Lexicon of Arguments


Philosophical and Scientific Issues in Dispute
 


 

Find counter arguments by entering NameVs… or …VsName.

The author or concept searched is found in the following 5 entries.
Disputed term/author/ism Author
Entry
Reference
Connectives Logic Texts
 
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Re III 268 ff
Tonk/Prior/Read: Do not introduce the link first and then assign meaning. - That cannot have the consequence that another pair of statements is equivalent. - Point: analytic validity cannot show that.
Re III 269
The meaning, even that of logic links, must be independent of and be prior to the determination of the validity of the inference structures. - BelnapVsPrior: (pro analytical validity): Must not define into existence, first show how it works.
Re III 271
>Classical negation illegitimate. - Negation-free fragment. - Peirce's law. - "If P, then Q, only if P, only if Q".
Re III 273
ReadVsBelnap: the true disagreement lies beyond constructivism and realism. - Belnap's condition (conservative extension) cannot show that the classical negation is illegitimate. - - -
Hoyningen-Huene II 66
Binding strength of the connectives: increases in the following order: ,>, v, u,
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
Introduction Belnap
 
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Nuel Belnap
Brandom II 94
Definition "tonk"/Belnap: 1. rule: licenses the transition from p to p tonk q for any q.
2. Rule: licenses the transition from p tonk q to q. Thus we have a "network map for inferences": any possible conclusion is allowed!
---
II 93
Conservativity/Conservative Expansion/Dummett: If a logical constant is introduced by introduction and elimination rules, we may call it a conservative extension of language. ---
II 94
For example, this might be true of Belnaps "tonk": the introduction rule of the disjunction and the elimination rule of the conjunction. PriorVsBelnap/PriorVsGentzen: this is the bankruptcy of definitions in the style of Gentzens.
BelnapVsPrior: if one introduces logical vocabulary, one can restrict such definitions by the condition that the rule does not allow inferences with only old vocabulary that was not already allowed before the introduction of the logical vocabulary. (Conservative expansion).
Such a restriction is necessary and sufficient.
Brandom: the expressive analysis of the logical vocabulary provides us with a deep reason for this condition: only in this way the logical vocabulary can perform its expressive function.
The introduction of new vocabulary would allow new material inferences without the constraining condition (conservativity) and would thus change the contents correlated with the old vocabulary.

Beln I
N. Belnap
Facing the Future: Agents and Choices in Our Indeterminist World Oxford 2001


Bra I
R. Brandom
Expressive Vernunft Frankfurt 2000

Bra II
R. Brandom
Begründen und Begreifen Frankfurt 2001
Metalanguage Kripke
 
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EMD II 342
Metalanguage/ML/Interpretation/Truth Theory/KripkeVsWallace/VsBelnap: Metalanguage should not be purely formally construed as uninterpreted - (object language should). ---
EMD II 347
Truth theory/Davidson//Kripke: meta language may contain semantic vocabulary as well - Translation is also guaranteed if both sides contain semantic vocabulary - Kripke: Very different in Tarski: truth and all semantic terms are explicitly defined in non-semantic vocabulary. ---
EMD 355F II
Modality/Metalanguage/Kripke: Modal operators disappear in the metalanguage - right side of a meaning theory/truth theory: no demonstratives, personal pronouns and no grammatical tenses - KripkeVsWallace: That does not make modal operators "misleading superficial properties". ---
EMD II 383
Metalanguage/Kripke: If meta language = object language + truth predicate, sentences that contain no truth predicate must be treated the same in both languages ​​ - but metalanguage should have more anyway: Variables about expressions of the object language.

K I
S.A. Kripke
Name und Notwendigkeit Frankfurt 1981

K III
S. A. Kripke
Outline of a Theory of Truth (1975)
In
Recent Essays on Truth and the Liar Paradox, R. L. Martin (Hg), Oxford/NY 1984


EMD II
G. Evans/J. McDowell
Truth and Meaning Oxford 1977

Ev I
G. Evans
The Varieties of Reference (Clarendon Paperbacks) Oxford 1989
Substitutional Quantification Belnap
 
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Nuel Belnap
AMD II p340
Substitutional Quantification/SQ//Belnap/Dunn: did not even require ontology of expressions - KripkeVs: it does - KripkeVsBelnap: if no ontological commitment (OC), then why should L be metalanguage of L0? - Then T (x) no predicate, then the metalanguage is a mere form without interpretation - then no truth theory
II 341
SQ/Belnap: the expressions of metalanguage designate, or they do not.
II 344
KripkeVsBelnap: cannot be answered so categorically - the answer depends on both: on L0 and on the existence of simple chain predicates - you can also define (and derive) many new symbol strings - That does not mean that the new ontology has anything to do with the alleged or real "designation" of the expressions
II 342
Truth Theory/KripkeVsWallace/VsBelnap: metalanguage may not purely formally be construed as uninterpreted - (object language may be)

