The cambridge companion to frege ebook

If there were, then we could define a determines relation after all:. The sense S determines the referent B iff there is a name n that expresses S and designates B.

Kremer concludes the Frege could not consistently hold onto one of his deeply held views: the possibility of sense without reference ; Weiner provides a different take on pages Some readers will decide that these conclusions are too much to swallow, and choose instead to interpret Frege's remarks on truth differently.

Kremer and Goldfarb argue, however, that allowing a truth predicate would fundamentally alter deep aspects of Frege's thought. According to Kremer, when Frege argues that thoughts relate to truth as sense to reference, not object to property, he is insisting that judgment is "something quite peculiar and incomparable" [5] -- and thus maintaining the special status of sentence meaning that Frege earlier expressed with his famous Context Principle.

Goldfarb argues that when Frege denies that there is a truth predicate, he is asserting that "there is no theory of how the thoughts expressed by sentences are determined to be true or false by the items referred to in them. More elusively, Goldfarb claims that Frege's conception of truth is "immanent within our making of judgements and inferences," which conception Goldfarb claims is opposed to realism Weiner adds a second line of defense.

If Frege countenances semantic facts such as the soundness or completeness of a formal language , and includes these facts as parts of logic , he would then maintain that logic or at least a part of it is not about everything, but instead about words and the senses of words.

Frege, however, insisted that logic is completely general -- its laws quantify over everything, and its primitive vocabulary is utilized in every special science Goldfarb calls this Frege's "universalist conception of logic" 68, By this Goldfarb seems to mean primarily that Frege thinks of logical laws as completely general, and so since truth values are objects is able to frame his logical laws as general truths without semantic ascent.

But, given this more recent argument from Weiner, many of the authors in this collection seem to think that the "universalist conception" entails that no semantic facts are included in the science of logic. This I take to be the state of the dialectic after all of the arguments from The Cambridge Companion are in. As I see it, the "no metatheory" interpreters owe us a story of how Frege can countenance no general theory of logicality while still maintaining that the logical status of a basic law is a substantive question.

They also need to give plausible readings of Frege's apparent semantic arguments in part I of Basic Laws. Those in Dummett's tradition need, on the other hand, a convincing alternative reading of Frege's apparent claims that truth is not a predicate. Potter's "Introduction" does a good job of giving an overview, in thirty short pages, of Frege's life, his major works, and their reception. Indeed, I think it the best introductory essay of its kind and length that I am aware of. It is written from a broadly Dummettian point of view.

Potter also gives a sympathetic one-page characterization of Neo-Fregean philosophy of mathematics -- the volume's longest discussion of this active field of Frege research. Potter does not, however, give an overview of the chapters in the volume -- an unfortunate omission, given that the complexity and size of many of the papers would have made an overview helpful for the reader. The content of roughly the second half of Weiner's deeply interesting "Understanding Frege's Project" concerns Frege's conception of truth, which I discussed above.

She begins with a puzzle. Surely, if Frege wants to define "1", he needs to assure us that his definition refers to the same object that we, prior to reading Frege, referred to with our numeral "1. Her solution is radical: on Frege's view, before his definition, the numeral "1" had no meaning. Frege's Basic Laws would then have been the first science.

Not only did Frege's project not integrally involve giving a theory of meaning for natural language, as Dummett argued: for Weiner's Frege, words in natural language do not even have meanings. Goldfarb's "Frege's Conception of Logic" contrasts what he calls Frege's "universalist conception of logic" with the contemporary "semantic conception" exemplified by Quine. The first half of Sullivan's "Dummett's Frege" sympathetically reconstructs Dummett's argument from the opening chapters of Frege: Philosophy of Language that Frege's logicist project necessitated that he give a theory of meaning.

The second half of the paper tries to resolve a paradox that arises for Dummett's Frege. Dummett believes that Frege wanted to fashion a compositional theory of meaning that explains how a speaker of a language can understand novel sentences in that language.

This led Dummett to distinguish, on Frege's behalf, between the simple predicates the grasp of which is needed to understand a novel sentence and the complex predicate into which an already understood sentence can be decomposed. Alex Oliver, in his "What is a Predicate? He argues convincingly against Dummett and Geach that Frege's view is v , but he argues against Frege that there is no principled reason to prefer any of the five candidates to another. The interpretation of Frege in Ricketts's paper, "Concepts, Objects, and the Context Principle," is distinctive in two respects.

And it gives what one might call a logical as opposed to a semantic or epistemological reading of the Context Principle. The paper is wide-ranging, highly original, and difficult; it repays close re-readings.

