Section 1: Propositional Logic
... of the equivalent statement forms ∼q ⇒ ∼p or p ⇒ q, whichever is most convenient for the discussion at hand. • if and only if: The biconditional, p ⇔ q is sometimes stated as “p if and only if q” and written “p iff q”. • sufficient: The expression, “p is sufficient for q”(or “p is a sufficient condi ...
... of the equivalent statement forms ∼q ⇒ ∼p or p ⇒ q, whichever is most convenient for the discussion at hand. • if and only if: The biconditional, p ⇔ q is sometimes stated as “p if and only if q” and written “p iff q”. • sufficient: The expression, “p is sufficient for q”(or “p is a sufficient condi ...
article - British Academy
... is entitled ‘The box as Bew(x)’. As I understand it, Williamson’s investigation is a generalization of this idea to different areas. Williamson suggests that the existence of deviant provability operators casts doubt on attempts to use Godel’s second theorem to show that humans are not Turing machin ...
... is entitled ‘The box as Bew(x)’. As I understand it, Williamson’s investigation is a generalization of this idea to different areas. Williamson suggests that the existence of deviant provability operators casts doubt on attempts to use Godel’s second theorem to show that humans are not Turing machin ...
The substitutional theory of logical consequence
... ‘intended interpretation’ is not one of these models and cannot easily be identified with one of these models. Models have set-sized domains, while the intended interpretation, if it could be conceived as a model, cannot be limited by any cardinality. Similarly, logical truth defined as truth in all ...
... ‘intended interpretation’ is not one of these models and cannot easily be identified with one of these models. Models have set-sized domains, while the intended interpretation, if it could be conceived as a model, cannot be limited by any cardinality. Similarly, logical truth defined as truth in all ...
THE LOGIC OF QUANTIFIED STATEMENTS
... A prime number is an integer greater than 1 whose only positive integer factors are itself and 1. Consider the statement “There is an integer that is both prime and even.” ...
... A prime number is an integer greater than 1 whose only positive integer factors are itself and 1. Consider the statement “There is an integer that is both prime and even.” ...
INTERMEDIATE LOGIC – Glossary of key terms
... A technique used to simplify logic circuits by visually applying De Morgan’s theorem. Byte Lesson 29, page 249 A set of bits (usually eight) required to encode one character. Circuit (see logic circuit) Closed branch Lesson 22, page 179 A path of decomposed propositions on a truth tree which include ...
... A technique used to simplify logic circuits by visually applying De Morgan’s theorem. Byte Lesson 29, page 249 A set of bits (usually eight) required to encode one character. Circuit (see logic circuit) Closed branch Lesson 22, page 179 A path of decomposed propositions on a truth tree which include ...
Lecture 2: Language of logic, truth tables
... • Suppose you see one of them and you want to find out his name. • How can you learn if you met Dave or Jim by asking just one short yes-no question? You don’t know which one of them is the liar. ...
... • Suppose you see one of them and you want to find out his name. • How can you learn if you met Dave or Jim by asking just one short yes-no question? You don’t know which one of them is the liar. ...
ppt - Duke Computer Science
... • Consider the final set of clauses C • Construct satisfying assignment as follows: ...
... • Consider the final set of clauses C • Construct satisfying assignment as follows: ...
Problems on Discrete Mathematics1
... We use Dx , Dy to denote the domains of x and y, respectively. Note that Dx and Dy do not have to be the same. In the above example, P (3, 2) is the proposition 3 ≥ 22 with truth value F . Similarly, Q(Boo, dog) is a proposition with truth value T if there is a dog named Boo. Note: Any proposition i ...
... We use Dx , Dy to denote the domains of x and y, respectively. Note that Dx and Dy do not have to be the same. In the above example, P (3, 2) is the proposition 3 ≥ 22 with truth value F . Similarly, Q(Boo, dog) is a proposition with truth value T if there is a dog named Boo. Note: Any proposition i ...
Keep Changing Your Beliefs, Aiming for the Truth
... (2009). The basic semantic concept is that of a (finite, single-agent) ‘‘plausibility’’ frame. This is a structure S = (S, B), consisting of a finite set S of ‘‘states’’ (or possible worlds) and a total preorder S S.1 We use the notation s \ t for the corresponding strict order (i.e. s \ t iff ...
... (2009). The basic semantic concept is that of a (finite, single-agent) ‘‘plausibility’’ frame. This is a structure S = (S, B), consisting of a finite set S of ‘‘states’’ (or possible worlds) and a total preorder S S.1 We use the notation s \ t for the corresponding strict order (i.e. s \ t iff ...
The logic and mathematics of occasion sentences
... that the reduction by translation of occasion sentences to eternal sentences, as proposed by Russell and Quine, is semantically and thus logically inadequate. Natural language is a system of occasion sentences, eternal sentences being merely boundary cases. The logic has fewer tasks than is standard ...
