Philosophy of mathematics asks questions about mathematical theories and practices. It can include questions about the nature or reality of numbers, the ground and limits of formal systems and the nature of the different mathematical disciplines.

learn more… | top users | synonyms (1)

4
votes
0answers
26 views

Is there a sheaf-theoretic description of para-consistent logics?

Paraconsistent logics drop the notion of global consistency, instead they have a notion of local consistency. In sheaf-theory, or categorical logic, as in topos theory, there is a notion of local ...
2
votes
0answers
22 views

Is there provably a largest cardinal consistent with ZF

Reinhardt cardinals are the largest cardinals yet defined in ZF (they are the critical points of a non-trivial elementary embeddig of V into itself), are they provably the largest possible? Is there ...
3
votes
1answer
78 views

On the Axiom of Infinity

Russell, in Principia Mathematica, says the following of his Axiom of Infinity: "The axiom of infinity will be true in some possible worlds and false in others" He is notoriously sheepish about ...
2
votes
2answers
90 views

What could we call as mathematical intelligence?

A professor once told me, for example, that the act of counting is widely regarded as a first sign of mathematical intelligence. Is it though?, can the act of counting (or performing simple arithmetic ...
5
votes
3answers
149 views

Is math independent of our sensory experience?

I've been asking myself this and other questions in the field of philosophy of mathematics. Could we, if we were isolated from any kind of sensory experience, be able to learn mathematics? This ...
3
votes
2answers
60 views

Badiou, Deicide & the return of the Transcendent

Badious philosophy is predicated on Set Theory, in its incarnation as the materialist set theory ZFC. He calls mathematics the very site of ontology. Nietszche famously declared the death of God (in ...
-2
votes
0answers
28 views

Is 2 and omega measurable,without being uncountable?

If we don't need measurable cardinals to be uncountable,then 2 and aleph-0 are measurable cardinals!I have just reading maddy's "believe the axioms",k is measurable if there is a smaller than ...
2
votes
4answers
179 views

What do we mean by the term “Number of things”?

I am reading the book "The Number-System of Algebra (2nd edition)." I have some problems with the the first article: "Number". The author has confined the concept of number of things to the groups ...
2
votes
1answer
66 views

A question about large cardinal axioms in set theory

In set theory,there are many kinds of large cardinal axioms.their existence cannot be proved in ZFC.but for many large cardinal properties,if we don't need they be uncountable infinity,they are ...
1
vote
1answer
54 views

References for intuitionistic meta-logic?

It seems to me that arguments about logical theories itself are often done using classical logic. For example, one says that a theorem is provable or not provable, which is not automatically valid ...
2
votes
3answers
108 views

Could our universe simply be abstract mathematical existence?

Say we imagined a mathematical model so detailed that it completely describes a universe like our own. Now if we simulated such a universe on a futuristic supercomputer then obviously the beings ...
4
votes
1answer
45 views

Recommendations for reading in Russell's Mathematical Philosophy

I am looking for any suggestions for research-level survey articles that expose Russell's type theory (in the context of his philosophy of mathematics). Of particular interest are: Russell's reasons ...
1
vote
2answers
71 views

Is the real number line actually real when we construct it?

Intuitionism is akin to constructivism in mathematics but not quite the same from what I can tell. In the usual treatment of the real line, the additional numbers are found between the rationals by ...
-1
votes
1answer
71 views

Contradiction, and the Being and Becoming of Mathematics

Mathematics is rife with contradictions, is shot through with them: the fault-lines lie where theories collide, fade or open up. Does this disturb the incarnation of mathematics - the Ideal ...
-2
votes
1answer
78 views

Mathematics and the Peano Event, or the sign thereof

One might say the Original Event in mathematics is Euclids axiomatisation of Plane Geometry. Subsequent axiomatisation - such as Peanos Axioms for the natural numbers being an echo of that Event, and ...
2
votes
2answers
99 views

Motion and contradiction

Zeno famously said an arrow cannot be in motion as it occupies some precise position at some precise time. And is thus at rest. Modern physics resolves this by stating the arrow has momentum. It is ...
0
votes
1answer
24 views

Descartes' Enlargement or Limitation of Cognition?

Descartes gives the metaphysical implications of freedom of the will as it relates to the power of cognition. This involves the function of judgement in its natural character and representational ...
3
votes
3answers
127 views

GUT and TOE as Fallacies of Misplaced Concreteness?

A.N. Whitehead warns in the introduction to Process and Reality, that the “chief error” of Western philosophy is “overstatement.” He states: “the aim at generalization is sound, but the estimate of ...
1
vote
3answers
157 views

Is Mathematics an art or a science? [closed]

Is Mathematics an art or a science? This is a deep question with which I have had many discussions with my friends and teachers.
5
votes
2answers
135 views

Recommendations for reading in Constructive Mathematics

I'm looking preferably for any survey articles on constructivism in the Philosophy of Mathematics - including Intuitionism in the tradition of Brouwer. Hopefully such an article(s) will cover: ...
0
votes
2answers
73 views

What is the justification for topological arguments in philosophy? [closed]

What is the justification for topological arguments in philosophy? For instance, it is common to say that we are not the only conscious animals because there is a continuity between humans and animals ...
1
vote
1answer
56 views

Are there n-valent classical propositional logics?

Classical propositional logic is truth-functional, that is the truth of propositions are determined by the assignment of truth-values taken from {false,true} to the atomic propositions. And it is this ...
-4
votes
3answers
107 views

Is it irrational to not believe in the existence of irrational numbers?

