is not a trivial matter. Intuition tells us what is important, what might be true, and what mathematical tools may be used to prove it. Rigorous proofs are used to verify that a given statement that appears intuitively true is indeed true. Ultimately, ...
PPT
... symbols , , ~, and parentheses ( , ) also we add two more , , • Propositional expressions (propositional forms) are formed using these elements of alphabet as follows: 1. Each variable is propositional expression 2. IF p and q are propositinal expressions then ~ p, p q, p q, p q, p q, (p ...
... symbols , , ~, and parentheses ( , ) also we add two more , , • Propositional expressions (propositional forms) are formed using these elements of alphabet as follows: 1. Each variable is propositional expression 2. IF p and q are propositinal expressions then ~ p, p q, p q, p q, p q, (p ...
Propositional Logic What is logic? Propositions Negation
... • Essentially, logic formalizes our reasoning process. – It provides a common language through which we can demonstrate to each other that our reasoning is valid. ...
... • Essentially, logic formalizes our reasoning process. – It provides a common language through which we can demonstrate to each other that our reasoning is valid. ...
Chapter 1: The Foundations: Logic and Proofs
... sentence that declares a fact) that is either true or false, but not both. ...
... sentence that declares a fact) that is either true or false, but not both. ...
Chapter 1 Logic and Set Theory
... The relation between intuition and formal rigor is not a trivial matter. Intuition tells us what is important, what might be true, and what mathematical tools may be used to prove it. Rigorous proofs are used to verify that a given statement that appears intuitively true is indeed true. Ultimately, ...
... The relation between intuition and formal rigor is not a trivial matter. Intuition tells us what is important, what might be true, and what mathematical tools may be used to prove it. Rigorous proofs are used to verify that a given statement that appears intuitively true is indeed true. Ultimately, ...
POSSIBLE WORLDS SEMANTICS AND THE LIAR Reflections on a
... cal languages where oblique constructions are represented by intensional operators. The direct-discourse approaches are, however, threatened by (self-referential) paradoxes. Montague (1963) showed that the syntactic treatment of necessity as a predicate of sentences in the object language leads to i ...
... cal languages where oblique constructions are represented by intensional operators. The direct-discourse approaches are, however, threatened by (self-referential) paradoxes. Montague (1963) showed that the syntactic treatment of necessity as a predicate of sentences in the object language leads to i ...
From p
... boolean value as a bit in a binary number, truth table values can be efficiently encoded as integer values in electronic design automation (EDA) software. For example, a 32-bit integer can encode the truth table for a LUT with up to 5 inputs. When using an integer representation of a truth table, th ...
... boolean value as a bit in a binary number, truth table values can be efficiently encoded as integer values in electronic design automation (EDA) software. For example, a 32-bit integer can encode the truth table for a LUT with up to 5 inputs. When using an integer representation of a truth table, th ...
Knowledge of Logical Truth Knowledge of Logical Truth
... 1st problem (basic truths): Any process that simply makes the subject believe p when p is a logical truth will be a reliable process intuitively since it will always yield true beliefs. However, it is only a conditionally reliable process unless it is preceded by a process that determines for a give ...
... 1st problem (basic truths): Any process that simply makes the subject believe p when p is a logical truth will be a reliable process intuitively since it will always yield true beliefs. However, it is only a conditionally reliable process unless it is preceded by a process that determines for a give ...
Chapter 7
... • Entailment: KB |= Q – Q is entailed by KB (a set of premises or assumptions) if and only if there is no logically possible world in which Q is false while all the premises in KB are true. – Or, stated positively, Q is entailed by KB if and only if the conclusion is true in every logically possible ...
... • Entailment: KB |= Q – Q is entailed by KB (a set of premises or assumptions) if and only if there is no logically possible world in which Q is false while all the premises in KB are true. – Or, stated positively, Q is entailed by KB if and only if the conclusion is true in every logically possible ...
p q
... tables. If we deal with n simple propositions p1,…,pn, our truth table will have size at least 2n. This becomes a substantial disadvantage if n is big. Sometimes there is a much more efficient way to prove equivalences. First, look at some very simple equivalences… ...
... tables. If we deal with n simple propositions p1,…,pn, our truth table will have size at least 2n. This becomes a substantial disadvantage if n is big. Sometimes there is a much more efficient way to prove equivalences. First, look at some very simple equivalences… ...
Modus ponens
... of definition" and the "rule of substitution". Modus ponens allows one to eliminate a conditional statement from a logical proof or argument (the antecedents) and thereby not carry these antecedents forward in an everlengthening string of symbols; for this reason modus ponens is sometimes called the ...
... of definition" and the "rule of substitution". Modus ponens allows one to eliminate a conditional statement from a logical proof or argument (the antecedents) and thereby not carry these antecedents forward in an everlengthening string of symbols; for this reason modus ponens is sometimes called the ...
