Lexicon of Arguments


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The author or concept searched is found in the following 4 entries.
Disputed term/author/ism Author
Entry
Reference
Analyticity/Syntheticity Bolzano
 
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Mates I 284
Bolzano/Mates: (1781 1848): logical workings are scattered in his work. Analytics: relatively exact definition with the help of interpretation. Likewise for inference.
Proposition/Bolzano: puts it against statements. One proposition can be obtained from another by substituting its constituents.
MatesVsBolzano: "Replacement" is unclear here,
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I 285
because it is applied to types of objects that are not to be spatial and not temporal. Analyticity/Bolzano:

Definition analytical/Bolzano: a proposition is generally valid with respect to a particular component if the result of any substitution of these parts by other terms is true.
Definition analytical in a broad sense: if the proposition is generally valid or generally invalid. Otherwise, it is synthetic.
Definition closely analytical: if the proposition in reference to all the components apart from the logical one is analytic.
MatesVs: Problem of arbitrary distinction of logical/non-logical constants.


Mate I
B. Mates
Elementare Logik Göttingen 1969

Mate II
B. Mates
Skeptical Essays Chicago 1981
Conditional Bolzano
 
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Berka I 8
Conditional/ relationship/Conclusion/Bolzano: for Bolzano follows M, N, O..from A, B, C... only if (1) each (semantic) model of A, B, C ... is also a model of M, N, O .... That is, if each of the final sentences M, N, O, can be deduced separately from the assumptions A, B, C.
and
(2) the premises are the (s) content-related) reason for the conclusion.
Berka: that is a very strong conclusion concept.
TarskiVsBolzano: it is enough for him if the first condition is fulfilled.
GentzenVsBolzano: for Gentzen it is sufficient if at least one of the final sentences is derivable from the set of premisses.

Special case: if the claim quantity contains only one final sentence, the Bolzano's and the Gentzen's inference system are identical.
Conclusion/Bolzano: additional condition: one must be able to decide which concepts are logical concepts.
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Berka I 20 f
E.g. Entailment/Bolzano: (content-wise): if it is warmer in a place, then there are higher temperatures at the location - in reality, higher temperatures are shown, because it's warmer - the thermometer does not generate the temperatures. I.e. the entailment only exists in one direction: heat > temperature: - different with Deducibility/Bolzano/(s): if the sentence "... higher temperatures" is true, the sentence "it's warmer" is true, and vice versa. Reversible relation of two true sentences. Content is not decisive here - entailment: only in one direction - derivability: goes in both directions, regardless of truth - Entailment/Bolzano: for reason - Derivability/>Mates: formal.


Brk I
K. Berka/L. Kreiser
Logik Texte Berlin 1983
Domains Logic Texts
 
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Re III 57
Substitution criterion / Vssubstitution criterion / VsBolzano: leads to absurd results: because it declares certain invalid inferences for valid - e.g. "there are at least two things." It is not a matter of logic, that there are at least two things - one can just as well say "there are two things, so there are 76 things" - solution / Tarski: establish a domain - then "there are at least 2 things" might be falsified and is not a logical truth any more.
Logic Texts
Me I Albert Menne Folgerichtig Denken Darmstadt 1988
HH II Hoyningen-Huene Formale Logik, Stuttgart 1998
Re III Stephen Read Philosophie der Logik Hamburg 1997
Sal IV Wesley C. Salmon Logik Stuttgart 1983
Sai V R.M.Sainsbury Paradoxien Stuttgart 2001
Proof of God’s Existence Bolzano
 
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Simons I 321
Cosmological proof of God/unconditioned existence/Bolzano/Simons: (circumvents the problem of being founded by referring to classes. A) there is something real, e.g. my thoughts that it is like that.
B) Suppose there is some thing A that is absolutely essential in its existence, then we already have it
(B) Suppose A is conditional. Then form the class of all conditional real things A, B, C, ... This is also possible if this class is infinite
D) the class of all conditioned real things is itself real. Is it conditional or unconditional? If it is absolute, we already have it
(E) Suppose it is conditional: every conditioned presupposes the existence of something else, whose existence it determines. Thus even the class of all conditional things, if conditioned, presupposes the existence of something that determines it.
(F) This other thing must be unconditioned, for if it were conditioned, it would belong to the class of all conditioned things
G) Therefore, there is something unconditional, e.g. a god.

