Dictionary of Arguments

Philosophical and Scientific Issues in Dispute

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The author or concept searched is found in the following 1 entries.
Disputed term/author/ism Author
Numbers Geach I, 215ff
Numbers/Geach: numbers do not name anything. Not: E.g.: "There are two Daimon and Phobos". How often a concept is realized is not a feature of the term. ((s) GeachVsMeixner).
Unity/Multiplicity/Geach: cannot be attributed to an object.
>Unity and Multiplicity.
Solution/Frege: Numbers are attributed to the terms under which the objects fall.
>Numbers/Frege, >Concept/Frege, >Object/Frege.
Numbers/Geach: in mathematics sometimes as objects with properties E.g. Divisibility.
Geach: then we need an identity criterion.
>Identity criterion.
Frege: Equality in numbers: "There is a one-to-one correspondence of Fs and Gs". - N.B.: this does not mean that the Fs or the Gs refer to a single object - a class.
Solution: Relation instead of class - E.g. Frege: One puts next to each plate a knife: no class but a relation.
>Equality, >Classes, >Sets, >Relation.
I 220
Numbers/Frege: Self-critique: Classes must not be used to explain what numbers are, otherwise contradiction: "one and the same object is both, the class of the M's and the class of the G's, although an object (this object, e.g. number(!)) can be an M without being a G. " - (+) - >Sets/Frege, >Classes/Frege.
This shows that the original concept of a class contained contradictions.
Numbers can be objects (with properties such as divisibility), classes cannot. - Not contradictory: "one and the same object: the number (not class!) of the F's and the number of K's".
I 221f
Numbers/GeachVsFrege: Number is not "number of objects". - With this he rejects his own concerns to say that "the object of a number belongs to a class" (wrong). "The number of the A's" is to mean: "the number of the class of all A's" (wrong).
Solution/Geach: (as Frege elsewhere): the empty place in "the number of ..." and "how many ...are there?" Can only be filled with a keyword in the plural, not with the name of an object or a list of objects. - A conceptual word instead of a class.
I 225
Numbers/Classes/Geach: Numbers are not classes of classes. If we connect a number (falsely) to a class a, we actually combine it with the property expressed by "___ is an element of a". This is not trivial because when we associate a number with a property, the property is usually not expressed in that form.
I 225
Numbers/Classes/Geach: false: "The number of F's is 0" - correct: "The class of F's is 0". Class as number are equally specified by the mention of a property.
I 235
Numbers/Frege/Geach: not classes of classes (Frege does not say this either). - The error stems from the idea that one could start with concrete objects and then group them into groups and supergroups.

Gea I
P.T. Geach
Logic Matters Oxford 1972

The author or concept searched is found in the following 2 controversies.
Disputed term/author/ism Author Vs Author
Chisholm, R.M. Meixner Vs Chisholm, R.M. I 49
Def continuant/Meixner: temporal, singular individuals that have at most spatial parts. No temporal parts! Therefore no accidentals. Temporal Parts/Meixner: but many individuals have temporal parts, the accidentals!
Individual/Modern Ontology/Meixner: (VsChisholm?) many modern ontologists however support the thesis that all existing individuals have temporal parts. According to this, a material individual is not at the same time in two different places, but also not as a whole at different times in the same place! ((s) The individual then changes constantly, from one point in time to another point in time, i.e. it is not the same in two consecutive moments. (>Lewis: "fragile").
"Four-Dimensionalism"/Meixner: the thesis that individuals consist of three spatial and one temporal dimension. MeixnerVs.
Irrespective of dimensions one can also say: all individuals have spatiotemporal parts, this applies in every reference system! And in each reference system, spatiotemporal parts can again be divided into spatial and temporal parts.
I 49/50
Theory of relativity: merely suggests four-dimensionalism, but by no means implies it! Temporal Parts/Meixner: we as individuals have no temporal parts! Only our life stories have temporal parts.
We do not say "he stretched from... to," but "he lived from... to..."
We do not say "an earlier phase of me was a craftsman"; but "in an earlier phase of my life I was a craftsman".
When we die, we die as whole individuals, it is not just the last temporal phase that dies.
For example, the object X exists to t1 and is F. But this is not an identity of X and F, but the exemplification of F by X.
((s) have/be: having a property is not identity with the property.)
And X also exists to t2, but not F.
VsMeixner: If now the three-dimensionalism would be correct, then both, X to t1 and X to t2 would be identical with X. Consequently, X to t1 and X to t2 would be identical with each other!
But they are not identical, because X is F at one time and not F at the other.
MeixnerVs: Solution: from the assumption of three-dimensionalism it does not follow that X is identical with
X to t1 or X to t2 would be identical! Although X is present as an individual as a whole, it is different from X to t1 as well as from X to t2, because these entities do not exist differently than X at several points in time.

