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9

Frege is the founder of a program called logicism that aimed to reduce all of mathematics to logic. In order to reduce mathematics to logic Frege had to expand what is meant by logic. Before him Locke, Kant and others understood by logic only Aristotle's syllogistic, which is a manipulation of simple implications (syllogisms). Frege's Logic went much further,...


8

Here is some historical context. In Grundlagen der Arithmetik (1884) Frege introduced his ill-fated Axiom V, now known as the axiom of unrestricted comprehension: every predicate defines a class of objects that satisfy it, called its extension (Frege's own formulation is more technical). This led to the set of all sets and then to the Russell's paradox in ...


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Regarding the twenty-one cards and letters from Frege to Wittgenstein discovered in 1988 [None of the letters from Wittgenstein to Frege are thought to have survived the bombing of the Munster library in 1945], you can see into: Enzo De Pellegrin (editor), Interactive Wittgenstein: Essays in Memory of Georg Henrik von Wright (2011): Frege-Wittgenstein ...


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I do not think a proper reaction to your criticism of Frege's posit (the reference of a sentence is its truth-value) can be made in the stackexchange format. The question, "Whether the truth value is an object or a property?" has a long intellectual history. (cf. https://plato.stanford.edu/entries/truth-values/) But your EDIT question can be answered ...


6

There are several important differences between the logics of Aristotle and Frege. 1.Aristotle understood sentences to be fundamentally of the form Subject-Predicate. He classified sentences into the figures (A) All S is P; (E) All S is not P; (I) Some S is P; (O) Some S is not P. This is very limiting. If we want to say "John loves Mary", is 'John' the ...


5

One key that can help unlocking Frege's argument is to realize that he is talking about two different viewpoints. The first viewpoint is of the thinker (T), the one who makes judgements like "the morning star is the brightest". The second viewpoint is of the attributor (A), the one who observes thinkers like T, and attributes propositional attitudes to them, ...


5

In a nutshell, the issue arises from the definition of number of as a second-order concept (i.e. a numerical quantifier) in Die Grundlagen der Arithmetik (1884). Consider e.g. 0xϕ(x)=df Card[xy] (y ≠ y) [ϕx], that reads: To assert 0xϕ(x) is to say that the objects that are ϕ are in one-to-one correlation with the objects that are not self-identical, i.e....


5

Frege's thesis was not that mathematics as a whole was analytic, just that arithmetic (the theory of whole numbers) was so. Frege criticized Kant about arithmetic, but he agreed with Kant that geometry was synthetic. As to that Pythagoras' theorem cannot be deduced from the definition of a triangle alone, there is surely no dispute. We shall do well in ...


4

In Frege's logical perfect language (Begriffsschrift) every well-formed expression must have a reference (Bedeutung). The Bedeutung of an expression is the actual thing corresponding to it. The Sinn of an expression, however, is the “mode of presentation” or cognitive content associated with the expression in virtue of which the Bedeutung is picked out. ...


4

The point raised in the quote is not the same as the question that you are asking. In the quote: It is a difference whether we define what one is, and then we define what two is, and so on, or whether we define the abstract concept of (natural) number (as pointed out by Mauro Allegranza in the comments). Of course we can say that natural number refers to ...


4

Consider a numerical function, defined by: f(1)=2, f(2)=4, ... The Wertverlauf is the "graph" of the function, i.e. the collection of couples: (1,2), (2,4),... For concepts, i.e. functions from objects to truth-values, like e.g. Philosopher, where we have: Phil(Plato)=True and Phil(Napoleon)=False, etc. we have similarly for the Wertverlauf: (...


4

This post is to answer your EDIT 2 question. Your confusion is legitimate since p.45 is indeed very confusing. I am not sure whether the fault is in me, in translation, or in Frege. Due to the unclarity of the text, to answer your question, I extrapolate stuff I learned about Frege’s work in graduate school. On page 45, Frege is in pain to explain the ...


4

You can see Frege's The Thought: A Logical Inquiry (1918-19): Without wishing to give a definition, I call a thought something for which the question of truth arises. [...] Two things must be distinguished in an indicative sentence: the content, which it has in common with the corresponding sentence-question, and the assertion. The former is the thought, ...


4

In Frege's universe there are two objects corresponding to truth values: the TRUE and the FALSE. According to Frege's semantics every expression has a sense: for a sentence a thought, and a reference: for a sentence one of the only two truth values. An imperative has no truth value and thus, according to Frege, it has no reference. We can compare it to ...


4

For Russell, sentences with definite descriptions of the form "The F is G" have the logical form: There is a unique x that is F, and x is G. So to believe that the present queen of American is bald, according to Russell, is to believe that there is a unique individual who is a queen of America and that individual is bald. There's no failure of reference ...


