Psychology Dictionary of Arguments

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Relevance: is the importance of previously identified aspects of an object, action or situation against other aspects in relation to a description or assessment. See also relevance logic.
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Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments.

 
Author Concept Summary/Quotes Sources

Gerhard Schurz on Relevance - Dictionary of Arguments

I 107
Def relevance/logic/conclusion/Schurz:
1. A conclusion K of a valid argument is relevant gdw. there is no predicate in K which is simultaneously replaceable at some occurrences by any other predicate salva veritate.
2. The set of premises P of a valid argument is relevant if there is no predicate in P which can be replaced at a single occurrence by any predicate salva veritate.
I 108
Ex P relevant, K irrelevant: p II- p v q,: p II- q > p ; p II- p u (q v ~q)
(x)(Fx > Gx) II- (x)(Fx > Gx v Hx)

P irrelevant, K relevant: p u q II p ; (x)(Fx v Hx > Gx) II- (x)(Fx > Gx)

P relevant and K relevant: p > q ; p II- q ; p > q II ~q > ~p ;
(x)(Fx > Gx) ; Fa II- Ga ; (x)(Fx II- Fa ; Fa II- (Ex(Fx)

P irrelevant and K irrelevant: p u q II- p v r ; (x)(Fx u Gx) II- (x)(Fx v Hx)

Notation: "II- " "logical consequence".

Relevance/Logic/Schurz: Cognitive psychology has shown that the concept of validity in classical logic does not capture everything that is important for applied reasoning.
Non-classical relevance logic/Anderson/Belnap: (1975)(1).
Relevance/Logic/Schurz: solution: the relevant consequences of a theory must be decomposed into the smallest relevant conjunctive parts. Ex If A is a true consequence, and B is a false consequence of T, the conjunction A u B must not count as a third false consequence.
PKN/Terminology/Schurz: prenex conjunctive normal form.
>Logic
, >Cognitive psychology.
I 109
Def relevant consequence element/Schurz: 1. a formula A is called elementary iff it is in PKN (prenex conjunctive normal form) and not L equivalent to a conjunction of PKN formulas, which are all shorter than A.
2. K is a relevant consequence element of P iff K is an elementary relevant consequence of O.
Def relevant content/relevance/logic/Schurz:
(a) the relevant logical content of a proposition or set of propositions S is the set of its relevant consequence elements.
Notation: Cr(S)
b) the relevant empirical content of S is the set of those relevant consequence elements of S that are empirical and not analytic true propositions.
Notation: Er(S).
Each set of sentences is L equivalent to the set of its relevant consequence elements.

1. Anderson, A.R. and Belnap N. D. (1975). Entailment, The Logic of Relevance and Necessity. Princeton: Princeton University Press.
- - -
I 125
Statistical relevance/correlation/qualitative/Schurz:

A is (statistically) relevant for K iff. p(Kx I Ax) unequal p(Kx)

A is irrelevant for K iff. p(Kx I Ax) = p(Kx)

A is positively relevant for K iff A increases K's probability, i.e. k(Kx I Ax) > p(Kx)

A is negatively relevant to Kx iff. A decreases K's probability.

Simple correlation measure for qualitative characteristics:

Corr(A,K) = p(Kx I Ax) - p(Kx)

Corr(A,K) is always between +1 and -1.

A is positively relevant if Korr (A,K) is positive, or negative if negative, irrelevant if 0.

I 127
Information/relevance/statistics/Schurz: in the strict case the all proposition (x)(Ax u Bx) > Kx is irrelevant, (Bx) has no information. Rather, it follows logically from (x)(Ax > Kx) .
In contrast:
probabilistic: here the irrelevant generalization p(Kx I Ax u Bx) = r has additional information compared to p(Kx I Ax) = r because it does not follow from it, but expresses an independent fact.
This information is needed if we want to predict Ka for an individual a to which both Aa and Ba apply. This is because, according to the principle of the closest reference class, we must ensure that conditionalization on Bs does not change the probability p(Ax I Ax).
Since empirical predictions must always exclude a myriad of irrelevant assumptions, one does this by default:
Default assumption/Schurz: one excludes something, or makes a decision, as long as there is nothing against it. Here against the irrelevance assumption.
>Generalization, >Probability. >Probability theory.

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Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments
The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.

Schu I
G. Schurz
Einführung in die Wissenschaftstheorie Darmstadt 2006


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