Mei I
U. Meixner
Einführung in die Ontologie Darmstadt 2004
Frege, G. Meixner Vs Frege, G. I 170
Numbers/Frege/Meixner: special properties, i.e. finite number of properties of properties (i.e. functions). Notation of Meixner: F0 (should be 0) is the abbreviation of "01[01 is different from 01]".
Def Equivalence/Frege/Meixner: f is a property equal to the property g, = Def is valid for at least one two-digit relation R:
1. each entity which has f stands for exactly one entity which has g, in the relation R
2. are entities that have f different, then also entities with g
3. inversion of 1: any entity having g.
Number/Meixner: one could therefore define non-circularly:
x is a natural number = Def x is a finite number property.
I 171
Number/MeixnerVsFrege: then you could simplify: the default property used for the definition of 1 λ01[01 is identical to F0] is definitorically the same as the property
λ01[01 is identical with 0].
Then you can simplify (which is a sign that numbers do not stand on ontologically safe feet):
x is a natural number = Def x is a standard property for determining finite numbers
then: f is 0 = Def f is a property that is equal to the property 0.
Meixner: this is simpler, but also has the strange consequence that each natural number is exemplified by all its predecessors.
I 172
FregeVsMeixner: Numbers are (saturated) objects, not properties. Each number is exemplified by an infinite number of entities. Number/Meixner: understood as property, they are untyped functions, i.e. they cannot be placed in any box of the form []
U. Meixner
I Uwe Meixner Einführung in die Ontologie Darmstadt, 2004

The author or concept searched is found in the following theses of the more related field of specialization.
Disputed term/author/ism Author
Actualism Meixner, U. I 21
Def Aktualismus: These alles ist wirklich ((s): VsMeinong).
I 62
Aktualismus/Meixner: These Alle Entitäten existieren (sind aktual, sind wirklich). Diese These wird von den meisten Ontologen für richtig gehalten.
epistemische/theoriefremde Begründung: man könne Nichtexistentes nicht erkennen. Aber selbst wenn dies richtig wäre, könnte man die Existenz von Entitäten nur daraus schließen, wenn man zusätzlich annähme, daß alle Entitäten grundsätzlich erkennbar sind. (Unbegründet).
I 65
Def eingeschränkter Aktualismus/Meixner: These alle ee maximalkonsistenten individuenähnlichen Entitäten existieren (sind aktual). Variante: uneingeschränkter: alle Entitäten existieren. (Possibilismus)
Variante aktualistische Minimalthese: alle Individuen sind aktual. ("Aktualismus").
I 66
Vertreter: Alvin Plantinga. (Obwohl er doch an nichtaktuale Sachverhalte glaubt). Possibilismus: Vertreter Leibniz, David Lewis. sie beziehen sich aber ausschließlich auf Individuale, mit denen sie wiederum die Individuen identifizieren.
I 127
Aktualität/Meixner: soll hier vereinfacht schlechthinnige A. sein, d.h. weder zeitlich relativiert noch unbestimmt zeitgezogen. MeixnerVsAktualismus: (These daß alle Entitäten aktual sind): unplausibel: es kann nicht bestritten werden, daß nicht alle SV aktual sind (es gibt MöWe).
Beweis: AG Schleuderargument: es gäbe nur zwei Sachverhalte, davon einer die Negation des anderen:
I 128
Würde nun einer der beiden nicht bestehen, wäre immer noch mancher SV nicht aktual.
I 139
absolute Aktualität/Meixner: These ist eine Qualität. Eine Qualität, die weder intrinsisch noch essentiell ist, sondern den Entitäten quasi von außen "verpaßt" ist, eine nichtessentielle extrinsische Qualität. LewisVsMeixner: würde sagen, das ist unverständlich.