37
votes
Accepted
Why would infinite monkeys not produce the works of Shakespeare?
Yes, the monkeys will do it. No, they don't have to.
It's mathematically true that after removing all logistical constraints - which is what we mean when we say there are infinitely many monkeys, ...
- 620
14
votes
Which field is more rigorous, mathematics or philosophy?
Mathematics was and is intended to furnish precise numerical answers to precisely-posed questions involving numbers and logic. It is intended, by design, to be rigorous. Once the truth of a ...
- 7,798
14
votes
Can Mathematics Fully Describe the Universe?
Clearly, no mathematics is ever going to describe redness and pain and love to any reasonable person's satisfaction.
To describe something is to say what you think this something is by using a subject-...
- 6,241
13
votes
Accepted
Can a totally ordered set with a last element but no first element exist, or is this contradictory?
Can a totally ordered set with a last element but no first element exist, or is this contradictory?
Taking the usual mathematical definition of total order, and taking "last element" to ...
- 648
12
votes
Accepted
Is mathematical creativity the same as artistic creativity?
There are caricatures of math and the arts, and then there are characterizations, the best of which are accurate. Many students get dragged through the drudgery of mathematical algorithms and washout ...
- 22.9k
12
votes
Accepted
Mathematical Platonism. Are numbers real?
By "real" here I assume, by your example, that you're talking about "physically real". And in that case real=experimentally_measurable. And that, in turn, means units. Even your ...
- 565
12
votes
Accepted
How many instances of 1 are there in the expression "1+1"?
The TLDR
One can instantiate the numeral '1' in a sequence or multiset multiple times, in a set '1' only once, and the concept of 1 cannot be instantiated more than once ever, given how the concept 1 ...
- 22.9k
10
votes
Mathematical Platonism. Are numbers real?
Asking whether a number, such as four, is real is like asking whether a word such as 'big' is real. The qualities which we think of as big are real. When we say a football stadium, for example, is big,...
- 13.5k
10
votes
Does single case chance actually exist?
You've hit upon a frequently debated topic in statistics, that is, what does "probability" actually mean?
At the moment, the philosophical arguments tend to boil down to two main camps: ...
- 1,214
9
votes
Is mathematics analytic or synthetic?
A possible counterargument is that the analytic-synthetic distinction you are using is inherently inadequate and outmoded language and thinking. For the first part, Quine in his Two Dogmas of ...
- 22.9k
8
votes
Mathematical Platonism. Are numbers real?
Mathematicians, specifically set theorists, have so little faith in the existence of numbers that they must posit an axiom for something even as fundamentally obvious as the existence of an empty set.
...
- 197
8
votes
Difference between how a physicist and mathematician approach science?
Sweeping generalisation alert. Physicists tend to be very pragmatic. If they can find a mathematical technique that predicts the results of experiments, they're happy- they won't have sleepless nights ...
- 13.5k
8
votes
Difference between how a physicist and mathematician approach science?
Mathematicians need not practice science at all, except as a personal hobby unrelated to their profession. If you search Physics SE for the inverse of this question - "how does the physicist's ...
- 3,525
8
votes
Can location be assigned to an entity, given a lack of length, depth, or width?
David Gudeman rightly points out that your entity is called a point. A point by definition has no extension. How that is possible is that Euclidean space is concerned with having dimensions that are ...
- 22.9k
8
votes
If Large Language Models can do Maths, is Formalism true?
As a constructivist brother who places as much credence in Platonic Forms as he does in the Irish tuatha da dannan or the Norwegian troll, let me dispute the premise that LLMs do math or have much in ...
- 22.9k
7
votes
What is the meaning of assertion?
A very rough approach is the following: humans use sentences, i.e. expressions made of words (spoken or written) in many contexts, i.e. speech acts.
See Assertion: "Asserting is the act of ...
- 36.2k
7
votes
How many instances of 1 are there in the expression "1+1"?
Two Instances
This is easy. Zoom in for a closer look.
Fig. A
In the figure I have zoomed in and circled and labelled both instances of 1 in the expression. I think I got all of them. Perhaps more ...
- 898
7
votes
Accepted
Which field is more rigorous, mathematics or philosophy?
Rigor is a methodological concept: it only applies to the system of analysis used within a particular investigation, as a measure of how thoroughly that investigation conformed to the intellectual ...
- 18.5k
6
votes
Can a totally ordered set with a last element but no first element exist, or is this contradictory?
Take the negative integers.
But remember that arbitrarily large numbers don’t require an infinite item. There are arbitrarily large and small integers, but no infinite ones.
- 5,243
6
votes
Can Mathematics Fully Describe the Universe?
Mathematics can be used to make a model of the universe. All models are necessarily simplifications of the thing they model - if they weren't they would be of no use as they would be no easier to ...
- 1,458
6
votes
How to understand the notion of majority when comparing infinite sets?
This is already a problem even for simple probability distributions in the real numbers, such as the normal (Gaussian) distribution. The reals are infinitely dense, so we cannot assign individual ...
- 1,733
5
votes
Is mathematical creativity the same as artistic creativity?
Yes, in essence.
For my argument I will consider mathematicians only as creators of mathematical stuff, not just copiers and learners. After all we don't call proof-readers and copy-typists authors.
...
- 1,094
5
votes
Mathematical Platonism. Are numbers real?
An interesting number like e, Euler's number, a 'constant of nature', as real as could be. It is known inexhaustively by many representations. Many discoveries and many perspectives, but never the ...
- 5,258
5
votes
Is topology used outside of cosmology in philosophy?
For an unfortunate preliminary example, Christopher Langan's infamous theory of everything uses the concept of topology in a way similar to how Alessio Moretti uses the concept of geometry. My take on ...
- 12.1k
5
votes
Is topology used outside of cosmology in philosophy?
Stone Spaces
If you consider formal logic to be part of philosophy then topology is relevant. The basic result is about Boolean Algebras. A Boolean algebra is something like a bunch of sets where you ...
- 898
5
votes
Is topology used outside of cosmology in philosophy?
I will elaborate a bit more on the connection between topology and the law of excluded middle (LEM), which Daron and Kristian have already mentioned.
In logic, the basic objects of study are formulas (...
- 151
5
votes
How is the concept of a topos in mathematics relevant to philosophy?
The word 'localization' here has a specific technical meaning; it's referring to the localization of a category:
[L]ocalization of a category consists of adding to a category inverse morphisms for ...
- 420
5
votes
How is the concept of a topos in mathematics relevant to philosophy?
Could you explain what are the various ways topoi are used in philosophy?
Let's start with a quotation Robert Goldblatt's text on the matter:
The notion of topos has great unifying power. It ...
- 22.9k
5
votes
What does it mean for something to be "more likely"? Whether you would bet on it? Whether history suggests it to be true? Or both?
I believe you are asking the same question over and over again in all these posts: can probability theory help me with subjective decisions?
Cutting to the chase, probability theory is a mathematical ...
- 2,402
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