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## Hot answers tagged frege

9 votes
Accepted

### 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 ...
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9 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 ...
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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 ...
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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 ...
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### Is Frege's axiom of unrestricted comprehension actually true after all?

∀F∃y ∀x[x ∈ y iff F(x)] [OSC1] ∀F∃y [α ∈ y iff F(α)] [UI] ∃y [α ∈ y iff α ∉ α] [UI] α ∈ x1 iff α ∉ α [EI] Step 2 is not how universal instantiation works. It only lets you remove the outermost ∀, but ...
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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&...
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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 ...
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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 ...
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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 ≠ ...
5 votes
Accepted

### 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 ...
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5 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, ...
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5 votes
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### Are Fregian abstract objects Kantian noumena?

At one point in the first Critique, Kant says: For if I cogitate an understanding which was itself intuitive (as, for example, a divine understanding which should not represent given objects, but by ...
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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 ...
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 ...
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:...
4 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 ...
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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 ...
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4 votes
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### Frege's implication theory

There is an link. The key-point of the Russell-MacColl's debate about the boolean formula 0A=0 is that for MacColl the symbol 0 means "the class of non-existents" while for Russell the ...
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 ...
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### 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 ...
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 ...
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 ...
3 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 ...
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3 votes

### Is Frege's axiom of unrestricted comprehension actually true after all?

There is a problem with representing the comprehension principle as a single axiom. It is more accurately read as an axiom scheme. So the specific formula that gives rise to the Russell set is an ...
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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") ...
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. ...
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 ...
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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 ...
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 ...
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