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15 votes
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What did Russell mean when he wrote that the null-class, the class having no members, did not exist?

Let me start by slightly rephrasing what Russell wrote, since Russell is using the word "exists" in an unusual and confusing way. With my changes in bold, here is what Russell wrote: (b) ...
Tanner Swett's user avatar
12 votes
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What is the axiom of reducibility? And what philosophical controversies did it incite?

To put it in simple words we have to describe in a couple of words the project of Principia Mathematica, which Russell inherited from Frege: reconstructing mathematics from logic alone. For a broader ...
Conifold's user avatar
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11 votes
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Is a set containing itself already a paradox?

Russell's paradox arises within naïve set theory by considering the set of all sets that are not members of themselves. Such a set appears to be a member of itself if and only if it is not a member of ...
Mauro ALLEGRANZA's user avatar
10 votes
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What sentence convinced Russell that Wittgenstein was not a "complete idiot"?

Welcome TCP Russell doesn't so far as I'm aware tell us what the subject was of the 'something' he asked or invited Wittgenstein to write - perhaps he left the topic entirely to Wittenstein. Nor does ...
Geoffrey Thomas's user avatar
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10 votes
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What is the burden of proof? Has this principle ever been challenged?

The burden of proof falls on the one who makes the claim because, usually, they don't make this claim in a vacuum, without any goal in mind: they want other people to accept their claim and adjust ...
armand's user avatar
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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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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 ...
causative's user avatar
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8 votes

Did Russell understand Gödel's incompleteness theorems?

As mentioned in a comment, Alasdair Urquhart has written a paper, Russell and Gödel (Bull. Symb. Logic 22 (2016), 504–520), that discusses a number of different topics, including Russell’s view of ...
Timothy Chow's user avatar
8 votes

Did Russell understand Gödel's incompleteness theorems?

Russell's comments on Gödel were scanty, but it was very unlikely that Russell did not understand what Gödel was talking about. The paradox presented by Gödel sentence was nothing new; it was the same ...
George Chen's user avatar
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8 votes

Is philosophy about organizing our ignorance?

"A man might say, with enough truth to justify a joke: 'Science is what we know, and philosophy is what we don’t know.'" -Bertrand Russell “Philosophy for Laymen” Universities Quarterly 1 (Nov 1946), ...
MmmHmm's user avatar
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8 votes

Can paraconsistent or other logics make the impossible happen?

Logic, paraconsistent or not, does not exactly make something happen, it is applied to reshuffle information already contained in a system. Paraconsistent logic does not even have to be applied to ...
Conifold's user avatar
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8 votes
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Why was Russell discontent with Wittgenstein's view on "logic as tautologies"?

Wittgenstein was reviving Kant's old view that logical deduction only brings out what is implicitly thought in the premises. Of course, Kant had in mind Aristotle's term logic, which is roughly ...
Conifold's user avatar
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7 votes
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Why was Russell's theory of descriptions taken seriously?

Russell's theory of definite descriptions is primarily concerned with denoting phrases (e.g. "the present king of France"), which are linguistic expressions that purport to refer to some object. The ...
E...'s user avatar
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7 votes

What are the main errors of Bertrand Russell's A History of Western Philosophy?

I can offer one example, which I take from Isaiah Berlin concerning Russell's treatment of Kant's doctrine of space and time. This treatment, Berlin suggests, profoundly miscontrues the central ...
Geoffrey Thomas's user avatar
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7 votes

Why was Russell discontent with Wittgenstein's view on "logic as tautologies"?

As a matter of terminology, some logicians use 'tautology' as a synonym for a logical truth, while others restrict it to logical truths of the propositional calculus. I shall use the more general term ...
Bumble's user avatar
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6 votes

A question regarding the similarity of relations from Russell's Introduction to Mathematical Philsophy

He says: it is often said that space and time are subjective, but they have objective counterparts; or that phenomena are subjective, but are caused by things in themselves, which must have ...
Mauro ALLEGRANZA's user avatar
6 votes
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What did Wittgenstein (mean to) achieve in the Tractatus?

There is a heated controversy as to what Wittgenstein tried to achieve in the Tractatus and whether he achieved it. Wittgenstein's own retrospect of the book is rather ambivalent, see Kuusela's ...
Conifold's user avatar
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6 votes
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Why is ZFC not as susceptible to Gödel's incompleteness as was the Principia Mathematica?

ZFC is susceptible to Gödel's incompleteness as was the Principia Mathematica. See Gödel’s Incompleteness Theorems for an introduction to the theorem : Any consistent formal system F within which ...
Mauro ALLEGRANZA's user avatar
6 votes
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Where does Bertrand Russell discuss mysticism?

From Russel's Mysticism and Logic Introduction Metaphysics has been developed, from the first, by the union and conflict of two very different human impulses, the one urging men towards mysticism, ...
Rushi's user avatar
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6 votes

Why was Russell discontent with Wittgenstein's view on "logic as tautologies"?

This scene seems to imply that Russell didn't view logic as tautologies. Correct. Wittgenstein's view about "logic=tautologies" was grounded on propositional logic and truth table. ...
Mauro ALLEGRANZA's user avatar
6 votes

What did Russell mean when he wrote that the null-class, the class having no members, did not exist?

In the passage above Russell discusses two uses of existence: (a) is the "common sense" use: "which occurs in philosophy and in daily life is the meaning which can be predicated of an ...
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

What is going on with Russell's "beauty cold and austere" of mathematics?

Belated and subjective, but I had an answer that didn't appear in the comments so I thought I'd mention it: The beauty of mathematics is cold and austere because of how dreadfully, terrifyingly ...
linkhyrule5's user avatar
5 votes

Is a barber a barber if he doesn't get paid?

You don't even need to use the word "barber," or to assume any exchange of money in this case. It takes a bit of elementary set theory (logic alone doesn't seem to be enough), but it is easy to prove ...
Dan Christensen's user avatar
5 votes

How did Wittgenstein become interested in the philosophy of language?

There were not "conversion" at all, but a progressive involvment with logic and language. For historical evidence, see e.g. Letter to B.Russell [Nov.1913], with refernce to Bedeutung [reference] (a ...
Mauro ALLEGRANZA's user avatar
5 votes
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Source of a Russell quote about purpose and meaninglessness

With further searching I found the answer in Hugh S. Moorhead's The Meaning of Life, page 164-165. The quote comes from a letter to Hugh Moorhead from Bertrand Russell on January 10, 1952. Moorhead ...
Frank Hubeny's user avatar
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5 votes

What did Russell mean when he wrote that the null-class, the class having no members, did not exist?

The definition that Russell provides for (b): To say that A exists means that A is a class which has at least one member. We translate this into modern mathematical notation as follows: "A ...
Kevin's user avatar
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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, ...
Kristian Berry's user avatar
4 votes

How inaccurate is Bertrand Russell's History of Western Philosophy?

It's what an introductory survey & history ought to be. I read it pretty quickly the summer between 8th & 9th grade when I wanted a map of where to go next. It's flawed in a way it ought to be....
James Myers's user avatar

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