Etchemendy and Bolzano on Logical Consequence

Rusnock, Paul; Burke, Mark E.

doi:10.1080/01445340903445063

Cited by 17 publications

(6 citation statements)

References 20 publications

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“…Scholz (1937), 470 ff.). For an elaborate discussion of Bolzano's concept of deducibility and its parallels to Tarski's notion of logical consequence, see Siebel (1996), Siebel (2002), Rusnock and Burke (2010).…”

Section: The Basic Concepts Of Bolzano's Philosophy and Logicmentioning

confidence: 99%

BOLZANO’S CONCEPT OF GROUNDING (ABFOLGE) AGAINST THE BACKGROUND OF NORMAL PROOFS

Rumberg

2013

The Review of Symbolic Logic

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In this paper I will provide a thorough discussion and reconstruction of Bernard Bolzano's theory of grounding and a detailed investigation into the parallels between his concept of grounding and current notions of normal proofs. Grounding (Abfolge) is an objective ground-consequence relation among true propositions that is explanatory in nature. The grounding relation plays a crucial role in Bolzano's proof-theory, and it is essential for his views on the ideal buildup of scientific theories. Occasionally, similarities have been pointed out between Bolzano's ideas on grounding and cut-free proofs in Gentzen's sequent calculus. My thesis is, however, that they bear an even stronger resemblance to the normal natural deduction proofs employed in proof-theoretic semantics in the tradition of Dummett and Prawitz.

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Section: The Basic Concepts Of Bolzano's Philosophy and Logicmentioning

confidence: 99%

BOLZANO’S CONCEPT OF GROUNDING (ABFOLGE) AGAINST THE BACKGROUND OF NORMAL PROOFS

Rumberg

2013

The Review of Symbolic Logic

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“…33 . Rusnock and Burke (2010) apply this point to Bolzano. They argue that the well-known criticisms that John Etchemendy has levelled against Tarski's theory of consequence do not apply to Bolzano's ostensibly similar account.…”

Section: Kant and Russell On The Mathematical Methods Trates This Poinmentioning

confidence: 89%

Logic as Universal Science

Korhonen

2013

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“…The debate continued in the 21st century (see [14], [111], [28], [88], [5], [108], [63], [77], [78], [31], [47], [89], [25], [101], and [104]). In the last work the author rejects the standard definition of logical consequence and suggests a sufficiently general form of the consequence relation between abstract signs.…”

Section: Century An Of Mathem Thementioning

confidence: 99%