Simons: this makes no use of being founded: c) leaves the possibility of an infinite chain open.
RussellVsBolzano/Simons: one might have doubts about the "class of all unconditioned things" (> paradoxes).
Solution/Bolzano: it's about the real things from which we can assume spatial-temporal localization.
2. SimonsVsBolzano: Step f)
---
I 322
Why should the class of all conditioned things not be conditioned by something within? This would be conditioned itself, etc. but any attempt to stop the recourse would again appeal to being founded. ((s) the thing that conditions would be within the class of conditioned things, it would be conditioned and conditional at the same time).
Solution/Simons: we need additionally a conditioning principle.
Definition Conditioning Principle/Simons: if a class C is such that each dependent element of it has all the objects on which it depends within X, then X is not dependent. (Simons pro).

Simons: this allows infinite chains of dependencies. A kind of infinite dependence already arises e.g. when two objects are mutually dependent.
If the conditioning principle applies, why should the class X be still externally conditioned?
Ad Bolzano: Suppose we accept his argument until e). Then it can go on like this:
H) if the class of all conditioned things is conditioned, then there is an element of it that is dependent on something that is not an element of that class. (Contraposition to the conditioning principle)
I) then such an (unconditioned) object is not an element of the class of all conditioned things, and is thus unconditional.
J) Therefore, there is in any case something unconditioned.

SimonsVsAtomism: that is better than anything that an atomism achieves.
Conditioning principle/Simons: is the best extension of the strong rigid dependency (7), i.e.

(N) (a 7 x ↔ (Ey) [x e a u a 7 x] u ~ x e a)

SimonsVsBlack: with the strong instead of the weak dependency, we can counter Black.
---
I 323
God/Mereology/Ontology/Simons: in any case, the strong rigid dependence does not prove the existence of God. Only the existence of an unconditional, which Bolzano cautiously calls "a God". Independence/Simons: does not include divinity.


Si I
P. Simons
Parts Oxford New York 1987

The author or concept searched is found in the following 3 controversies.
Disputed term/author/ism Author Vs Author
Entry
Reference
Bolzano, B. Tarski Vs Bolzano, B.
 
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Berka I 8
Folgebeziehung/Folgerung/Bolzano: für Bolzano folgt M,N,O..aus A,B,C.. nur dann, wenn 1. jedes (semantische) Modell von A,B,C... auch ein Modell von M,N,O... ist. D.h. wenn jeder der Schlußsätze M,N,O, aus den Prämissen A,B,C... einzeln ableitbar ist. und
2. die Prämissen der ((s) inhaltliche) Grund für die Schlußsätze sind.
Berka: das ist ein sehr starker Folgerungsbegriff.
TarskiVsBolzano: für ihn reicht es, wenn die 1. Bedingung erfüllt ist.
GentzenVsBolzano: für Gentzen reicht es, wenn wenigstens einer der Schlußsätze aus der Menge der Prämissen ableitbar ist.
Sonderfall: enthält die Forderungsmenge nur einen Schlußsatz, sind das Bolzanosche und das Gentzensche Folgerungssystem identisch.
Folgerung/Bolzano: zusätzliche Bedingung. man muß entscheiden können, welche Begriffe logische Begriffe sind.

Tarsk I
A. Tarski
Logic, Semantics, Metamathematics: Papers from 1923-38 Indianapolis 1983

Brk I
K. Berka/L. Kreiser
Logik Texte Berlin 1983
Bolzano, B. Simons Vs Bolzano, B.
 