Moreover, Frege's definition presupposes an appreciation of the revolutionary features of his new logic -- in particular its treatment of quantification -- which Frege is trying to communicate informally to an uninformed audience.

Putting these ideas together, Ricketts claims that the Context Principle "sets forth the connection between logical segmentation and quantificational generality" More specifically:. The Context Principle encapsulates the connection between names and quantificational generality: an expression is a meaningful designating name by occurring in true or false sentences that express instances of generalizations expressible by replacing the name with a variable. This use of variables introduces predicates, and this notion of quantification allows for quantifying over predicates.

The principle thus motivates a type distinction between proper names and predicates, and the ontological distinction between concepts and objects. Of the many interesting consequences of this approach, I'll highlight two. Against epistemological readings that see the principle as answering the question of how we can know numbers that are not given to us, Ricketts reads the principle as motivating a logical notion of objecthood that makes non-spatial, non-causal objects philosophically innocent Further, Ricketts gives a purely logical reading of the "unsaturatedness" of concepts.

By the Context Principle, concepts are distinct from objects inasmuch as second-order quantification is distinct from first-order quantification. But the relation coextensive which is the surrogate for concepts of the identity relation among objects presuppose s first-order quantification, since F is coextensive with G iff for all x , Fx iff Gx Kremer's rich and thought provoking "Sense and Reference: The Origins and Development of the Distinction" is a high point of the collection.

The paper gives not only a close reading of Frege's paper "On Sense and Reference," but also a convincing and detailed account of Frege's development of this distinction from his early notion of "conceptual content.

These notions come in conflict when two expressions with coreferential names differ in inferential potential. Frege solves this conflict by distinguishing cognitive value or sense which Kremer controversially reads as inferential potential from reference. Along the way, Kremer elaborates on the "no metatheory" interpretation by arguing that, for Frege, p , "the reference of p ", and "the reference determined by the sense of p " all have the same sense.

This reading gives Kremer an interesting third way between the traditional readers of "On Sense and Reference" who see Frege as there rejecting the metalinguistic reading of identity proposed in Begriffscchrift and the revisionist readers who see Frege as retaining the metalinguistic reading.

Kremer closes the paper by arguing that this is what Frege should have said anyway, since senses that determine no reference would have to be understood either psychologistically or platonistically. The goal of Taschek's "On Sense and Reference: A Critical Reception" is to articulate and defend -- both as a reading of Frege and in its own right -- a logical, as opposed to epistemic, theory of sense.

The phenomenon Frege wanted to account for, Taschek claims, is the possibility that two expressions with the same referential truth conditions may nevertheless differ in logically relevant ways. A sense of an expression is that the grasp of which enables a speaker to think about its reference in a way that enables the speaker to appreciate its logical properties.

This way of interpreting sense does not require that Frege construe the sense of a singular term in epistemic terms -- say, as a description, a cluster of descriptions, or even a procedure for identifying the referent. And this is good, he thinks, since these proposals are refuted by standard Kripkean arguments. Neo-Russellian accounts, like those of Scott Soames or Nathan Salmon, do not even meet the challenge for which Frege introduced the notion of sense. Since they claim that "Superman flies" and "Clark Kent flies" do not differ in semantic but only pragmatic content, they cannot respect our deeply held conviction that these sentences differ in logical potential which, Taschek claims, was Frege's starting point.

Taschek ends by acknowledging that his logical account of sense, though it respects the logical differences in coreferential expressions, cannot give an independent explanation of these differences. A highlight of his paper is a reading of Frege's use of roman letters, which Heck claims gives an account of quantification that is a "perfectly coherent alternative to Tarski's treatment in terms of satisfaction" Mark Wilson's "Frege's Mathematical Setting" continues the project of some of Wilson's earlier papers and similar work by Jamie Tappenden to locate Frege's philosophical writings within the context of nineteenth-century mathematics.

There are at least five goals of this project: to understand how a trained mathematician could end up producing the philosophical works that Frege did; to argue that Frege's motivations were mathematical, and not entirely philosophical; to show, by Frege's example, how rich a philosophy of mathematics engaged with mathematical examples can be; to locate Frege's "absolute logicism" within the context of late nineteenth-century "relative logicist" projects within number theory i.

Wilson builds on this point to give a novel and provocative explanation for why Frege was unimpressed with some of Hilbert's geometrical work, such as his proof of the independence of Desargues' Theorem in two-dimensional projective space.

