9 votes
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How does Frege's definition of number solve the Julius Caesar problem?

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 ...
Conifold's user avatar
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8 votes

Is there anything more fundamental than quantification?

What is most fundamental to a logic is the set of mechanical procedures by which we may derive theorems in the logic; the inference rules. These procedures are not specified within the logic. The ...
causative's user avatar
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7 votes
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Frege's Argument About the Sense and Reference of a Sentence

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 ...
Nanhee Byrnes PhD's user avatar
7 votes

What's the difference between Aristotle's logic and Frege's logic especially with regard to predicates?

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 ...
Bumble's user avatar
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7 votes
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Did Frege criticize the style of the Tractatus?

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 ...
Mauro ALLEGRANZA's user avatar
5 votes

How does Frege's definition of number solve the Julius Caesar problem?

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 ≠ ...
Mauro ALLEGRANZA's user avatar
5 votes

Frege's Argument About the Sense and Reference of a Sentence

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 ...
Nanhee Byrnes PhD's user avatar
5 votes

Frege's Argument About the Sense and Reference of a Sentence

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 ...
Ram Tobolski's user avatar
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5 votes
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What is the difference between concepts of number and natural number?

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 ...
Arno's user avatar
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5 votes
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Who first used the phrase "Deflationary Theory of Truth"?

Yes, none of those authors used the label, not Frege, not Ramsey, not Quine, and not even Dummett writing about Frege. One can see on the Google Ngram how the term "deflationary theory of truth&...
Conifold's user avatar
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4 votes
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Frege and Value-Range

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 ...
Mauro ALLEGRANZA's user avatar
4 votes

What does Frege mean by "Cognitive Significance" in "On Sense and Nominatum"?

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 ...
Mauro ALLEGRANZA's user avatar
4 votes

Why are imperatives not propositions according to Frege?

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:...
Mauro ALLEGRANZA's user avatar
4 votes
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What does it mean to say, "Philosophy really started in 1884"?

I presume analytic philosophy is implied and Frege's 1884 book The Foundations of Arithmetic (Die Grundlagen der Arithmetik) is mentioned in more of a rhetorical manner, as a synecdoche of Frege's ...
Tankut Beygu's user avatar
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4 votes

Is there anything more fundamental than quantification?

Existence as a subject of which other things are predicated, vs. as a predicate of other subjects, is where the role of the (mostly classical, even so) subsistence relation comes in to play. That is, ...
Kristian Berry's user avatar
3 votes

What is this snippet from Frege's Begriffsschrift saying?

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 ...
Mauro ALLEGRANZA's user avatar
3 votes

Difference between Frege and Russell on Definite Descriptions?

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 ...
E...'s user avatar
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3 votes

Truth values of sentences

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 ...
Mauro ALLEGRANZA's user avatar
3 votes
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Frege: Truth as an expression of assertoric force

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 ...
Conifold's user avatar
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3 votes

Any great commentary of "On Sense and Nominatum" by Frege?

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 ...
Mauro ALLEGRANZA's user avatar
2 votes

What is the Fregeian meaning of "grasping"?

Long comment "Grasping a Thought" (or a sense) is a sort of "primitive" in Frege's philosophy; it is a basic assumption that is not analyzed further. Frege says that thoughts are real ("wirklich") ...
Mauro ALLEGRANZA's user avatar
2 votes

Why should a system of set theory represent the following property of x: ((x = h) or (x = k))) using the set that Frege used?

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. ...
Mauro ALLEGRANZA's user avatar
2 votes

Did logicists use mathematical entities (in their attempt) to reduce mathematics to logic?

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 ...
sequitur's user avatar
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2 votes

Can Fregean sense of proper names be described in terms of intension?

I don't think Frege's theory of sense and reference is compatible with the rigid designator theory of reference (or, at least, it would take some sophisticated theoretical footwork to render them ...
Dayv87's user avatar
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2 votes
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How can you make sense of "equinumerosity" in Hume's Principle in a logicist approach to math, without first having functions defined?

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 ...
Mauro ALLEGRANZA's user avatar
2 votes

Does Wittgenstein's picture theory contradict Frege's theory of Sinn and Bedeutung?

Not exactly. See Tractatus, 3.13: A proposition, therefore, does not actually contain its sense, but does contain the possibility of expressing it. (‘The content of a proposition’ means the content of ...
Mauro ALLEGRANZA's user avatar
2 votes

Why did it take 3000 years for theories of mathematical foundations to emerge?

The mathematics from 3000 years ago would have very little to do with some topics in mathematics today. There was a "crisis of the foundations" at the end of the 19th century and early 20th ...
Frank's user avatar
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2 votes
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Why did it take 3000 years for theories of mathematical foundations to emerge?

At the end of the 19th century there was a crisis in the epistemology of mathematics. Previously, it had always been assumed that mathematics was just obviously and intuitively correct. There was ...
Bumble's user avatar
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2 votes

Is there anything more fundamental than quantification?

I wasn't going to respond, however: It is difficult metaphysically to draw the line between what is a property and what is an object. Some people argue yes. If existence is an abstraction and not ...
J D's user avatar
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1 vote
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Why Frege thinks geometry is synthetic?

In Frege's time, geometry had exploded as a discipline. Descartes' invention of the "Cartesian" coordinate system had been analytic, even founded analytic geometry, but over the centuries ...
Guy Inchbald's user avatar
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