# Dictionary of Arguments

Philosophical and Scientific Issues in Dispute

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Consistency Quine IX 209/10
Consistency/Set Theory/Quine: we have been able to prove it twice as we have a simple model in finite sets - which does not apply if we once have added an axiom of infinity. Consistency is questionable and more difficult and more urgent to prove. And the evidence is even less convincing - problem: the question of whether the methods themselves are consistent. >Set Theory/Quine.
II 178
The essence of the Corollary of Goedel's incompleteness theorem is that the internal consistency of a mathematical theory can usually only be proved by resorting to another theory based on further premises and it is therefore less reliable than the original one. This has a melancholic connotation. But this helps us to prove that one theory is stronger than another: This is achieved by proving in one theory that the other is consistent.
II 180
Goedel's third great discovery: the consistency of the continuum hypothesis and the axiom of choice.
II 210
Possible Worlds/QuineVsKripke: possible worlds allow proof of consistency, but no clear interpretation: when are objects equal? For example Bishop Buttler said that any thing is this thing and "no other thing": Problem/QuineVsButler: Identity does not follow necessarily. >Possible Worlds/Quine.
IX 192
Set theory/Modern Type Theory/Consistency/Quine: we can prove the freedom of contradiction of this version of set theory with cumulative types: Def Cumulative Types/Set Theory/Quine:
Type 0: only L is of type 0.
Type 1: L and {L} and nothing else.
Type n: should generally include and only include the 2n sets belonging to type n -1.
So each quantification interprets only finitely many cases. Every closed statement can be checked mechanically for truth.
Such a simple proof will no longer work if the infinity axiom is added.
IX 210
Infinite Classes/Consistency: the proof also becomes less convincing if we have to accept infinite amounts. Problem: whether the methods themselves are consistent (only with infinite classes).
The highest thing we can often strive for is that we prove that such a system is consistent when another, corresponding system is less distrusted.
IX 239
If the consistency of one set theory can be proven in another, the latter is the stronger (unless both are contradictory). Zermelo's system is stronger than type theory.

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