Lexicon of Arguments

Philosophical and Scientific Issues in Dispute
 
[german]


Complaints - Corrections

Table
Concepts
Versus
Sc. Camps
Theses I
Theses II

Concept/Author*  

What is wrong?
Page
Other metadata
Translation
Excerpt or content
Other

Correction: Year / Place / Page
/ /

Correction:
(max 500 charact.)

Your username*
or User-ID

Email address*

The complaint
will not be published.

 
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.
>Mention.
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.

Found an error? Use our Complaint Form. Perhaps someone forgot to close a bracket? A page number is wrong?
Help us to improve our lexicon.
However, if you are of a different opinion, as regards the validity of the argument, post your own argument beside the contested one.
The correction will be sent to the contributor of the original entry to get his opinion about.