Online research in philosophy

In this entry, Frege's logic is introduced and described in some detail. It is shown how the Dedekind-Peano axioms for number theory can be derived from a consistent fragment of Frege's logic, with Hume's Principle replacing Basic Law V.

La argumentación de Frege contra la definibilidad de la verdad pretende mostrar que una definición de verdad es circular o nos involucra en un regreso al infinito. En la obra de Frege cabe distinguir dos nociones de verdad: la verdad expresada mediante el termine “verdadero” y la verdad expresada mediante la aserción. La argumentación de Frege no muestra que el términe “verdadero” sea indefinible, pero, si se acepta la concepción de Frege acerca de la aserción, de su argumentación, adecuadamente reformulada, cabe concluir la indefinibilidad de la verdad en su segunda acepción.Frege’s argumentation against the definability of truth aims to show that a definition of truth is circular or involves us in an infinite regress. In Frege’s work two notions of truth can be distinguished: truth expressed by the word “true” and truth conveyed by the assertion. Frege’s argumentation does not show that the word “true” is undefinable, but, if Frege’s view on assertion is accepted, then from his argumentation, suitably reformulated, the undefinability of truth in the second sense can be concluded.

Frege's life and character -- The project -- Frege's new logic -- Defining the numbers -- The reconception of the logic, I-"Function and concept" -- The reconception of the logic, II- "On sense and meaning" and "on concept and object" -- Basic laws, the great contradiction, and its aftermath -- On the foundations of geometry -- Logical investigations -- Frege's influence on recent philosophy.

The founder of modern logic and grandfather of analytic philosophy was 70 years old when he published his paper 'Der Gedanke' (The Thought ) in 1918. This essay contains some of Gottlob Frege's deepest and most provocative reflections on the concept of truth, and it will play a prominent role in my lectures. The plan for my lectures is as follows. What is it that is (primarily) true or false? 'Thoughts', is Frege's answer. In §1, I shall explain and defend this answer. In §2, I shall briefly consider his enthymematic argument for the conclusion that the word 'true' resists any attempt at defining it. In §3, I shall discuss his thesis that the thought that things are thus and so is identical with the thought that it is true that things are thus and so. The reasons we are offered for this thesis will be found wanting. In §4, I shall comment extensively on Frege's claim that, in a non-formal language like the one I am currently trying to speak, we can say whatever we want to say without ever using the word 'true' or any of its synonyms. I will reject the propositional-redundancy claim, endorse the assertive-redundancy claim and deny the connection Frege ascribes to them. In his classic 1892 paper 'Über Sinn und Bedeutung' (On Sense and Signification) Frege argues that truth-values are objects. In §5, I shall scrutinize his argument. In §6, I will show that in Frege's ideography (Begriffsschrift) truth, far from being redundant, is omnipresent. The final §7 is again on truth-bearers, this time as a topic in the theory of intentionality and in metaphysics. In the course of discussing Frege's views on the objecthood, the objectivity of thoughts and the timelessness of truth(s), I will plead for a somewhat mitigated Platonism.

Frege's account of indirect proof has been thought to be problematic. This thought seems to rest on the supposition that some notion of logical consequence ? which Frege did not have ? is indispensable for a satisfactory account of indirect proof. It is not so. Frege's account is no less workable than the account predominant today. Indeed, Frege's account may be best understood as a restatement of the latter, although from a higher order point of view. I argue that this ascent is motivated by Frege's conception of logic.

Joan Weiner has recently claimed that Frege neither uses, nor has any need to use, a truth-predicate in his justification of the logical laws. She argues that because of the assimilation of sentences to proper names in his system, Frege does not need to make use of the Quinean device of semantic ascent in order to formulate the logical laws, and that the predicate ‘is the True’, which is used in Frege's justification, is not to be considered as a truth-predicate, because it does not apply to true sentences or true thoughts. The present paper aims to show that Frege needs to use, and does use, a truth-predicate in this context. It is argued, first, that Frege needs to use a truthpredicate in order to show that the truth of the logical laws is evident from the senses of the sentences by means of which they are formulated, and second, that the predicate that he actually uses, ‘is the True’, must be considered as a truth-predicate in the relevant sense, because it can be used and is actually used by Frege to explain the truth-conditions of thoughts. To defend this interpretation, it is discussed whether the explanatory use of ‘is the True’ in Frege's system is compatible with his deflationary analysis of ‘true’. The paper's conclusion is that there is indeed a conflict here; but, from Frege's point of view, this conflict is due merely to the logical imperfection of natural language and does not affect the proper system but only its propaedeutic. CiteULike    Connotea    Del.icio.us    What's this?