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Mark Textor, Routledge Philosophy GuideBook to Frege on Sense and Reference (2010). Wolfgang Carl, Frege's Theory of Sense and Reference: Its Origin and Scope (1994). Kevin Klement, Frege and the Logic of Sense and Reference (2002).


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The more common term is deflationary theory of truth, where "assertions of predicate truth of a statement do not attribute a property called "truth" to such a statement". I did not find reference to conditionals and disjunctives specifically in Baldwin's essay in Frege: Sense and Reference One Hundred Years Later, but Frege's own example of a conditional ...


3

I think the confusion comes from schematic identification of logicism with realism, intuitionism with conceptualism, and formalism with nominalism, referencing positions in the old debate on the nature of universals. This is mostly right, but not quite: Hilbert is a nominalist about mathematical objects, but he is a conceptualist (Kantian) about mathematical ...


3

See Sense and Reference, Eng.transl. (1948), page 214 : "So far we have considered the sense and referents only of such expressions, words, or signs as we have called proper names. We now inquire concerning the sense and referent of an entire declarative sentence. Such a sentence contains a thought."


3

The formula is used into the third part of Begriffsschrift (1879), regarding the General theory of sequences, not translated in modern symbols by Mendelsohn. You have to look at: G.Landini, Frege’s Notations: What They Are and How They Mean (2012). The basic component of the complex formula is the "gamma-on-beta of f(x,y)" symbol. It is defined in §...


2

The "foundations" of Frege's analysis of language are in his articles : Funktion und Begriff (1891) Über Sinn und Bedeutung (1892) Über Begriff und Gegenstand (1892). Relevant for your question is the first one; see : Translations from the Philosophical Writings of Gottlob Frege (P.Geach & M.Black editors, 1952), page 21-on, or : ...


2

Frege considered the notion of functions to be logically primitive and so to be undefinable. He tried to give some elucidations of his idea of functions by saying that functions comprise all and only the unsaturated or incomplete things. So Frege's logicism simply takes functions for granted as it does regarding objects (the complement of functions). As a ...


2

it's not clear what the motivation for the ZFC pairing axiom would be. On the early development of set theory, it is very useful the SEP's entry dedicated to The Early Development of Set Theory. Regarding the Pair axiom, see Zermelo’s Axiomatization of Set Theory : Zermelo's 1908 original monograph uses the Axiom of elementary sets, that asserts the ...


2

See Frege's Theorem: Equinumerosity: the "bijection" is not defined set-theoretically, and thus there is no need of the ordered pair notion. F and G are equinumerous just in case there is a relation R such that: (1) every object falling under F is R-related to a unique object falling under G, and (2) every object falling under G is such that there ...


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We have a very brief introduction How does Frege's definition of number solve the Julius Caesar problem? here on SE. Zalta's review of it for SEP is a good place to start more scholarly research. Dummett's book Frege: Philosophy of Mathematics is a comprehensive classical commentary. In 2005 Dialectica devoted a whole issue to the Julius Caesar problem, with ...


1

For Frege, thought (Gedanke) is objective while idea (Vorstellung) is mental. The thought is the "conceptual content" expressed by a sentence. Ideas live in the so-called second realm of mental facts, while thoughts live in the third realm of timelessly truth. According to Descartes’ Theory of Ideas, ideas are modes of the thinking substance, and thus ...


1

Ampliatian is, according to ch. 14 of John of St. Thomas's Outlines of Formal Logic, "the extension of a term from a lesser to a greater supposition." For example, Man can be just is extended to possible men. Explanation (explicare) literally means "to unfold, uncoil, unroll, unfurl, unclose," etc. what is already there. But with ampliation something new ...


1

Depends on waht you're looking for. You could read him for logic, phil. of mathematics or phil. of language. I am starting out in analytic philosophy Because of this I'll assume it's the latter. I recommend getting context on two things. 1) Read up on criticism of psychologism. This should give you an idea what Frege aims at. It should also give you ...


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Just as a rider to the above : 'I' presents me as (roughly) 'the speaker', and this 'mode of presentation' is, of course, very different than that associated with 'he'. The two sentences, 'I am about to be attacked' and 'He is about to be attacked' thus differ in cognitive significance. They can express the same proposition, but, even when they do so, ...


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We call lots of things true or false: pictures, sentences, sounds. But, as he says, we call these things true or false only insofar as they express something. This something that they express is their sense. For Frege a sentence gains "sense" when it makes sense to the person who provides the sentence. In simple words cognitive significance means that it'...


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