Questions tagged [numbers]
38 questions
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What are computable numbers, and what is their philosophical significance?
What are Computable Numbers? Is computability (or non-computability) some sort of technology-dependent characteristic of numbers (via e.g. Turing Machines)? What are the philosophical implications or significance of computable (and non-computable)…
L.M. Student
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What did Poincaré mean by intuition of pure number?
To what does Poincaré refer in his article Intuition and Logic in mathematics when he speaks about the intuition of pure number? He refers also to two other forms of intuition, besides the "intuition of pure number", namely, "analogical intution"…
Always learning
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How does Frege's definition of number solve the Julius Caesar problem?
How does Frege's definition of number solve the Julius Caesar problem?
Frege's definition of number in the end of Foundation is such: the number belonging to the concept F is the extension of the concept equal to the concept F such that F and G are…
Frank Booth
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Is number π empirical or a priori?
I used the example of π, but this applies to other transcendental numbers as well, such as e
Kant classified statements into 4 epistemic categories based on two criteria: The Analytic/Synthetic distinction (Are statements true by definition or do we…
Alexander S King
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What is the difference (if any) between the concepts of natural numbers and finite cardinals?
The definition of natural numbers from Wikipedia:
In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").
And the cardinal…
bg5
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What are functions in the Peano axioms?
I'm posting this here because it's more of a philosophical question than a mathematical one.
In set theory, we define a function as a particular type of set; and since the natural numbers are defined as particular sets, we know exactly what we mean…
user4894
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Square of Opposition with percentages?
What happens if you replace the statements of the Traditional Square of Opposition with "percentages of the subject term"? Do all the relationships from the Traditional Square of Opposition still apply?
A: 100% of x have y. -- ("All dogs have…
Mike
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Why is 2+2=4 a necessary truth?
A necessary truth is something which is true in all possible worlds. How can we be sure that there is no other universe where 2+2=4 can be untrue.
stack exchange
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Are numbers, given just as mathematical objects, quantities in themselves?
If we are talking just about '5', without it being with respect to any 'amount', does the idea of the number itself as a point on a line imply that it is itself some kind of abstract 'quantity'. It can be used to talk about quantity, and as an idea…
Confused
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What is the difference between concepts of number and natural number?
When reading an article about Frege on Stanford Encyclopedia of Philosophy (https://plato.stanford.edu/entries/frege/#AnaStaNum), in section 2.5 I encountered the following sentence:
But though this defines a sequence of entities which are numbers,…
bg5
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How do our minds divide spaces and create "entities?"
I've been thinking about how any object can be split into infinitely smaller pieces and how we may say that there is a particular object or entity, but it has an upper portion and lower portion. In essence, what we are doing in these cases is…
Morella Almånd
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What are the "undefinable numbers" in real analysis and philosophy?
What if any important results in real analysis make use of the notion of an "undefinable" real number? (Whatever "important" may mean to the reader.) Or is it used more in the philosophy of mathematics?
Dan Christensen
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The "slow and gradual" reduction of numbers from qualitative elements to pure quantities
In a well-known book of classical scholarship, Jaeger's Paideia, Vol.1, there is the claim that "it has been justly observed that the Greek conception of number originally contained a qualitative element, and the process by which numbers were…
exp8j
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Did all numbers exist at the beginning of the universe?
So I am hoping this question spurs the thought of,"Ok, lets say they didn't all exist at the beginning of the universe then how did they all come to be?". Then the next step would hopefully be that someone doesn't come up with numerical order…
Joe
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Discerning between a number 'x' as a Natural or Real number
The usual way of teaching is to explain the numbers that are element of the reals and naturals as being the same, this was a perfectly valid way of understanding for me, why do some consider '2' as an element of the reals, different to '2' as an…
user37577
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