Beln I
N. Belnap
Facing the Future: Agents and Choices in Our Indeterminist World Oxford 2001

Vocabulary Brandom
 
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I 199
Conservativeness/Expansion/Language/Tonk/Brandom: pro conservative expansion: if the rules are not inferentially conservative, they allow new material inferences and thus change the contents that were associated with the old vocabulary expressive logic/Brandom: requires that no new inferences that only contain old vocabulary be rendered appropriate by this (if they were not before). ---
I 200
E.g. "boche"/Dummett: non-conservative extension, statements that do not (!) contain the expression might now be inferred from others that do not contain it either E.g. inference from German nationality to cruelty BrandomVsDummett: this is not about non-conservatism: it only shows that the expression "boche" has a content which is not contained in the other expressions E.g. the cocnept "temperature" has also changed with the methods of measurement. It's not about novelty of a concept, but undesirable inferences. ---
I 204
In particular the material content of concepts is lost when the conceptual content is identified with the truth conditions. ---
I 427/8
Definition Supervenience/Brandom: one vocabulary supervenes another if and only if there could be no two situations in which true assertions (i.e. facts) would differ expressably in the supervening vocabulary, while the true assertions do not differ expressably in the vocabulary that is being supervened more neutral: if it is clear what is defined in one language, then it is clear what is defined in the other. ---
I 958
Order/Twin Earth/TE/Brandom: it does not help to speak in concepts of what can be distinguished by the individuals, because what they can react depends on which reactions are considered to be different, and then the same problem occurs with regard to the vocabulary used Problem: specifying a vocabulary that satisfies two conditions: 1) The twins are indistinguishable in different environments because of their description in that vocabulary (physical language is not sufficient for that). 2) The sub-determination of the semantic properties of their states in this limited vocabulary must point at something interesting. ---
II 76
Material inference/Sellars/Brandom: from "a east of b" to "b west of a" also from flash to thunder, needs no logic. ---
II 79
Formally valid ones can be derived from good material inferences, but not vice versa Proof: if a subset of somehow privileged vocabulary is given, such an inference is correct if it is materially good and it cannot become a bad one if non-privileged vocabulary is replaced by privileged vocabulary. If one is only interested in logical form, one must be able to distinguish a part of the vocabulary as a especially logical beforehand. E.g. if one wants to explore theological inferences, one must investigate which replacement of non-theological vocabulary with non-theological preserves the material quality of the inference. ---
II 94
Definition "tonk"/Belnap: Rule 1): licenses the transition from p to p tonk q for any q. Rule 2): licenses the transition from p tonk q to q. With that we have a "network map" for inferences: any conclusion is thus permitted. PriorVsBelnap: Bankruptcy of all definitions in the style of Gentzen BelnapVsPrior: Solution: Restriction: no inferences with only old vocabulary that were not allowed previously,otherwise the old contents would be changed retrospectively.

Bra I
R. Brandom
Expressive Vernunft Frankfurt 2000

Bra II
R. Brandom
Begründen und Begreifen Frankfurt 2001


The author or concept searched is found in the following 7 controversies.
Disputed term/author/ism Author Vs Author
Entry
Reference
Belnap, Nuel Kripke Vs Belnap, Nuel
 
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EMD II 341
Substitutional quantification/SQ/Belnap/Dunn: Here an ontology of terms is not even necessary because the quantifiers of metalanguage (m.l.) could also be constructed by substitution! KripkeVsBelnap: This is a case of purely mechanical acquisition of Quine’s criteria for Ontological Commitment/OC: "referential quantifiers carry a OC with it and nothing else." Substitutional ml/Kripke: There are two possible interpretations: It is assumed that substitution quantification have (structurally descriptive) names for the expressions of the object language (o.l.) as substitutes ((s) The names have have the term for which they stand for, not the part). (see below, EMD II 365). Then: a) the interpretation of m.l. is as such that these terms denote those of the o.l. or b) they do not denote.
ad a): If they denote, Wallace is right that the difference between substitutional quantification with names of expressions and referential quantification which work through expressions, is negligible. Both quantifiers carry the same amount of ontological commitment. ad b): then the m.l. has indeed no ontological commitment for expressions of the o.l.
But what is the justification then to call M a metalanguage of L? How should a theory which is formulated in M say anything about the semantics of L? Then T(x) is also no predicate anymore, filled with the true sentences of L and only them, but rather a form of M, without any interpretation.
KripkeVsBelnap: it is only possible to argue this mechanically if one has lost his or her philosophical goals.

