Questions tagged [numbers]
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numerable diagonalization [closed]
If I understand Cantor demonstrated by using a strategy using the diagonal of a matrix, that there are decimal numbers which cannot be a part of an enumeration.
We can build a Table, the rows ...
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How Probable is the Philosophical Significance of Numerical Patterns in Religious Texts?
I have a Muslim friend who told me about a chapter in the Quran (the holy book of Muslims) in which he claims there is a "numerical miracle."
This chapter is unique in the Quran because a ...
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Why are pure powers of the empty set insufficient as a definition for ordinals?
I recently discovered a philosophical term that gives expression to a paradigm that had been circling in my head. G. E. Moore discussed the “paradox of analysis”, which is similar to what I think of ...
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How small can we measure space? [closed]
I got this question after looking into transcendental numbers and I noticed how there are some distinctions that should be made from numbers and reality especially in measurement of length for example ...
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Is the conceptual possibility of amorphous infinite sets "evidence against" countabilism?
Countabilism is, roughly, a family of standpoints inclusive of:
There is one infinite proper set, of size ℵ0, and one infinite proper class, ℵ0ℵ0. (See about e.g. "pocket-sized" and ...
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Is it consistent with beginning/ending principles for an interval-based temporal logic to cover a time that is exactly ω+ω intervals long?
The SEP article on temporal logic reports on possible beginning/ending principles for instant-based temporal logics:
beginning: ∃x¬∃y(y≺x)
end: ∃x¬∃y(x≺y)
Note that ≺ is the prior-to relation, here. ...
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Numbers and Time
This is my first post on philosophy stack exchange, so I apologize in advance if this question is not well-defined or if it happens to be a duplicate. If so, feel free to link the corresponding post(s)...
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Infinitesimals and plural quantification
In reply to, "Does nature jump?" Mikhail Katz notes that:
There is a different idea in Leibniz called the Law of Continuity. One of its formulations is
the rules of the finite are found to ...
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Why not move from proof numbers to theories instead of theories to proof numbers?
In mathematics, they do this thing where they figure out what are called "proof-theoretic ordinals" (see this section of the SEP article on proof theory for background details) of theories, ...
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Why do numbers apply to such disparate concepts?
I understand numbers to be defined as objects defined to have certain convenient properties in relation to certain operations. It is very surprising that the exact same group objects should be ...
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Would Frege's version of the empty set contain "parafinitesimal elements," at least from the multiversal standpoint?
Frege's definition of the empty set was not a raw extensional one: he did not simply write the partial string {} and say, "That's it: that's the empty set." His account was more intensional: ...
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Is there a paradox of third-order arithmetic?
Calculus, sometimes analysis or second-order arithmetic, seems more intuitive when formulated in infinitesimal terms than in terms of real-valued limits. However, the meta-theory of analysis, i.e. its ...
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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 ...
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Is this a legitimate way to reframe structuralism in the philosophy of mathematics?
As an umbrella term, "structuralism" has to cover realist and nonrealist versions, while also carrying through the theme of its name nontrivially (for there is a trivial way to make ...
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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 ...
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