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QUANTIFICATIONAL ACCOUNTS OF LOGICAL CONSEQUENCE III. THE MODEL-THEORETIC ACCOUNT: QUANTIFICATIONAL ACCOUNT TRIUMPHANT?

100%
Koreň L.
Organon F. medzinárodný časopis pre analytickú filozofiu
|
2014
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vol. 21
|
issue 4
492 – 515
EN
This concluding study devoted to quantificational accounts of consequence and related logical properties deals with the model-theoretic account (MTA). In response to objections questioning its intuitive adequacy, it is argued that MTA does not aim to analyse “the” alleged intuitive notion of consequence, but aims to formally reconstruct one specific semantic account, according to which valid arguments preserve truth in virtue of their logic-semantic structure and irrespectively of particular semantic values of the non-logical vocabulary. So conceived, MTA is arguably superior to any other quantificational account, being based on a principled account of the semantic structure and the specific contribution of logical elements to it.
2

QUANTIFICATIONAL ACCOUNTS OF LOGICAL CONSEQUENCE 1: FROM ARISTOTLE TO BOLZANO

88%
Koreň L.
Organon F. medzinárodný časopis pre analytickú filozofiu
|
2014
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vol. 21
|
issue 1
22 – 44
EN
So-called quantificational accounts explicate logical consequence or validity as truth-preservation in all cases, cases being construed as admissible substitution variants or as admissible interpretations with respect to non-logical terms. In the present study, which is the first from three successive studies devoted to quantification accounts, the author focus on the beginning of systematic theorizing of consequence in Aristotle‘s work, which contains the rudiments of both modal and formal accounts of consequence. He argues, inter alia, that there is no evidence for the claim that Aristotle propounded a quantificational account and that for a full-fledged quantificational approach in a modern style we need to turn to Bolzano’s substitution approach, whose motivation, structure and problems are explained in the second part of this study.
3

QUANTIFICATIONAL ACCOUNTS OF LOGICAL CONSEQUENCE II: IN THE FOOTSTEPS OF BOLZANO

88%
Koreň L.
Organon F. medzinárodný časopis pre analytickú filozofiu
|
2014
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vol. 21
|
issue 3
303 – 326
EN
Quantificational accounts of logical consequence account for it in terms of truth-preservation in all cases – be it admissible substitution variants or interpretations with respect to non-logical terms. In this second of the three connected studies devoted to the quantificational tradition the author set out to reconstruct the seminal contributions of Russell, Carnap, Tarski and Quine and evaluate them vis-à-vis some of the most pressing objections. This study also prepares the ground for his discussion of the standard model-theoretic account of consequence to be found in the concluding study.
4

NON-LOGICAL CONSEQUENCE

63%
Hitchcock D.
Studies in Logic, Grammar and Rhetoric
|
2009
|
issue 16(29)
137-158
EN
Contemporary philosophers generally conceive of consequence as necessary truth-preservation. They generally construe this necessity as logical, and operationalize it in substitutional, formal or model-theoretic terms as the absence of a counter-example. A minority tradition allows for grounding truth-preservation also on non-logical necessities, especially on the semantics of extra-logical constants. The present article reviews and updates the author's previous proposals to modify the received conception of consequence so as to require truth-preservation to be non-trivial (i.e. not a mere consequence of a necessarily true implicatum or a necessarily untrue implicans) and to allow variants of the substitutional, formal and model-theoretic realizations of the received conception where the condition underwriting truth-preservation is not purely formal. Indeed, the condition may be contingent rather than necessary. Allowing contingent non-trivial truth-preservation as a consequence relation fits our inferential practices, but turns out to be subject to counter-examples. We are left with an unhappy choice between an overly strict requirement that non-trivial truth-preservation be underwritten by a necessary truth and an overly loose recognition of non-trivial truth-preservation wherever some truth underwrites it. We need to look for a principled intermediate position between these alternatives.
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