I shall make two main claims. My first main claim is that Frege started out with a view of logic that is closer to Kant’s than is generally recognized, but that he gradually came to reject this Kantian view, or at least totally to transform it. My second main claim concerns Frege’s reasons for distancing himself from the Kantian conception of logic. It is natural to speculate that this change in Frege’s view of logic may have been spurred by a desire to establish the logicality of the axiom system he needed for his logicist reduction, including the infamous Basic Law V. I admit this may have been one of Frege’s motives. But I shall argue that Frege also had a deeper and more interesting reason to reject his early Kantian view of logic, having to do with his increasingly vehement anti-psychologism.

One of the most striking differences between Frege's Begriffsschrift (logical system) and standard contemporary systems of logic is the inclusion in the former of the judgement stroke: a symbol which marks those propositions which are being asserted , that is, which are being used to express judgements . There has been considerable controversy regarding both the exact purpose of the judgement stroke, and whether a system of logic should include such a symbol. This paper explains the intended role of the judgement stroke in a way that renders it readily comprehensible why Frege insisted that this symbol was an essential part of his logical system. The key point here is that Frege viewed logic as the study of inference relations amongst acts of judgement , rather than – as in the typical contemporary view – of consequence relations amongst certain objects (propositions or well-formed formulae). The paper also explains why Frege's use of the judgement stroke is not in conflict with his avowed anti-psychologism, and why Wittgenstein's criticism of the judgement stroke as 'logically quite meaningless' is unfounded. The key point here is that while the judgement stroke has no content , its use in logic and mathematics is subject to a very stringent norm of assertion.

I argued that Frege does not have a metatheory in the following sense: the justifications he offers for his basic laws and rules of inference neither employ nor require a truth-predicate or metalinguistic variables. In ‘Does Frege Use a Truth-predicate in his "Justification" of the Laws of Logic?’, Dirk Greimann disputes this. As Greimann interprets Frege, (i) Frege's remarks commit him to giving a metatheoretic justification of the basic laws and rules of his logic, and (ii) Frege actually gives such a justification in the early sections of Grundgesetze—although the truth-predicate that Frege employs is a non-standard one: it is neither a predicate that holds of all and only true sentences nor a predicate that holds of all and only true thoughts. I argue that Greimann's interpretation is not, in the end, true to the text, and that his non-standard view of what is required of a Tarskian truth-predicate is ultimately not viable. CiteULike    Connotea    Del.icio.us    What's this?

In this paper, we explore Fregean metatheory, what Frege called the New Science. The New Science arises in the context of Frege’s debate with Hilbert over independence proofs in geometry and we begin by considering their dispute. We propose that Frege’s critique rests on his view that language is a set of propositions, each immutably equipped with a truth value (as determined by the thought it expresses), so to Frege it was inconceivable that axioms could even be considered to be other than true. Because of his adherence to this view, Frege was precluded from the sort of metatheoretical considerations that were available to Hilbert; but from this, we shall argue, it does not follow that Frege was blocked from metatheory in toto. Indeed, Frege suggests in Die Grundlagen der Geometrie a metatheoretical method for establishing independence proofs in the context of the New Science. Frege had reservations about the method, however, primarily because of the apparent need to stipulate the logical terms, those terms that must be held invariant to obtain such proofs. We argue that Frege’s skepticism on this score is not warranted, by showing that within the New Science a characterization of logical truth and logical constant can be obtained by a suitable adaptation of the permutation argument Frege employs in indicating how to prove independence. This establishes a foundation for Frege’s metatheoretical method of which he himself was unsure, and allows us to obtain a clearer understanding of Frege’s conception of logic, especially in relation to contemporary conceptions.