Frege's debate with Hilbert is the dedicated topic of the next chapter Michael Hallett, "Frege and Hilbert". Hallett focuses the debate around the importance that Frege but not Hilbert assigned to fixed reference.

There are three noteworthy features of Hallett's detailed and interesting piece. First, he illuminatingly locates Frege's criticisms of Hilbert's failure to provide fixed referents for the terms in his Foundations of Geometry against Frege's own similar criticisms of the proposal -- which Frege considered but then rejected on account of the notorious Julius Caesar objection -- to found arithmetic on Hume's Principle alone.

Second, he argues that Frege's system fails to meet his own standards. Frege's recognized need for elucidations raises the possibility of ineliminable failures to fix reference. Third, Hilbert saw this failure of fixed reference as an intrinsic feature of mathematics: it allows a mathematician to study what does not follow in an axiom system.

Frege never appreciated, Hallett claims, Hilbert's insight that studying what does not follow from a mathematical theory is just as important as understanding what does. Peter Milne's wide-ranging essay, "Frege's Folly: Bearerless Names and Basic Law V," opens with the proof within Frege's system of the paradoxical claim that every truth-value gap implies a glut:.

It's not true that P and it's not false that P only if it's both true that P and false that P. Frege, of course, would resolve this paradox by prescribing that a logically perfected language have no bearerless names. Milne advocates instead adopting a semantic as opposed to Frege's functional theory of negation.

Milne's essay ends by sketching an alternative system to Frege's in second-order classical free logic. Milne's essay illustrates very starkly the divisions between the two interpretive traditions represented in the book.

Milne assumes, without acknowledging the many readers who disagree, that Frege uses a truth predicate that holds of all and only true sentences, and that Frege wanted a semantics for ordinary language. His derivation of the paradox uses modern notions of entailment, although as Kremer points out Frege's notion of inference differs fundamentally from modern notions of entailment.

Thus, what other readers would see as demonstrating the elucidatory character of truth-talk, Milne sees as exposing a paradox in Frege's thought that needs to be corrected using contemporary logical machinery. Peter Hylton's very clear, accessible, and illuminating chapter, "Frege and Russell," locates the well-known differences between them say, concerning sense in fundamental features of their thought. Russell takes acquaintance, a direct and unmediated relation between the mind and an object, to be the foundation of all our knowledge.

This makes him suspicious of intermediate entities, such as Fregean senses, between the mind and the objects it represents. Moreover, for Hylton, Russell's thought -- but not Frege's -- raises questions that force a foundationalist epistemology, because there is a basic difference between Russell's "object-based" and Frege's "judgment-based" metaphysics.

In the first half she notes two features of Wittgenstein's thought, early and late, that derive from Frege. Wittgenstein, like Frege, insists that differences in logical kind are not differences in properties: Fregean concepts did not differ from objects in having the property being unsaturated ; mental processes did not differ from other processes, according to the later Wittgenstein, in having the property being incorporeal.

Further, Wittgenstein adopted from Frege's critique of other philosophers a "quasi-moralistic" approach to thinking: a philosopher should mean something "all the way, without dependence on equivocation or evasion" Diamond might also have emphasized the affinity, implicit in many chapters in this volume, between the "resolute" reading of the Tractatus and the "no metatheory" reading of Frege.

On this reading, Frege's audience -- after mastering the Begriffsschrift -- is meant to "discard" Frege's talk of concepts, objects, sense, reference, and truth. Though novel and interesting, I found this reading less persuasive than the simpler and less revisionist reading proffered by Goldfarb which Diamond considers and rejects in the paper's appendix.

Beaney, Oxford: Blackwell, , original: Frege's Answer" Mind , , In the latter paper, she argues that on Frege's view, the numeral "1" prior to his definition has neither sense nor reference. The Central Debate In his influential Frege: Philosophy of Language and in subsequent writings, Dummett defended the following interpretive claims: Frege gave a semantic theory of the workings of language.

This theory is a form of realism , whose articulation makes ineliminable use of a truth-predicate applied to sentences or the thoughts expressed by them.

This theory, when applied to Frege's logical symbolism "Begriffsschrift" , justifies its logical laws and rules of inference, by stating that the conclusion of each inference licensed by his system is indeed a semantic consequence of its premises.

On this view, a logical law such as If p , then if q then p is not an interpreted sentence in the object-language, but a schematic sentence in the meta-language. To say that this logical law holds whatever p and q might be, we need to practice semantic ascent and attribute a truth-predicate to a bit of language: All sentences of the form 'If p, then if q then p' are true.

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