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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._____________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
W.V.O. Quine on Implication - Dictionary of Arguments
I 339
Material implication "p implies q" is not equal to p > q (> mention/use) - implicit and analytical are the best general terms.
>General Term/Quine.
X 46
Material Implication/Quine: occurs when the sense can be reproduced only with negation and conjunction. Normal implication: in addition to existential quantification.
III 67
Implication/Conditional/Quine: Implication only exists if the conditional is true.
I 68
Implication/Mention/Use/Quine: not sentences or schemata are implied, but their descriptions.
For we cannot write "implies" between the sentences themselves, but only between their descriptions. So we mention the sentences by using their descriptions. We are talking about the sentences. ((s) implication is done via the sentences.
Different:
Conditional/Quine: (">" or "if...then...") here we use the sentences or schemes themselves, we do not mention them. No reference is made to them. They appear only as parts of a longer sentence or schema.
Example: If Cassius is not hungry, then he is not skinny and hungry.
This mentions Cassius but it does not mention a sentence. It is the same with conjunction, negation and alternation.
Implication/Quine/(s): only example "p implies q" but not "Cassius' skinniness implies..."
III 72
"Only if....then"/Quine: is the sign for the hind leg! It also does not have the meaning of the whole "then and only then" (biconditional).
I 389/90
Conditional with a false antecedent/Quine: > truth value gap._____________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.
Quine I
W.V.O. Quine
Word and Object, Cambridge/MA 1960
German Edition:
Wort und Gegenstand Stuttgart 1980
Quine II
W.V.O. Quine
Theories and Things, Cambridge/MA 1986
German Edition:
Theorien und Dinge Frankfurt 1985
Quine III
W.V.O. Quine
Methods of Logic, 4th edition Cambridge/MA 1982
German Edition:
Grundzüge der Logik Frankfurt 1978
Quine V
W.V.O. Quine
The Roots of Reference, La Salle/Illinois 1974
German Edition:
Die Wurzeln der Referenz Frankfurt 1989
Quine VI
W.V.O. Quine
Pursuit of Truth, Cambridge/MA 1992
German Edition:
Unterwegs zur Wahrheit Paderborn 1995
Quine VII
W.V.O. Quine
From a logical point of view Cambridge, Mass. 1953
Quine VII (a)
W. V. A. Quine
On what there is
In
From a Logical Point of View, , Cambridge, MA 1953
Quine VII (b)
W. V. A. Quine
Two dogmas of empiricism
In
From a Logical Point of View, , Cambridge, MA 1953
Quine VII (c)
W. V. A. Quine
The problem of meaning in linguistics
In
From a Logical Point of View, , Cambridge, MA 1953
Quine VII (d)
W. V. A. Quine
Identity, ostension and hypostasis
In
From a Logical Point of View, , Cambridge, MA 1953
Quine VII (e)
W. V. A. Quine
New foundations for mathematical logic
In
From a Logical Point of View, , Cambridge, MA 1953
Quine VII (f)
W. V. A. Quine
Logic and the reification of universals
In
From a Logical Point of View, , Cambridge, MA 1953
Quine VII (g)
W. V. A. Quine
Notes on the theory of reference
In
From a Logical Point of View, , Cambridge, MA 1953
Quine VII (h)
W. V. A. Quine
Reference and modality
In
From a Logical Point of View, , Cambridge, MA 1953
Quine VII (i)
W. V. A. Quine
Meaning and existential inference
In
From a Logical Point of View, , Cambridge, MA 1953
Quine VIII
W.V.O. Quine
Designation and Existence, in: The Journal of Philosophy 36 (1939)
German Edition:
Bezeichnung und Referenz
In
Zur Philosophie der idealen Sprache, J. Sinnreich (Hg), München 1982
Quine IX
W.V.O. Quine
Set Theory and its Logic, Cambridge/MA 1963
German Edition:
Mengenlehre und ihre Logik Wiesbaden 1967
Quine X
W.V.O. Quine
The Philosophy of Logic, Cambridge/MA 1970, 1986
German Edition:
Philosophie der Logik Bamberg 2005
Quine XII
W.V.O. Quine
Ontological Relativity and Other Essays, New York 1969
German Edition:
Ontologische Relativität Frankfurt 2003
Quine XIII
Willard Van Orman Quine
Quiddities Cambridge/London 1987