28

After a bit of searching, I found some promising leads (and quite a few consistent descriptions) which suggest that Russell thought Gödel's results were of cardinal importance, but misunderstood their implications. In particular, he thought that Gödel's result essentially entailed that Peano Arithmetic was inconsistent rather than incomplete; but ...


12

The quotation is incomplete and Russell's thought is cut off right in the middle. The full quote by Russell continues thus: "… None of us would seriously consider the possibility that all the gods of Homer really exist, and yet if you were to set to work to give a logical demonstration that Zeus, Hera, Poseidon, and the rest of them did not exist you ...


12

The history of ideas and the history of philosophy is a world riddled with boogeymen versions of certain philosophers. Some of the more common historical boogeymen are "Plato", "Aristotle", "scholasticism" / "Medieval philosophy" , "Descartes", "Kant", "Hegel", "Nietzsche", and "Kierkegaard" . You may notice two things about this list: (1) every name is in ...


11

I think Russell is fairly clear in this passage --his gripe is not so much with Aristotle, but with how (in his opinion) Aristotelian thought continued to dominate the fields of science, philosophy, and logic long after it had outlived its usefulness. In particular, he saw the field of logic as having ossified for thousands of years after Aristotle's death....


11

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 itself. Hence the paradox. The "root" of the paradox is the so-called unrestriceted Comprehension Principle of naïve set theory: for every property ...


10

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 context see What is the philosophical ground for distinguishing logic and mathematics? Frege himself could not complete the project because Russell discovered ...


9

The following is from a late paper of Russell's titled "Logical Positivism". It can be found in "Logic and Knowledge" It appeared that, given any language, it must have a certain incompleteness, in the sense that there are things to be said about the language which cannot be said in the language. This is connected with the paradoxes - the liar, the class ...


9

Very funny gag. I don't wish to ruin the gag for others, so hover over the block quote to reveal :


8

To me, this sounds like a set-theory joke resting on existence of the "empty set". "Some apples" might be taken to ask whether, in the set of apples in your basket, are there multiple elements. "Any apples" might be taken to ask whether this set has at least one element. As in, if you have no apples, there are no elements in the set, resolving the ...


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 ...


8

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 Wittgenstein provide information from his side. Some slight conjectural indication of what Wittgenstein wrote on is provided by the subject-matter of Russell'...


7

Since R's 'objecthood' is primary, why doesn't it make sense to say that R can neither have the attributes is a member of R nor not-is a member of R correctly attributed to it? If this is the case then Russell's Paradox is dissolved, since it is the assumption that R must satisfy either is a member of R or not-'is a member of R that seemingly gets us into ...


7

Regarding specifically Russell's attitude towards Aristotle's logic, I have come to wonder if in the course of a justified complaint about an enormous time span of intellectual stagnation, Russell maybe missed an opportunity to recognize a few excellent aspects of Aristotle's logic, which, after dismissing them, took much effort to be rediscovered by Russell ...


7

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 definite article in English is just one type of linguistic device that creates denoting phrases, but it is not essential to the theory. I don't know much Russian ...


7

"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), 38-49 Unpopular Essays, Chapter 2 (George Allen & Unwin, 1951) No, philosophy is not taxonomy. Philosophy is respect for obtaining knowledge - whether ...


7

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 inconsistent systems, and even when it is, derivable contradictions do not have to be interpreted as "true". What we need is not logic but semantics, although ...


7

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 doctrine of the Critique of Pure Reason: Kant is treated in greater detail [than Hume], and once more Russell follows his preferred and somewhat Napoleonic ...


6

The natural rebuttal to Russell here is that he has misunderstood the Stoic understanding of Happiness. In choosing their actions and goods in a principle of "Rational decision in accordance with nature", Stoics do not deny what would make them happy. Happiness for the Stoics just is making that choice willfully. Perhaps Russell might be right were he to ...


6

There is no justification for one or the other. Russell's paradox is a paradox if you believe** in unrestricted comprehension (for each P there is a set {x | P}), or at least if you believe** that the set {x | x ∉ x} exists. Russel's paradox is not a paradox if you use it to conclude that the set {x | x ∉ x} does not exist. Cantor's diagonal argument is a ...


6

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 his views during these periods. The short answer to your question: Russell's terminology is confusing because he has two uses of the word "term" in POM: -A ...


6

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 differences inter se corresponding with the differences in the phenomena to which they give rise. He assume that the "phenomenal" world is the counterpart of a "...


5

I believe you're referring to the fallacy of inferring the “sum” (or “I am”) part from the “cogito” (or “I think”) part, right? The “ergo” (or “therefore”) makes it sound like Descartes is expressing an argument which has as its premise that he thinks, and the conclusion that he exists. The potential fallacy in this representation of the Cogito statement ...


5

The key point is the sentence:"Even if this proposition is never true, it is nevertheless significant", I italicized "significant", as Russell does in his text. Russell is talking about manipulating objects in a formal system (of Principia Mathematica). What he says is that while objects can be "actually" distinct if they are "equal" in his system this fact ...


5

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 Development of Wittgenstein’s Philosophy for a review. In a 1936 manuscript he writes "Language is much more complex than logicians and the author of the Tract. Log....


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

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 simple it is. It certainly doesn't look like it from the outside, I'm sure -- but having studied, you quickly realize that unlike any other field mathematics ...


5

In the realm of philosophy, it seems like just about anything is possible. So I would say we can't know the world wasn't created just five minutes ago. But by the same token, we could argue that the world might have been created SEVEN minutes ago or thirteen years in the future. Or maybe there is no world at all. If you're going to accept one "flaky" ...


5

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 key-term of Frege's Philosophy of language) in relation to facts and proposition. For W's philosophy of language in the Tractatus (1921), you can see ...


5

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, the other urging them towards science. Some men have achieved greatness through one of these impulses alone, others through the other alone: in Hume, for example, ...


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