Lexicon of Arguments


Philosophical and Scientific Issues in Dispute
 


[german]  

Find counter arguments by entering NameVs… or …VsName.

The author or concept searched is found in the following 1 entries.
Disputed term/author/ism Author
Entry
Reference
Dialethism Priest
 
Books on Amazon:
Graham Priest
Field II 145
Dialethism/Priest/Paradoxa/Field: (Priest 1998): Thesis: the sentence of the liar as well as its negation are both assertable (and also their conjunction). The rules of the logic are weakened (> stronger/weaker), so that not every assertion can be asserted by this. Most attractive variant: builds on Kleene's trivalent logic.
Trivalent logic/Kleene/Priest/Field: Priest assumes here that the valid inferences are those that guarantee "correct assertion". But an assertion is only correct if it has one of the two highest truth values in the truth value table.
Curry paradox: is thus excluded, since the only conditional in this language is the material conditional.
Material conditional/Field: the material conditional is defined by ~ and v. It does not fully support the modus ponens in the logic of Kleene/Priest.
Liar/KleeneVsPriest: (and other "deviant" sentences): have truth-value gaps. But there are no agglomerations of truth values.
Deviating Sentence: E.g. Liar sentence, has no truth-value agglomerations but truth-value gaps.
Liar/PriestVsKleene: (and other deviating sentences): have, conversely, truth-value agglomerations and no gaps.
Problem/Kleene: here one cannot establish an equivalence between "p" and "p" is true! For to assert a truth-value gap in a sentence "A" would be to assert: "~ [true ("A") v true ("~A")]" and this should be equivalent to "~ (A v ~ A)". But one sentence of this form can never be legitimate in Kleene.
Truth-value gap/logical form/Field: to assert a truth-value gap in a sentence "A" would mean to assert: "~ [true ("A") v true ("~ A")]" and this should be equivalent to "~ (A v ~ A)".
Solution/Priest: if "A" is a deviating sentence, this is then a correct assertion in Priest. Also the assertion of the absence of a truth-value agglomeration in a sentence "A" would be the assertion "~ [(true ("A") u true ("A)"]" which should be equivalent to "~(a u ~A)". Kleene cannot claim this absence for deviant sentences, Priest can do this.

Pries I
G. Priest
Beyond the Limits of Thought Oxford 2001


Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie II
H. Field
Truth and the Absence of Fact Oxford New York 2001

Fie III
H. Field
Science without numbers Princeton New Jersey 1980

The author or concept searched is found in the following 2 controversies.
Disputed term/author/ism Author Vs Author
Entry
Reference
Dialethism Field Vs Dialethism
 
Books on Amazon
II 145
Deflationism/Paradoxes/Kleene/Priest/Field: deflationistically, Kleene and Priest can be distinguished as follows: 1) Kleene: cannot assert of a differing sentence that it either has a truth value gap or not, not that it has a truth value agglomeration or not.
2) Priest: here, every single case can be asserted.
Def "solely true"/Priest/Field: ("Solely true"): true and not false. This can be said of each differing sentence with Priest (E.g. liar sentence), and also that it is "solely wrong" (incorrect and not true).
Opposition/Truth/FieldVsPriest/FieldVsDialethism: he often says that contradictions are "true". Field: It would be better to say that sentences of the form "p and not-p" are not always genuinely contradictory.
FieldVsPriest: He also overlooks the fact that, according to his theory, the "true contradictions" are also not true!.
Truth Value Agglomeration/Truth Value Gap/Kleene/Field: in both logics there is no distinction between agglomeration and gaps!.
Paradoxes/Kleene/Priest/Field: the two theories differ only in the "threshold of assertibility". Differing sentences are always assertible with Priest and never with Kleene.
Differing Sentence/Field: a sentence which attributes truth or non-truth, falsehood or non-falsehood to a differing sentence is differing itself. That means Kleene can never say anything about the truth value of differing sentences, Priest can say what he wants.
Additionally:
Paradoxes/Deflationism/Field: they do not undermine deflationism as reconstruction of our normal T theoretical concepts. Certainly not in the weak (Tarskian) version, but also not in certain stronger forms.

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie II
H. Field
Truth and the Absence of Fact Oxford New York 2001

Fie III
H. Field
Science without numbers Princeton New Jersey 1980
Kleene, St. C. Priest Vs Kleene, St. C.
 
Books on Amazon:
Graham Priest
Field II 145
Dialethism/Priest/Paradoxes/Field: (Priest 1998): Thesis: the sentence of the liar and its negation are both assertible (and also their conjunction). The rules of logic are attenuated (>stronger/weaker), so that not every assertion is assertible. Most attractive variant: builds on Kleene's trivalent logic.
Trivalent Logic/Kleene/Priest/Field: Priest assumes here that the valid inferences are those that guarantee "correct assertion". But an assertion is only correct if it has one of the two highest truth values in the truth value table.
Curry Paradox: is thus precluded, because the only conditional in this language is the material conditional.
Material Conditional/Field: defined by ~ and v. In the logic of Kleene/Priest it does not entirely support the modus ponens.
Liar/KleeneVsPriest: (and other "deviating" sentences): have truth value gaps. But there are no truth value clusters.
Deviating Sentence: E.g. liar-sentence has no truth value clusters, but truth value gaps.
Liar/PriestVsKleene: (and other deviating sentences): conversely have truth value clusters and no gaps.
Problem/Kleene: here you cannot establish an equivalence between "p" and ""p"is true"! Because to assert a truth value gap in a sentence "A" would be to say: "~[true ("A") v true ("~A")]" and that should be equivalent to "~(A v ~A)", but a sentence of this form can never be legitimate in Kleene.
Truth Value Gap/Logical Form/Field: asserting a truth value gap in a sentence "A" would be to say: "~[true ("A") v true ("~A")]" and that should be equivalent to "~(A v ~A)".
Solution/Priest: if "A" is a deviating sentence, then it is a correct assertion as by Priest. The assertion of the absence of a truth value cluster in a sentence "A" would be the assertion "~ [(true ("A") and true ("~A)"]" which should be equivalent to "~(a u ~A)". Kleene cannot assert this absence for deviating sentences, Priest can.

Pries I
G. Priest
Beyond the Limits of Thought Oxford 2001

Fie III
H. Field
Science without numbers Princeton New Jersey 1980