CLASSICAL LOGIC and FUZZY LOGIC
... Another example comes from ancient Greece. Does the liar from Crete lie when he claims, ‘‘All Cretians are liars?’’ If he is telling the truth, his statement is false. But if his statement is false, he is not telling the truth. A simpler form of this paradox is the two-word proposition, ‘‘I lie.’’ T ...
... Another example comes from ancient Greece. Does the liar from Crete lie when he claims, ‘‘All Cretians are liars?’’ If he is telling the truth, his statement is false. But if his statement is false, he is not telling the truth. A simpler form of this paradox is the two-word proposition, ‘‘I lie.’’ T ...
ch1_Logic_and_proofs
... are definitions: Two triangles are congruent if their vertices can be paired so that the corresponding sides are equal and so are the corresponding angles. Two angles are supplementary if the sum of their measures is 180 degrees. ...
... are definitions: Two triangles are congruent if their vertices can be paired so that the corresponding sides are equal and so are the corresponding angles. Two angles are supplementary if the sum of their measures is 180 degrees. ...
Lecture 6 Induction
... • A proposition denoted by symbols P(n) are propositions having to do with all numbers of value n. • Terminology and notation: If we say that proposition P(n) is true for all natural numbers n, then we mean that: P(1) ∧ P(2) ∧ P(3) ∧ ... is true. That is the logical “and” of all of these proposition ...
... • A proposition denoted by symbols P(n) are propositions having to do with all numbers of value n. • Terminology and notation: If we say that proposition P(n) is true for all natural numbers n, then we mean that: P(1) ∧ P(2) ∧ P(3) ∧ ... is true. That is the logical “and” of all of these proposition ...
Basic Logic - Progetto e
... assertion in English language can be initially interpreted as “for any x, Dx entails Sx”, and then translated into ∀x(Dx⟶Sx). As the example shows, predicate logic provide a tool to handle propositions ...
... assertion in English language can be initially interpreted as “for any x, Dx entails Sx”, and then translated into ∀x(Dx⟶Sx). As the example shows, predicate logic provide a tool to handle propositions ...
Horseshoe and Turnstiles
... that is, if φ’s truth is not dependent on any other proposition(s). It is always true. We can express this as, (2) ⊧ φ. In this case, φ is also sometimes called a ‘logical truth’. More controversially, we could say that (2) says that φ is an axiom or a self-evident truth. Now, (3) Γ ⊧ φ iff there is ...
... that is, if φ’s truth is not dependent on any other proposition(s). It is always true. We can express this as, (2) ⊧ φ. In this case, φ is also sometimes called a ‘logical truth’. More controversially, we could say that (2) says that φ is an axiom or a self-evident truth. Now, (3) Γ ⊧ φ iff there is ...
Chapter 4. Logical Notions This chapter introduces various logical
... paraphrase there are at least two cats as there is an x such that there is a y such that x is a cat and y is cat and it is not the case that x is identical to y. The numerical sentence and its "identity" paraphrase are equivalent in virtue of their forms, but not in virtue of any logical forms. On a ...
... paraphrase there are at least two cats as there is an x such that there is a y such that x is a cat and y is cat and it is not the case that x is identical to y. The numerical sentence and its "identity" paraphrase are equivalent in virtue of their forms, but not in virtue of any logical forms. On a ...
2/TRUTH-FUNCTIONS
... ForclassDiscussionsOnly.Teacher.Armand.L.Tan.AssociateProfessor. PhilosophyDepartment.SillimanUniversity s6. S.variable: letter use to symbolize statements such as p, q, r, and s. Statements are either simple such as `Roses are Red’ or compound: `Aristotle is Greek and Russell is English.’ Statement ...
... ForclassDiscussionsOnly.Teacher.Armand.L.Tan.AssociateProfessor. PhilosophyDepartment.SillimanUniversity s6. S.variable: letter use to symbolize statements such as p, q, r, and s. Statements are either simple such as `Roses are Red’ or compound: `Aristotle is Greek and Russell is English.’ Statement ...
1 Proof of set properties, concluded
... asserting membership, i.e. for sets A and B, let P be the statement x ∈ A, and Q be the statement x ∈ B. Then, we can translate many statements about sets to logical combinations of these statments. In particular, the statement A ⊆ B asserts that for any x ∈ A, it follows that x ∈ B; in other words, ...
... asserting membership, i.e. for sets A and B, let P be the statement x ∈ A, and Q be the statement x ∈ B. Then, we can translate many statements about sets to logical combinations of these statments. In particular, the statement A ⊆ B asserts that for any x ∈ A, it follows that x ∈ B; in other words, ...
Document
... that’s always false –a contradiction. EG: p ¬p On the other hand, a compound proposition whose truth value isn’t constant is called a contingency. EG: p ¬p ...
... that’s always false –a contradiction. EG: p ¬p On the other hand, a compound proposition whose truth value isn’t constant is called a contingency. EG: p ¬p ...
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.