2. Truth functions—or not?

2017 ◽  
pp. 7-16
Author(s):  
Graham Priest
Keyword(s):  
Truth Table ◽  
Gottlob Frege ◽  
Truth Values ◽  
Invalid Inference

We are strongly intuitive about the validity of various inferences. This may or may not be hard-wired into us. Intuition gets us into trouble sometimes. ‘Truth functions—or not?’ plays around with the idea of invalid and valid inferences and, using phrases such as ‘or’ or ‘it is not the case that’, shows that chaining valid inferences together doesn’t necessarily result in an invalid inference. People’s intuition can be misleading. Sentences can be true or false. Gottlob Frege called these truth values. If we assume that every sentence is either true or false, but not both, we can predict the conditions in what logicians call a truth table.

Truth and Meaning

2009 ◽  
Author(s):  
Gabriel Segal
Keyword(s):  
Twentieth Century ◽  
Possible Worlds ◽  
Gottlob Frege ◽  
Truth Values ◽  
Work Related

This article says something about previous work related to truth and meaning, goes on to discuss Davidson (1967) and related papers of his, and then discusses some issues arising. It begins with the work of Gottlob Frege. Much work in the twentieth century developed Frege's ideas. A great deal of that work continued with the assumption that semantics is fundamentally concerned with the assignments of entities (objects, sets, functions, and truth-values) to expressions. So, for example, those who tried to develop a formal account of sense did so by treating senses as functions of various kinds; the sense of a predicate, for example, was often seen as a function from possible worlds to extensions.

Graphing True-False Statements

1969 ◽  
Vol 62 (7) ◽  
pp. 553-556
Author(s):  
Margaret Wiscamb
Keyword(s):  
Truth Table ◽  
Graphic Representation ◽  
Truth Values ◽  
Truth Tables ◽  
True False ◽  
Tedious Process ◽  
Three Components

In elementary logic the construction of truth tables, while not difficult, can be a long and tedious process. In this article I would like to present a simple graphic representation of the truth values of compound statements involving two or three components. The graph gives all the information found in a truth table and pictures the statement as an easily recognizable pattern. By using this graphing procedure, the simplifying of statements is shortened considerably. In fact, for statements involving only two components, with a little practice it can usually be done by inspection. Proving that a statement is a tautology becomes almost trivial.

A purely topological form of non-Aristotelian logic

1937 ◽  
Vol 2 (3) ◽  
pp. 97-112 ◽  
Author(s):  
Carl G. Hempel
Keyword(s):  
Truth Table ◽  
Aristotelian Logic ◽  
Truth Values ◽  
Symbolic Notation ◽  
Sentential Logic ◽  
New Type ◽  
Points Of View ◽  
Topological Form

1. The problem. The aim of the following considerations is to introduce a new type of non-Aristotelian logic by generalizing the truth-table methods so far employed for establishing non-Aristotelian sentential calculi. We shall expound the intended generalization by applying it to the particular set of pluri-valued systems introduced by J. Łukasiewicz. One will remark that the points of view illustrated by this example may serve to generalize quite analogously any other plurivalued systems, such as those originated by E. L. Post, by H. Reichenbach, and by others.2. J. Łukasiewicz's plurivalued systems of sentential logic. First of all, we consider briefly the structure of the Łukasiewicz systems themselves.As to the symbolic notation in which to represent those systems, we make the following agreements: For representing the expressions of the (two- or plurivalued) calculus of sentences, we make use of the Principia mathematica symbolism; however, we employ brackets instead of dots. We call the small italic letters “p”, “q”, “r”, … sentential variables or elementary sentences, and employ the term “sentence” as a general designation of both elementary sentences and the composites made up of elementary sentences and connective symbols (“~”, “ν” “.”, “⊃” “≡”).Now, the different possible sentences (or, properly speaking, the different possible shapes of sentences, such as “p”, “p∨q”, “~p.(q∨ r)”, etc.) are the objects to which truth-values are ascribed; and just as in every other case one wants a designation for an object in order to be able to speak of it, we want now a system of designations for the sentences with which we are going to deal in our truth-table considerations.