K I
S.A. Kripke
Name und Notwendigkeit Frankfurt 1981

K III
S. A. Kripke
Outline of a Theory of Truth (1975)
In
Recent Essays on Truth and the Liar Paradox, R. L. Martin (Hg), Oxford/NY 1984

EMD II
G. Evans/J. McDowell
Truth and Meaning Oxford 1977

Ev I
G. Evans
The Varieties of Reference (Clarendon Paperbacks) Oxford 1989
Belnap, Nuel Prior Vs Belnap, Nuel
 
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"Tonk": (Belnap) PriorVsBelnap: bankruptcy of definitions of the inferential roles in the style of Gentz. ​​"Network card for arbitrary conclusions". Brandom I 198 (>Dummett: "Boche" conservative extension).
Prior: "tonk": Do not start by introducing the link first and then the meaning - cannot have the consequence that another pair of statements is equivalent - Important Argument: "analytical validity" cannot show this - BelnapVsPrior: (per analytical validity): must not define into existence, first show how it works -> typical negation is illegitimate - negation-free fragment - Peirce's law: Read, Logical III 268
Prior: thesis: it is absurd to assume an "analytical validity", a "carte blanche", to introduce a possibility link and then to give them a meaning by simply determining it. His well-known example was "tonk". Absurd: how can the simple introduction of a new link have the consequence that any pair of statements (without "tonk") is equivalent? III 269 If we learned what "tonk" meant, we would see that one or another inference is not truth-preserving. But, and that's Prior's point:
the representative of the view of the analytical validity cannot say this, because he has no independent explanation of the meaning of "tonk" with respect to which he could show that the conclusions are invalid.
Meaning: the meaning, even that of logic links, must be independent of and prior to the determination of the validity of the inference structures! (>BelnapVsPrior).

Pri I
A. Prior
Objects of thought Oxford 1971

Pri II
Arthur N. Prior
Papers on Time and Tense 2nd Edition Oxford 2003
Belnap, Nuel Read Vs Belnap, Nuel
 
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Re III 270
Belnap: we have not shown, and cannot show that there is such a link. The same applies for "tonk". Read: One problem remains: why is there ever an analogy between definitions and links. It cannot always be wrong to expand a language with new links. Calculation rules for 'conservative' extensions of languages are conceivable. The old rules must persist.
Re III 271
Peirce's Law: (>Peirce): "If P, then Q, or if Q only if P, then R" is negation-free, but still not, as the constructivist claims, part of the negation-free fragment (>Gentzen). The law cannot be proved within the classical calculus without using classic negation rules.
Re III 273
The crucial step in all cases is certainly that the implication "If P, then Q or R" from "If P then Q or R" (Note: the comma is missing here) is allowed. A step which foresees the establishment of the multiple conclusion, the LK, and not the establishment of the individual conclusion. (Peirce's Law: "If P, then Q or, if Q only if P, then R") The constructivist objects against such a step, because he introduces a disjunction in a way that does not guarantee that you know which member of the disjunction is the justification!
ReadVsBelnap: The true disagreement lies beyond constructivism and realism. Belnap's condition (conservative extension) cannot show that the classical negation is illegitimate.

Re III
St. Read
Philosophie der Logik Hamburg 1997

Re IV
St. Read
Thinking About Logic: An Introduction to the Philosophy of Logic 1st Edition Oxford 1995
Belnap, Nuel Cresswell Vs Belnap, Nuel
 
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HCI 299
Paradoxes of implication/Hughes/Cresswell: are at worst harmless. In most cases, we wish to speak of entailment. VsEntailment/VsBelnap/VsAnderson: Their system E (see above) pays too high a price with the absence of the disjunctive syllogism (see below principle C). I 300 Problem: the mere construction of such an axiom system does not provide us with a clear notion of entailment. Paradoxes of implication/Hughes/Cresswell: are even desirable: we want to be able to say: "If you accept that, you can prove anything." I.e. in a contradictory system everything can be proven. aca

Cr I
M. J. Cresswell
Semantical Essays (Possible worlds and their rivals) Dordrecht Boston 1988

Cr II
M. J. Cresswell
Structured Meanings Cambridge Mass. 1984
Belnap, Nuel Brendel Vs Belnap, Nuel
 
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I 89
Relevance Logic/Brendel: it is not explicitly about an alternative handling of contradictions. Problem: how the different formal semantics are to be interpreted philosophically for the relevance logic.
VsAnderson/VsBelnap: Although its system R corresponds to certain association theoretical structures, it is controversial how these structures are to be interpreted as truth values.
Solution/Dunn/Brendel: tetravalent semantics with additional "true-and-false" and "neither-true-nor-false". However, epistemically and not to be understood ontologically. It should explain that someone can have conflicting or incomplete information.
DunnVsDialethism/Brendel: Dunn does not claim the existence of "true contradictions". (Dunn, 1986, 192f).
"True-and-

Bre I
E. Brendel
Wahrheit und Wissen Paderborn 1999
Dunn, J. M. Wessel Vs Dunn, J. M.
 
