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Implication: Implication in logic is a relationship between two statements, where the second statement follows from the first statement. It is symbolized by the arrow symbol (→). See also Konditional, Inference, Conclusion, Logic.
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Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments.

 
Author Concept Summary/Quotes Sources

Hartry Field on Implication - Dictionary of Arguments

II 255
Material conditional/paradoxes of the material implication/Jackson/Field: best solution: (Jackson, 1979)(1): Thesis: Contraintuitive conclusions are unacceptable here: the conclusions cannot be asserted, but nevertheless true.
>Acceptability
, >Truth, >Conclusions.
There is a conventional implication for that if we assert "if A then B", not only the probability is high (A > B), but also the conditional probability P (A > B I A).
>Probability, >Probability conditionals.
N.B.: the demand that P (A > B I A) should be high is equivalent to the demand of the nonfactualist that P (B I A) is high.
>Nonfactualism.
"Surface logic": has to do with assertibility - "depth logic": says what is truth-maintaining.
>Assertibility, >Truth transfer.
II 256
Factualism: has then to distinguish between levels of total unacceptability (i.e., on the surface) and acceptability at a deep level.
>Facts/Field.
Deflationism: in the same way the deflationism can distinguish between nonfactualism and factualism without using the terms "true" or "fact".
>Deflationism.
Factualism: the factualism does not accept any contraintive conclusions.
Nonfactualism: seems committed to it.

1.Frank Jackson, On Assertion and Indicative Conditionals. The Philosophical Review
Vol. 88, No. 4 (Oct., 1979), pp. 565-589

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Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments
The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.

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

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

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

Field IV
Hartry Field
"Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67
In
Theories of Truth, Paul Horwich, Aldershot 1994


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