Logical Objects in Frege's Grundgesetze, Section 10

Ruffino, Marco

doi:10.1093/0195133269.003.0006

Cited by 3 publications

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“…With this in mind, I hold that the restriction of Frege's solution to value-ranges and truth-values is not a violation of the principle of complete determination, at least in the form it takes in the system of GGA. Second, I hold that the problem of indeterminacy of reference is merely a matter of fixing the reference of the value-ranges names of the system, whereas the Caesar problem-as previously stated by Ruffino (2002)-is concerned with the question of establishing the nature of numbers as logical objects. Thus, I claim that there is no analogy between those two problems, as it is typically assumed in the literature.…”

Section: The Problem Of the Indeterminacy Of Referencementioning

confidence: 96%

“…That is, recall that Frege did not decide in the theory of GGA whether an arbitrary urelement is a value-range or not-and I believe this should be thought as signaling that something must be wrong with the strong interpretation rather than with Frege's very procedures, a frequent claim in the literature. 34 Therefore, instead of mitigating the shortcomings of the strong view, I would like to consider an alternative interpretation of the Caesar problem due to Ruffino (2002) that has proved faithful to Frege's procedures regarding identities in GGA, while confirming 33 In fact, questions such as this one are pointless or even meaningless for the working mathematician. As Kemp (2005) remarks, "If only in the context of a sentence has a word really a meaning, then why is it not the case that only in the context of a theory or language has a sentence really a meaning?"…”

Section: The Caesar Problemmentioning

confidence: 99%

“…In the previous section, I raised some questions regarding Frege's commitment to the principle of complete determination in GGA. Shouldn't the fact that Frege's view on the referentiality of valuerange names does not take into account urelements as objects be 20 This fact has led some scholars such as Heck (1999) and Ruffino (2002) to question whether Frege wasn't operating in a domain restricted to valueranges and truth-values after all. Heck (1999, p. 272) considers this possibility, but quickly argues against it, under the allegation that Frege sharply criticizes other logicians who talk of restricted domains-Heck is referring here to Frege's objection in GGA II §65, which, as he admits, is the only passage he found in which Frege speaks directly against this possibility (cf.…”

Section: The Principle Of Complete Determinationmentioning

confidence: 99%

“…For a more detailed account of this view, seeRuffino (2000Ruffino ( , 2002.37 Insofar as the domain of the system of GGA is limited to logical objects, see fn. 20.…”

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confidence: 99%

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Frege on Referentiality and Julius Caesar in Grundgesetze Section 10

Bentzen¹

2019

Notre Dame J. Formal Logic

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This paper aims to answer the question of whether or not Frege's solution limited to value-ranges and truth-values proposed to resolve the "problem of indeterminacy of reference" in section 10 of Grundgesetze is a violation of his principle of complete determination, which states that a predicate must be defined to apply for all objects in general. Closely related to this doubt is the common allegation that Frege was unable to solve a persistent version of the Caesar problem for value-ranges. It is argued that, in Frege's standards of reducing arithmetic to logic, his solution to the indeterminacy does not give rise to any sort of Caesar problem in the book.

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Section: The Problem Of the Indeterminacy Of Referencementioning

confidence: 96%

Section: The Caesar Problemmentioning

confidence: 99%

Section: The Principle Of Complete Determinationmentioning

confidence: 99%

“…For a more detailed account of this view, seeRuffino (2000Ruffino ( , 2002.37 Insofar as the domain of the system of GGA is limited to logical objects, see fn. 20.…”

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Frege on Referentiality and Julius Caesar in Grundgesetze Section 10

Bentzen¹

2019

Notre Dame J. Formal Logic

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“…The range of the first-order variables in Grundgesetze. Several Frege scholars, including Dummett (1991), Heck (1997Heck ( , 1999Heck ( , 2005Heck ( , 2011Heck ( , 2012, Ruffino (2002), and Blanchette (2012aBlanchette ( , 2012bBlanchette ( , 2015Blanchette ( , 2016 assume or even categorically contend that in Grundgesetze Frege takes the first-order domain to comprise only the truth-values and value-ranges-henceforth referred to as assumption A. We already know that the way Frege proceeds in §10 and especially in §31 seems to favour A.…”

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confidence: 99%

The Semantics of Value-Range Names and Frege’s Proof of Referentiality

Schirn

2018

The Review of Symbolic Logic

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In this article, I try to shed some new light on Grundgesetze §10, §29–§31 with special emphasis on Frege’s criteria and proof of referentiality and his treatment of the semantics of canonical value-range names. I begin by arguing against the claim, recently defended by several Frege scholars, that the first-order domain in Grundgesetze is restricted to value-ranges (including the truth-values), but conclude that there is an irresolvable tension in Frege’s view. The tension has a direct impact on the semantics of the concept-script, not least on the semantics of value-range names. I further argue that despite first appearances truth-value names (sentences) play a distinguished role as semantic “target names” for “test names” in the criteria of referentiality (§29) and do not figure themselves as “test names” regarding referentiality. Accordingly, I show in detail that Frege’s attempt to demonstrate that by virtue of his stipulations “regular” value-range names have indeed been endowed with a unique reference, can plausibly be regarded as a direct application of the context principle. In a subsequent section, I turn to some special issues involved in §10. §10 is closely intertwined with §31 and in my and Richard Heck’s view would have been better positioned between §30 and §31. In a first step, I discuss the piecemeal strategy which Frege applies when he attempts to bestow a unique reference on value-range names in §3, §10–§12. In a second step, I critically analyze his tentative, but predictably unsuccessful proposal (in a long footnote to §10) to identify all objects whatsoever, including those already clad in the garb of value-ranges, with their unit classes. In conclusion, I present two arguments for my claim that Frege’s identification of the True and the False with their unit classes in §10 is illicit even if both the permutation argument and the identifiability thesis that he states in §10 are regarded as formally sound. The first argument is set out from the point of view of the syntax of his formal language. It suggests though that a reorganization of the exposition of the concept-script would have solved at least one of the problems to which the twin stipulations in §10 give rise. The second argument rests on semantic considerations. If it is sound, it may call into question, if not undermine the legitimacy of the twin stipulations.

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When Logic Gives Out. Frege on Basic Logical Laws

Pedriali¹

2019

Essays on Frege's Basic Laws of Arithmetic

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At the end of Grundgesetze Frege tells us that the Urproblem of arithmetic is the question of how we apprehend logical objects. The success of Frege’s logicist enterprise thus essentially depends on the provision of a satisfactory answer to the question of how we can justifiedly hold certain basic truths to be logical, since for Frege it is only through those laws that we can come to grasp logical objects by purely logical means. And yet, despite its crucial importance, the question of what kind of justification we might provide for basic logical laws is one that Frege never fully addressed. In this chapter, I critically examine, and dismiss, three justificatory strategies briefly canvassed, but not wholly endorsed by Frege (respectively, the appeal to constitutivity, self-evidence, and sense-compositionality). I close by discussing a position that I label pragmatic foundationalism, a position that includes a strong externalist component. I claim that pragmatic foundationalism provides the best attempt one could make, on behalf of Frege, towards answering what he took to be the fundamental problem facing a mature philosophy of arithmetic.

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Logical Objects in Frege's Grundgesetze, Section 10

Cited by 3 publications

References 7 publications

Frege on Referentiality and Julius Caesar in Grundgesetze Section 10

Frege on Referentiality and Julius Caesar in Grundgesetze Section 10

The Semantics of Value-Range Names and Frege’s Proof of Referentiality

When Logic Gives Out. Frege on Basic Logical Laws

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