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I 134
WesselVsDunn
System E/Dunn: (Teilsystem von E): WGS Kriterium (Wright, Geach, Smiley): Aus A folgt B genau dann, wenn
1. A > B eine Einsetzung in eine Tautologie A’ > B’ ist, wobei
2. A’ keine Kontradiktion und
3. B’ keine Tautologie ist.
Vs: das kann nicht als Kriterium für eine gültige logische Folgebeziehung akzeptiert werden, weil es nicht transitiv ist.
Verbesserung:
2. .A’ keine partielle Kontradiktion. 3. .B’ .keine partielle Tautologie.
Def Wahrheitsbaum/Falschheitsbaum/Dunn: baumartiges Diagramm für die Bedingungen, nach denen eine Folgebeziehung (Implikation) den Wahrheitswert w bzw. f annehmen kann.
Def "geschlossener Ast": enthält sowohl eine Aussagenvariable, als auch deren Negation (Negat) enthält. Die übrigen sind offene.
Regeln zur Herstellung eines Wahrheitsbaums für Negation, Konjunktion und Adjunktion:

A U B ~(A u B) A v B ~(A v B) ~~A_
A ~ A ~B A B ~A A
B ~B

I 135
Bsp Falschheitsbaum:
A u B ~ (A u B) A v B ~(A v B) ~~A
A B ~A A ~A ~B A
~B B ((s) gleiche obere Zeile).
Def partielle Kontradiktion/partielle Tautologie/Dunn/Wessel:
Tautologie: liegt vor, wenn ihr Falschheitsbaum geschlossen ist.
Kontradiktion: wenn ihr Wahrheitsbaum geschlossen.
partielle Tautologie: wenn der Falschheitsbaum mindestens einen geschlossenen Ast besitzt
partielle Kontradiktion: wenn der Wahrheitsbaum mindestens einen geschlossenen Ast besitzt. Bsp (A v B) u ~A.
L Kriterium/Dunn/WesselVsDunn: entspricht nicht der intuitiven Auffassung der logischen Folgebeziehung.
Grund: nach dem L Kriterium ist (A v B) u ~A -> B keine gültige Regel, da das Vorderglied eine partielle Kontradiktion ist.
((System E/Belnap/Anderson/Dunn/Wessel: A -> B ist eine Folgebeziehung der ersten Stufe des Systems E genau dann, wenn A logisch aus B gemäß dem L-Kriterium folgt. ) (nach oben setzen!)
Bsp Wahrheitsbaum: der Formel
(A v B) u ~A
~A
A v B
A B.
(Der linke Ast ist geschlossen, weil er A und ~A enthält.)
WesselVsDunn: das bedeutet aber gerade nicht, dass der Schluss von (A v B) u ~A auf B ungültig ist! Im Gegenteil ist der W Baum gerade die Voraussetzung für die Gültigkeit.
Daher ist das L Kriterium nicht brauchbar.
Folgebeziehung/erste Stufe/Dunn/Wessel: dass Dunns Teilsystem von E nur für die erste Stufe gilt, ist kein Zufall:
bei einer inhaltlichen Deutung des Operators z.B. bei den Axiomen E1 E3 und E6 (I 133) müssen verschiedene Vorkommen des Operators verschiedene inhaltliche Deutungen bekommen:
E1. A -> A -> B -> B
E2. A -> B ->(B -> (A -> C)) E3. A -> (A >B) -> (A -> B)
E6. (A -> B) u (A -> C) -> (A -> B u C).
I 136
WesselVsDunn: die Forderungen, dass A keine partielle Kontradiktion und B keine partielle Tautologie sein dürfen, sind zu stark. Wir wollen in unserer eigenen Theorie (s.u.) nur Tautologien und Kontradiktionen ausschließen. Adjunktion/Wessel: die Beseitigungsregel der Adjunktion ist umstritten! (Dunn: "verrufen", "infamous"). Im System E fehlt sie.
Adjunktionseinführung: ist eigentlich keine logische Schlussregel, sie ist eine Hilfsregel, die es gestattet, neue Tautologien (bzw. Kontradiktionen) zu erhalten. Diese problematische Einführungsregel A -> A v B ist im System E beweisbar.
System E/Wessel: hier gilt nicht die Einsetzungsregel A l- A {a/B}.
WesselVsBelnap/VsDunn: hier gibt es kein Kriterium für Paradoxienfreiheit. Es ist nicht garantiert, dass diese Systeme paradoxienfrei sind.
Außerdem ist -> wieder ein Operator!

