15
votes
Accepted
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) ...
- 813
11
votes
Accepted
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 ...
- 42.5k
11
votes
Accepted
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 ...
- 36.1k
10
votes
Accepted
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 ...
- 35.4k
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 ...
- 42.5k
9
votes
Accepted
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 ...
- 5,106
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), ...
- 2,401
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 ...
- 42.5k
8
votes
Accepted
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 ...
- 42.5k
7
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 ...
- 171
7
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 ...
- 2,178
7
votes
Accepted
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 ...
- 6,456
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 ...
- 35.4k
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 ...
- 22.7k
6
votes
Accepted
What does Russell mean by "term" in Principles of Mathematics?
The answer already given by user3451767 is not in my view correct. Logical atomism characterizes Russell's work from roughly 1910-1925. POM was published in 1903. There are many differences between ...
- 852
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 ...
- 36.1k
6
votes
Accepted
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 ...
- 42.5k
6
votes
Accepted
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 ...
- 36.1k
6
votes
Accepted
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, ...
- 1,401
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. ...
- 36.1k
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 ...
- 36.1k
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 ≠ ...
- 36.1k
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 ...
- 151
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 ...
- 36.1k
5
votes
Accepted
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 ...
- 19.2k
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 ...
- 1,733
4
votes
Accepted
What sources discuss Russell's response to Gödel's incompleteness theorems?
Irvine in Bertrand Russell also writes that "Russell did not understand Gödel's celebrated results, which he interpreted as implying that arithmetic is inconsistent". Berto in Gödel Paradox and ...
- 42.5k
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....
- 41
4
votes
Accepted
In which sense Wittgenstein criticizes Schopenhauer's WILL?
Bryan Magee, The Philosophy of Schopenhauer (1997) has Ch.14 dedicated to: Schopenhauer's Influence on Wittgenstein.
[page 310] This influence can be asserted with absolute certainty; it is clear ...
- 36.1k
Only top scored, non community-wiki answers of a minimum length are eligible