A test for the existence of tautologies according to many-valued truth-tables

1950 ◽  
Vol 15 (3) ◽  
pp. 182-184 ◽  
Author(s):  
Jan Kalicki
Keyword(s):  
Finite Number ◽  
Truth Table ◽  
Effective Procedure ◽  
Single Variable ◽  
Truth Values ◽  
Contraction Process ◽  
The One ◽  
Image Position ◽  
Truth Tables

Theorem. There is an effective procedure to decide whether the set of tautologies determined by a given truth-table with a finite number of elements is empty or not.Proof. Let W(P) be a w.f.f. with a single variable P and n a given n-valued truth-table with elements (values)Substitute 1, 2, 3, …, n in succession for P. By the usual contraction process let W(P) assume the truth-values w1, w2, w3, …, wn respectively. The sequencewill be called the value sequence of W(P).Value sequences consisting of designated elements of exclusively will be called designated; others will be called undesignated.All the W(P)'s will be classified in the following way:(a) to the first class CL1 of W(P)'s there belongs the one element P,(b) to the (t + 1)th class CLt + 1 belong all the w.f.f. which can be built up by means of one generating connective from constituent w.f.f. of which one is an element of CLt and all the others (if any) are elements of CLn ≤ t.For example, if N and C are the connectives described by a truth-table etc.Let ∣CLn∣ stand for the set of value sequences of the elements of CLn.

Conditioned disjunction as a primitive connective for the erweiterter Aussagenkalkül

1953 ◽  
Vol 18 (1) ◽  
pp. 63-65
Author(s):  
Alan Rose
Keyword(s):  
Propositional Calculus ◽  
Free Variable ◽  
Truth Table ◽  
Propositional Variable ◽  
Logical Constants ◽  
Truth Values ◽  
Complete Set ◽  
Truth Value

It has been shown that the conditioned disjunction function [X, Y, Z] with the same truth-table as (X & Y) ∨ (Z & ) together with the logical constants t and f, form a complete set of independent connectives for the 2-valued propositional calculus and that these connectives are self-dual. This has since been generalised to the theorem which states that the conditioned disjunction function [Y, X1, X2, …, Xm, Y] with the same truth-table as (X1 & J1(Y)) ∨ (X2 & J2(Y)) ∨ … ∨ (Xm & Jm(Y)) together with the logical constants 1, 2, …, m form a complete set of independent connectives for the m-valued propositional calculus and that these connectives are self-dual. It has been conjectured by Church that conditioned disjunction together with the universal and existential quantifiers form a complete set of independent connectives for the 2-valued erweiterter Aussagenkalkül. The object of the present paper is to prove a theorem for the m-valued erweiterter Aussagenkalkül which reduces, in the case m = 2, to the conjecture of Church. In the m-valued propositional calculus if the propositional variable X occurs as a free variable in the formula then (∃X) and (X) are read “there exists X such that ” and “for all X, ”, respectively. If for a given assignment of truth-values to the remaining free propositional variables occurring in , takes the truth-value f(x), where x is the truth-value of X, then (∃X) and (X) take the truth-values min (f(1), f(2), …, f(m)), max(f(1), f(2), …, f(m)), respectively. We shall prove:Theorem. The conditioned disjunction function, together with the universal and existential quantifiers, form a complete set of independent connectives for the m-valued erweiterter Aussagenkalkül.

Derrida and Frege

Paragraph ◽  
2018 ◽  
Vol 41 (2) ◽  
pp. 184-195
Author(s):  
Marian Hobson
Keyword(s):  
Gottlob Frege

Derrida, for reasons which he never made clear publicly, published his mémoire for the diplôme d'études supérieures only in 1990, some thirty-five years after it had been written. Had it been published much earlier, some of the dispiritingly ill-informed remarks about his work might have been avoided. The mémoire, entitled The Problem of Genesis in Husserl's Philosophy, reveals that he is, when required, perfectly able to write a standard thesis in straightforward French. And that, in particular, he is aware of the work of the great logician Gottlob Frege in its relation to Husserl.

Gottlob Frege, One More Time1

Hypatia ◽  
2000 ◽  
Vol 15 (4) ◽  
pp. 156-173
Author(s):  
CLAUDE IMBERT
Keyword(s):  
Gottlob Frege

Combinational Logic Analysis Using Laser Voltage Probing

2015 ◽  
Author(s):  
Venkat Krishnan Ravikumar ◽  
Winson Lua ◽  
Seah Yi Xuan ◽  
Gopinath Ranganathan ◽  
Angeline Phoa
Keyword(s):  
Failure Analysis ◽  
Continuous Wave ◽  
Truth Table ◽  
Combinational Logic ◽  
Infra Red ◽  
Analysis Design ◽  
Logic State

Abstract Laser Voltage Probing (LVP) using continuous-wave near infra-red lasers are popular for failure analysis, design and test debug. LVP waveforms provide information on the logic state of the circuitry. This paper aims to explain the waveforms observed from combinational circuitries and use it to rebuild the truth table.

Modal logics with Belnapian truth values

2010 ◽  
Vol 20 (3) ◽  
pp. 279-304 ◽  
Author(s):  
Serge P Odintsov ◽  
Heinrich Wansing
Keyword(s):  
Modal Logics ◽  
Truth Values
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