All Questions
Tagged with terminology philosophy-of-mathematics
26 questions
24
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8
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4k
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What do all branches of Mathematics have in common to be considered "Mathematics", or parts of the same field?
At some point in my life I think I've read what all branches of Mathematics had in common were numbers. But then I remembered a branch of the many Mathematics I had when I was an university student, ...
- 807
3
votes
2
answers
165
views
Two kinds of abstract objects - circles and sets
Both circles and sets are considered abstract objects. I can visualise a circle in my mind (can 'see it through my mind's eye') but can't visualise a set or a number. I have no picture of a set in my ...
- 633
3
votes
3
answers
368
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"Impredicative" definitions in mathematics
In this blog post, the following definition of an "impredicative definition" is offered:
A definition is said to be impredicative if it defines an object E by means of a quantification over a ...
- 2,501
1
vote
0
answers
101
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Is 'a level of quantity' a poor definition of 'real number'?
I was thinking about how we define numbers with respect to their uses, and came up with the definition of 'a level of quantity' which can have a different physical consequence for each quantity ...
- 1,237
1
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4
answers
289
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Is '=' a relationship between the objects or their expressions?
The Wikipedia definiton of equality gives it as a 'relationship between two expressions'
This confuses me as when we define mathematical expressions like 2+2=4 it makes no sense to say that '=' or '...
- 1,237
3
votes
3
answers
151
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Can an 'abstract object' be a collection of constituent parts?
When I ask this, the use of collection or set is not necessarily 'mathematical', so if in this case I mean a collection of ideas that encapsulate it, 'make up' the idea in the same way the various ...
- 1,237
0
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1
answer
148
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When does 'number' become 'quantity'?
Numbers themselves are simply conceptual objects, but when does number become a quantity? Is the 'cardinality' of a set a 'quantity'? it is a count but we represent it with just a number that we ...
user58502
0
votes
1
answer
160
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Is there an alternative to infinity?
We can say that a discrete set with 1 and 2 allows us to count just from 1 to 2 but a sequential set with 1 and 2 allows us to count from 1 to 2 in an infinite way (1.1, 1.2, 1.3 ...) but no man can ...
- 11
1
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3
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183
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Definition of 'Identity' [duplicate]
This may seem like a very specific or stupid question, but I'm new to this, I'm interested in the idea of 'identity' and 'identical. I've heard some description of the idea different 'copies' or ...
- 1,237
1
vote
3
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335
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Mathematical objects existing as different instances
I have a slightly complex conceptual question about the idea of 'multiple' instances of mathematical objects. In particular Real Numbers, and generally the idea of having multiple instances of ...
- 1,237
0
votes
3
answers
112
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Is there any philosophical difference between "I have no horns" and "I have horns, but they have zero volume"?
The common idea is that, on one hand we have "I don't have X", on the other hand we have "I have X, but X has some its quality equal to zero, making it to behave the same way as if it ...
- 380
3
votes
7
answers
614
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Is there an idea of non-spatial reality in philosophy?
Our world is spatial. In particular there are 3 dimensions and we can measure lengths of objects in either of them.
However, when thinking about metaphysics I came to the conclusion that there might ...
- 2,764
4
votes
1
answer
185
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What should be the definition of absurdity?
I several times have encountered questions, asked by myself and other people about different things, subjects, phenomena, considered to be absurd to common perception. But, sometimes through rigourous ...
- 286
6
votes
3
answers
768
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What is the fallacy of defining a square as “a closed-plane figure whose sides are all equal”?
I am determined to prove my professor wrong. Here is a question from a recent exam:
Using the six definitional criteria, evaluate the following definition.
A square is a closed-plane figure whose ...
6
votes
4
answers
431
views
What does the term "mathematical logic" mean?
What is "mathematical logic"? Is it the logic of mathematical reasoning, or is it the claim that mathematics and logic are identical?
Also, is "quantificational logic" a particular type of "...
- 8,615
6
votes
2
answers
736
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What does Russell mean by "term" in Principles of Mathematics?
Bertrand Russell in Principles of Mathematics defines a term as "Whatever may be an object of thought, or may occur in any true or false proposition or can be counted as one." Can someone elaborate on ...
- 163
6
votes
5
answers
7k
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What is the difference between a probability and a possibility?
I ask this in a fairly naive way. I understand that "probabilities" can be quantified in frequencies, degrees of belief, etc. with some defined "space" of probability.But I know little about modal ...
- 13.7k
-2
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2
answers
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How to define a number [closed]
What is the positive real number (say less than one) that is not a rational nor an irrational number?
I have encountered a mathematical problem that confused me about the definition of real numbers,...
- 101
3
votes
3
answers
1k
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Truth for logicians, mathematicians, and philosophers
How does the logician define truth?
What is the precise definition of truth for mathematicians?
How does a philosopher define truth?
What are the similarities and differences between these ...
- 139
20
votes
9
answers
4k
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Interpret Bayesian probability as frequentist probability?
It is usually said that the Bayesian probability is a subjective concept, quantifying one's degree of belief in something, while the frequentist probability is the the fraction of certain outcomes ...
- 303
8
votes
3
answers
544
views
What does it mean for an axiom to be logical?
I have recently been hearing the phrase logical axiom being thrown around in reference to the philosophy of mathematics and I'm having a hard time understanding what one might mean when they are using ...
5
votes
1
answer
525
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What does "aggregative mechanical thought" mean in Frege's works?
In *The Foundations of Arithmetic: A Logico-Mathematical Enquiry Into the Concept of Number" by G. Frege pages XV and XVi we read:
A typical crudity confronts me, when I find calculation
...
- 51
5
votes
3
answers
793
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How could the concept of 'evidence' be defined, and how significant is it?
What is evidence, and how much of it means that a proposition is true? Does a partial / total lack of evidence mean that a proposition should be ignored?
Is the concept evidence more important to ...
- 51
7
votes
3
answers
245
views
What's a name for the impossibility of identity?
It appears to me that no two things can ever be identical, yet the notion that they can has been deployed rather without pause about a billion times in theoretical literature in philosophy and ...
- 171
1
vote
1
answer
224
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The represenation of nothing
If zero is the representation of nothing, then nothing must me something because it is being represented, correct?
Now, if the above is incorrect, and zero is actually nothing, then why is it that ...
- 113
7
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2
answers
272
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Genus-Differentia and Mathematical Categories
I am a mathematician by training. Category theory has become a major subfield of mathematics --- major enough that some have tried to recast the logical foundations of mathematics in terms of ...
- 253