﻿ Willard Van Orman Quine on Intuitionism - Dictionary of Arguments

# Dictionary of Arguments

Intuitionism: A) intuitionism in mathematics assumes that the objects to be inspected, e.g. numbers are only constructed in the process of the investigation and are therefore not ready objects, which are discovered. This has an effect on the double negation and the sentence of the excluded middle.
B) Intuitionism of ethics assumes that moral principles are fixed and are immediately (or intuitively) knowable.

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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 Item Summary Meta data
II 178
Intuitionism: shows us that Truth is not assertibility.
X 118
Intuitionism/Quine: one could characterize it as follows: it rejects adjunction if one does not know how to decide which of the subsets is true.
Sentence of the excluded middle: we had wanted to protect it via the negation.
Logic/Quine: in reality you cannot make any distinction: once you have changed the relationships between the logical operators ((s) logical constants), you can consider any or all of them as changed. (>Holism).
You can tell from that:
Adjunction/Negation/Logical Operators/Quine: are inherent, not transcendent. Because with a deviating logic we cannot maintain its meanings.
Intuitionism: is therefore no different opinion about the laws for the operators. He rather fights them as useless for science.
QuineVsIntuitionistic Logic: it lacks manageability and familiarity. Their sentence links have no probability function but an intuitive meaning, which we explain with the help of "refute" and "follow from...". However, these explanations become unclear if one wants to maintain the difference between pronouncing a sentence and speaking about the sentence (mention/use)!
Quine: then you can also go straight to Heyting's axioms and not interpose a translation, but
X 119
apply the direct method of the language teacher.
Intuitionism: gained even more impetus through Goedel's proof of incompleteness.
QuineVsIntuitionistic Logic: changes the meanings of quantification and constants.
Solution: one can proceed constructivistically, but still use the orthodox logic: this is Weyl's constructive set theory.
X 121
Ontology/QuineVsIntuitionism/VsIntuitionist Logic: we may not even find what the Intuitionist declares existing.
Solution: we have to translate his language into ours first. And not necessarily into our logic, but in our overall language!
Then we can say what he sees as existing (in our sense of "exist").

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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.
The note [Author1]Vs[Author2] or [Author]Vs[term] 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:

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

> Counter arguments against Quine
> Counter arguments in relation to Intuitionism

Ed. Martin Schulz, access date 2019-05-25