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I 321
Cosmological proof of God’s existence/unconditional existence/Bolzano/Simons: (avoids the problem of foundedness by referring to classes. a) There is something real e.g. my thoughts that it is so.
b) Suppose there is any thing, A that is unconditional in its existence, then we have it already
c) Suppose A is conditional. Then the class of all conditional real things forms A, B, C, ... This is also possible if this class is infinite
d) The class of all conditional real things is itself real. Is it conditional or unconditional? If unconditional, we have it already.
e) Suppose it is conditional: each conditional presupposes the existence of something else, the existence of which it requires. So even the class of all conditioned things, if conditional, requires the existence of something that it presupposes.
f) This other thing has to be unconditional because if it were conditional, it would belong to the class of all conditional things
g) Therefore, there is something unconditional e.g. a God.
Simons: This does not use foundedness: c) leaves the possibility of an infinite chain open.
RussellVsBolzano/Simons: one could have doubts about the "class of all unconditional things" (> paradoxes).
Solution/Bolzano: it is exactly about the real things of which we can assume spatiotemporal localization.
2. SimonsVsBolzano: step f)
I 322
Why should the class of all conditional things not be required by something within? This itself would be conditional, etc. but any attempt to stop the recourse would again appeal to foundedness. ((S) the conditional would be within the class of conditional things, it would be conditional and conditioning at the same time).
Solution/Simons: we need in addition a
Def Conditioning Principle/Simons: if a class C is such that each dependent member of her has all of the objects on which it depends within X, then X is not dependent. (Simons pro).
Simons: this allows infinite chains of dependencies. A kind of infinite dependence appears already if e.g. two objects mutually require each other.
If the conditioning principle applies, why should the class X then be even conditioned from the outside?
ad Bolzano: Suppose we accept his argument up to e). Then it can go on like this:
h) if the class of all conditional things is conditional, then there is an element of it which is dependent on something that is not a member of this class. (Contraposition to the conditioning principle)
i) then such an (unconditional) object is no member of the class of all conditional things and therefore unconditional.
j) Therefore definitely something unconditional exists.
SimonsVsAtomism: that is better than anything the atomism accomplishes.
Conditioning Principle/Simons: is the best extension of strong rigid dependence (7), that means that
(N) (a 7 x ↔ (Ey)[x e a u a 7 x] u ~ x e a)
SimonsVsBlack: we can face Black with the strong rather than with the weak dependence.
I 323
God/mereology/ontology/Simons: in any case the strong rigid dependence does not prove the existence of God. Only the existence of something unconditional that Bolzano prudently called "a god". Independence/Simons: includes by no means divinity.

Si I
P. Simons
Parts Oxford New York 1987
Bolzano, B. Mates Vs Bolzano, B.
 
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I 284
Bolzano/Mates: (1781 1848): logische Ausarbeitungen finden sich verstreut in seinem Werk. Analytizität: relativ exakte Definition mit Hilfe von Interpretation. Ebenso für Folgerung.
Proposition/Bolzano: stellt sie Aussagen gegenüber. Eine Proposition ist aus einer anderen dadurch zu erhalten, dass man für ihre Bestandteile Ersetzungen vornimmt.
MatesVsBolzano: "Ersetzung" ist hier unklar,
I 285
weil sie auf Gegenstandsarten angewendet wird, die nicht räumlich und nicht zeitlich sein sollen. Analytizität/Bolzano:
Def analytisch/Bolzano: eine Proposition ist allgemeingültig in Bezug auf einen bestimmten Bestandteil, wenn das Ergebnis jeder Ersetzung dieser Teile durch andere Begriffe wahr ist.
Def analytisch im weiteren Sinn: wenn die Proposition allgemeingültig oder allgemein ungültig ist. Sonst ist sie synthetisch.
Def eng analytisch: wenn die Proposition in Beug auf alle Bestandteile mit Ausnahme der logischen analytisch ist.
MatesVs: Problem der willkürlichen Unterscheidung logische/nicht-logische Konstanten.

Mate I
B. Mates
Elementare Logik Göttingen 1969

Mate II
B. Mates
Skeptical Essays Chicago 1981