We I
H. Wessel
Logik Berlin 1999
Prior, A. Belnap Vs Prior, A.
 
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Nuel Belnap
BelnapVsPrior: wenn man logisches Vokabular einführt, muß man solche Definitionen durch die Bedingung einschränken, daß die Regel keine nur altes Vokabular enthaltende Inferenzen zuläßt. LL. Das heißt, die neuen Regeln müssen das Repertoire konservativ erweitern. > Bsp "boche" Brandom 198
Brandom: Wenn diese Regeln nicht inferentiell konservativ sind, gestatten sie neue materiale Inferenzen und ändern damit die Gehalte, die mit dem alten Vokabular verbunden waren.
Die expressive Auffassung der Logik verlangt, daß keine neuen Inferenzen, die nur altes Vokabular enthalten, dadurch angemessen gemacht werden.
Konservativität/konservative Erweiterung/Dummett: wenn eine logische Konstante durch Einführungs-und Eliminationsregeln eingeführt ist, können wir das eine konservative Erweiterung der Sprache nennen.II 93
Bsp das könnte auf Belnaps "tonk" zutreffen: Einführungsregel der Disjunktion und Eliminationsregel der Konjunktion:
Def "tonk"/Belnap: 1. Regel: lizensiert den Übergang von p zu p tonk q für beliebige q. 2. Regel: lizensiert den Übergang von p tonk q zu q. Damit haben wir eine "Netzkarte für Inferenzen": jede beliebige Folgerung ist damit gestattet! II 94
PriorVsBelnap/PriorVsGentzen: das ist der Bankrott von Definitionen im Stile Gentzens.
BelnapVsPrior: man kann, wenn man logisches Vokabular einführt, solche Definitionen durch die Bedingung einschränken, daß die Regel keine Inferenzen mit ausschließlich altem Vokabular zuläßt, die nicht bereits vor der Einführung des logischen Vokabulars erlaubt waren. (Konservative Erweiterung).Eine solche Einschränkung ist notwendig und hinreichend.
Brandom: die expressive Analyse des logischen Vokabulars liefert uns nun einen tiefen Grund für diese Bedingung: nur so kann das logische Vokabular seine expressive Funktion ausüben.Die Einführung neuen Vokabulars würde ohne die einschränkende Bedingung (Konservativität) neue materiale Inferenzen gestatten und würde so die Gehalte ändern, die mit dem alten Vokabular korreliert sind. ((s) rückwirkende Änderung, auch der Wahrheitswerte etablierter Sätze).
Read:Bedeutung: die Bedeutung, selbst die logischer Verknüpfungen, muss unabhängig sein von und vor der Bestimmung der Gültigkeit der Folgerungsstrukturen. Logik III 269
Belnap: kam der Ansicht der »analytischen Gültigkeit« zu Hilfe. Was ihr fehlt, sagte er, ist jeder Beweis, daß es eine solche Verknüpfung wie "tonk" überhaupt gibt. Das ist ein Problem für Definitionen allgemein. Man kann nicht in die Existenz hinein definieren. Man muss zuallererst zeigen, dass es ein solches Ding (und nur 1) gibt. Bsp "Pro-Summe" zweier Brüche.
(a/b)!(c/d) wird definiert als ( a+c)/ (b+d).
Wenn man Zahlen einsetzt,kommt man schnell zu Ergebnissen, bei denen völlig falsche Rechenergebnisse herauskommen.Zwar ist es leicht, usprünglich passende Zahlen zu finden, doch sie lassen sich nicht kürzen.(> Dubislav). Logik III 270
Belnap: wir haben nicht gezeigt, und können es nicht zeigen, dass es eine solche Verknüpfung gibt. Dasselbe gilt für "tonk".
Read: Ein Problem bleibt: wieso gibt es hier überhaupt eine Analogie zwischen Definitionen und Verknüpfungen. Es kann nicht immer falsch sein, eine Sprache durch neue Verknüpfungen zu erweitern. Man könnte sich Rechenregeln für »konservative« Erweiterungen von Sprachen vorstellen. Die alten Regeln müssen fortbestehen.

Beln I
N. Belnap
Facing the Future: Agents and Choices in Our Indeterminist World Oxford 2001