... that the reduction by translation of occasion sentences to eternal sentences, as proposed by Russell and Quine, is semantically and thus logically inadequate. Natural language is a system of occasion sentences, eternal sentences being merely boundary cases. The logic has fewer tasks than is standard ...
Variables In Real Life: A Jar Of Spare Change
... Depending on the values going into the gates, the end result will be either a logical 0 or 1. This corresponds with false or true. ...
... Depending on the values going into the gates, the end result will be either a logical 0 or 1. This corresponds with false or true. ...
Not Every Truth Can Be Known (at least, not all
... logic in which these principles are couched, defeating the inference from (1) to omniscience [1, 5], these answers do not address the question I take to be asked by Fitch’s paradox. I say this because upon reflection, the principles motivating a knowability thesis in fact undercut its application in ...
... logic in which these principles are couched, defeating the inference from (1) to omniscience [1, 5], these answers do not address the question I take to be asked by Fitch’s paradox. I say this because upon reflection, the principles motivating a knowability thesis in fact undercut its application in ...
Lecture 1: Elements of Mathematical Logic
... fundamental skills of a mathematician; the ability to read, write, and understand proofs. This is a course where proofs matter more than the material covered. That said, I should also stress that this is not supposed to be a killer course. Yes, we are going to be rigorous and meticulous; but we will ...
... fundamental skills of a mathematician; the ability to read, write, and understand proofs. This is a course where proofs matter more than the material covered. That said, I should also stress that this is not supposed to be a killer course. Yes, we are going to be rigorous and meticulous; but we will ...
āgārjuna’s Logic N 8 8.1 N
... Notice that this result does not turn on our earlier assumption that e is undesignated. For if e were designated, then every sentence would be designated, and hence every argument from X (whether empty or not) to A would be non-vacuously valid. ...
... Notice that this result does not turn on our earlier assumption that e is undesignated. For if e were designated, then every sentence would be designated, and hence every argument from X (whether empty or not) to A would be non-vacuously valid. ...
Foucault and Rorty on Truth and Ideology: A
... In his ‘Two Lectures’ Foucault expressed scepticism about the critique of ideology partly on the grounds that power in modern society has much less to do with ideology than critical theorists assume. Instead of focusing on the role of ideological belief-systems in the manner of critical theorists, F ...
... In his ‘Two Lectures’ Foucault expressed scepticism about the critique of ideology partly on the grounds that power in modern society has much less to do with ideology than critical theorists assume. Instead of focusing on the role of ideological belief-systems in the manner of critical theorists, F ...
Truth
Truth is most often used to mean being in accord with fact or reality, or fidelity to an original or to a standard or ideal. Truth may also often be used in modern contexts to refer to an idea of ""truth to self,"" or authenticity.The commonly understood opposite of truth is falsehood, which, correspondingly, can also take on a logical, factual, or ethical meaning. The concept of truth is discussed and debated in several contexts, including philosophy, art, and religion. Many human activities depend upon the concept, where its nature as a concept is assumed rather than being a subject of discussion; these include most (but not all) of the sciences, law, journalism, and everyday life. Some philosophers view the concept of truth as basic, and unable to be explained in any terms that are more easily understood than the concept of truth itself. Commonly, truth is viewed as the correspondence of language or thought to an independent reality, in what is sometimes called the correspondence theory of truth.Other philosophers take this common meaning to be secondary and derivative. According to Martin Heidegger, the original meaning and essence of ""Truth"" in Ancient Greece was unconcealment, or the revealing or bringing of what was previously hidden into the open, as indicated by the original Greek term for truth, ""Aletheia."" On this view, the conception of truth as correctness is a later derivation from the concept's original essence, a development Heidegger traces to the Latin term ""Veritas.""Pragmatists like C.S. Pierce take Truth to have some manner of essential relation to human practices for inquiring into and discovering Truth, with Pierce himself holding that Truth is what human inquiry would find out on a matter, if our practice of inquiry were taken as far as it could profitably go: ""The opinion which is fated to be ultimately agreed to by all who investigate, is what we mean by the truth...""Various theories and views of truth continue to be debated among scholars, philosophers, and theologians. Language and words are a means by which humans convey information to one another and the method used to determine what is a ""truth"" is termed a criterion of truth. There are differing claims on such questions as what constitutes truth: what things are truthbearers capable of being true or false; how to define and identify truth; the roles that faith-based and empirically based knowledge play; and whether truth is subjective or objective, relative or absolute.Friedrich Nietzsche famously suggested that an ancient, metaphysical belief in the divinity of Truth lies at the heart of and has served as the foundation for the entire subsequent Western intellectual tradition: ""But you will have gathered what I am getting at, namely, that it is still a metaphysical faith on which our faith in science rests--that even we knowers of today, we godless anti-metaphysicians still take our fire too, from the flame lit by the thousand-year old faith, the Christian faith which was also Plato's faith, that God is Truth; that Truth is 'Divine'...""