Peirce's paradoxical solution to the Liar's Paradox.

Michael, Emily

doi:10.1305/ndjfl/1093891797

Cited by 6 publications

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“…Hence, LP is false. 5 As Emily Michael (1975) notes at the conclusion of her essay, Peirce stood by this solution as late as 1896, when he writes, "Every proposition is either true or false. .…”

Section: The Self-contradiction Solution Of 1869mentioning

confidence: 99%

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This Proposition is Not True: C.S. Peirce and the Liar Paradox

Atkins¹

2011

Transactions of the Charles S. Peirce Society

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Section: The Self-contradiction Solution Of 1869mentioning

confidence: 99%

“…Peirce and the Liar Paradox • Richard Kenneth Atkins NOTES 1. Emily Michael (1975) has already explicated Peirce's 1865 and 1869 solutions to the Liar Paradox. However, a brief review of them will be relevant to understanding Peirce's 1903 rejection of his 1869 solution.…”

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confidence: 99%

This Proposition is Not True: C.S. Peirce and the Liar Paradox

Atkins¹

2011

Transactions of the Charles S. Peirce Society

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“…Strong crazy people are persons who can say only paradoxical statements. Various types of paradoxical statements and issues with self-reference in puzzles were also presented in [31][32][33][34][35][36][37][38][39]. Rather than strong types of crazy persons, we may also have the weak crazy type, similar to the already mentioned weak truthtellers and liars [22].…”

Section: Introductionmentioning

confidence: 99%

A Comparison of Various Extensions of Strong Truthteller and Strong Liar Puzzles (Mutes and Crazies)

Alzboon

Nagy

2022

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Truthteller liar puzzles are popular in science and also in recreational mathematics. In this paper, we compare five different types of puzzles. In each of our puzzles, the persons of the puzzle may state some statements about their types. In strong truthteller–strong liar puzzles (SS puzzles), each statement of a truthteller must be true and each statement of a liar must be false, and there is no third type of person in these puzzles. It is known that there is no good SS puzzle, where a puzzle is good if it has exactly one solution. In fact, because of symmetry, by flipping the type of person in a solution, another (dual) solution is obtained. Therefore, to break this symmetry, there are various ways to introduce a third type of person, e.g., Mutes and crazies. In SSS puzzles, crazy people may appear, each of whom can tell only a self-contradicting statement. In SSW puzzles, a crazy person may say some additional statements apart from his or her self-contradicting statement. In SSM puzzles, that we investigate here, there can also be some Mute people (as the third type together with truthtellers and liars). We differentiate two types of SSM puzzles. In SSMW puzzles a mute person may be a Mute (type), but he or she could also be either a truthteller or a liar (type). In SSMS puzzles, each person who did not say any statement must be a Mute in the solution. Various examples are presented and it is also highlighted how a puzzle changes from unsolvable to solvable or to a good puzzle when the interpretation, the type of the puzzle changes, i.e., shifted from one to other, and symmetry breaks. Among other data, the number of solvable and good puzzles are counted and compared for the five types when few people appear.

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“…It can be noted that the study of self  external -which describes the reaction of self include the popular studies of Priest in 1978 (LP), see [9] and Dunn [1];  internal -when the emphasis is on the study of the structure of self with Peirce in 1855, [8], [4]. We will devote our article The constructive analysis of the Liar sentence was carried out by Charles Peirce, [8], who, as far as we know, was the first to notice in his lectures in 1864 an infinite sequence of substitutions into themselves. That was the first application of the principle, which in the second half of the 20th century was called…”

Section: Introductionmentioning

confidence: 99%

“…We will devote our article to this last approach. The constructive analysis of the Liar sentence was carried out by Charles Peirce, [8], who, as far as we know, was the first to notice in his lectures in 1864 -1865, that self-referential sentences generate substitutions into themselves. That was the first application of the principle, which in the second half of the 20th century was called "turning a vicious circle into a generating circle"…”

Section: Introductionmentioning

confidence: 99%

Dynamic Approximation of Self-Referential Sentences

Степанов

2022

Studia Humana

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Non-classical logic via approximation of self-referential sentences by dynamical systems are consistently presented. The new 6-valued truth values <T, va, A, V, av, F> (here A=Liar, V=TruthTeller) are presented as a function of the classical truth values x i ∈ {0,1}, which resulted in a philosophical standpoint known as Suszko’s Thesis. Three-valued truth tables were created corresponding to Priest’s tables of the same name. In the process of constructing 4-valued truth tables, two more new truth values (va, av) were revealed that do not coincide with the four original ones. Therefore, the closed tables turned out to be 6-valued. Prof Dunn’s 4-valued truth tables are compared with our 4-valued truth tables. De Morgan’s laws are confirmed by six-valued truth tables. Constructed 3-, 4- and 6-valued lattices obeying De Morgan’s laws.

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Peirce's paradoxical solution to the Liar's Paradox.

Cited by 6 publications

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This Proposition is Not True: C.S. Peirce and the Liar Paradox

This Proposition is Not True: C.S. Peirce and the Liar Paradox

A Comparison of Various Extensions of Strong Truthteller and Strong Liar Puzzles (Mutes and Crazies)

Dynamic Approximation of Self-Referential Sentences

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