Suppose some agent doesn't believe in the existence of the positive square root of 2. Question: Is the agent's disbelief (or lack of belief) in the existence of +sqrt(2) irrational? The question ...
5
votes
3answers
203 views

What are the truth-values of intuitionistic logic?

Classical propositional logic is bivalent, that is its set of truth-values has cardinality 2 (True & False). Intuitionistic logic drops the law of the excluded middle; does it have the same set of ...
2
votes
1answer
107 views

Is it more than a simple technical device that we have at infinite axioms in ZFC?

Take the axiom of Comprehension that was introduced by Zermelo. This, as usually stated has one instance for every single formula. Presumably this is to contain the axiom within first-order logic. ...
1
vote
1answer
72 views

Is mathematics discovered through introspection?

Referring to this question on the significance of the division of senses between inner and outer. Can one say that mathematics is discovered by introspection or to coin a new word, extrospection? ...
1
vote
2answers
124 views

Can there be a universe with different mathematics?

I do not know what exactly I means by other universes, but I just have a feeling that mathematics is somehow inevitable. For example the law of "exclude in the middle". If there are aliens, can we ...
1
vote
2answers
106 views

Has logic been formalised?

The headline question is mainly a rhetorical question. Paul Cohen, a major set theorist who invented 'forcing' in Set Theory for independence results and used by Badiou in his philosophy has this to ...
2
votes
0answers
69 views

Are numbers universal in Set Theory and nominalist in Category Theory?

The number 3, when considered as a universal, abstracts the property of 3'ness from all groups of 3 objects. One supposes that this universal, by conceptual neccessity of what is understood by the ...
2
votes
2answers
137 views

What are the 'structures' of structuralism?

Structuralism has for many become the buzzword in the philosophy of mathematics in the past 30 or so years. My question can be stated simply as: What are the structures of structuralism? ...
1
vote
1answer
60 views

What were the 'costs' in completeness in formulating ZFC in first-order logic?

Wikipedia on [2nd order-logic] states: Predicate logic was primarily introduced to the mathematical community by C. S. Peirce, who coined the term second-order logic and whose notation is most ...
5
votes
2answers
179 views

Are there theories of arithmetic that are inconsistent with the natural numbers?

The programme of ultrfinitism dispenses with the notion of very large finite numbers simply becaause they argue that such large finite numbers have no way of being conceptualised in our universe in a ...
2
votes
2answers
142 views

What are the useful outcomes of denying the Continuum Hypothesis?

The continuum Hypothesis says: There is no set whose cardinality is strictly between that of the integers and the real numbers and the generalised Continuum Hypothesis, additionally says: if ...
0
votes
1answer
75 views

What is Naive Set Theory?

Is naive set theory, simply set theory that has been left unformalised as the entry in Wikipedia suggests? However, the SEP, in its entry on inconsistent mathematics, suggests that: It should ...
1
vote
1answer
56 views

What are the ramifications of the limitations of ZFC set theory?

In the Wikipedia article on Zermelo-Fraenkel set theory says that the theory sets out to formalize a notion of sets such that "all entities in the universe of discourse are such sets." It goes on to ...
-2
votes
1answer
64 views

What is the absolute ultimate subject (like math, literature, etc)? [closed]

Seems like all subjects are branches of more general subject. Pretty much all sciences seem to find their roots in physics but physics is just math. There are many branches of math but still all just ...
3
votes
1answer
130 views

Looking for mathematical models of awareness, consciousness, and unconsciousness e.g. Matte Blanco

Question: Do you know of any resources for mathematical models of awareness, consciousness, and unconsciousness? I am doing some work relating pure mathematics (among other things) to ideas of the ...
0
votes
2answers
55 views

What does philosophy exactly do? [closed]

I need your help understanding philosophy. For some reason, I'm not understanding the objective of this subject. Frankly, I only had 1 semester of philosophy so maybe it isn't enough to really ...
6
votes
3answers
742 views

In what sense are proofs just arguments that convince us, not arguments that establish truth?

In mathematics and logic, it seems that once a proof of some theorem is discovered, then it is taken to be "absolute truth" within the axiomatic system from which it was derived. My question is: are ...
3
votes
1answer
144 views

Is Immortality a Relative Property?

People talk about immortality like they know what it is. They say it is "living forever". But we can imagine somebody who experiences life getting asymptotically slower and slower, so that they never ...
-2
votes
4answers
225 views

Can we measure the effort to create a mathematical theory in terms of energy?

Sir Karl Popper says that products of our mind, like speech, music, math,... are things on their own. We create them. We put effort in them. I wonder where the difference of creating these things, is ...
-3
votes
1answer
72 views

The median of infinity [closed]

Would it be logical to assume that 1 is the median of countable infinity since all the whole numbers can also be used as its' denominator?
0
votes
1answer
94 views

Question regarding proof of ❋3.47 in Principia Mathematica by Whitehead and Russell

❋3.03 in the the last step seems unnecessary. Can someone explain to me why 3.03 is listed? The last step can be written out in full like this: ⊦: p .⊃. q ⊃ r ...
0
votes
2answers
142 views

Question regarding the proof 3.3 in the Principia Mathematica

As far as I can understand, the key of PM is to make sure there are no leaps and gaps when making inferences. In other words, all the premises and rules of inferences should be explicitly enumerated ...
3
votes
2answers
141 views

Why are set theory and numbers important to philosophy?

I'm reading David Papineau's Philosophical Devices, and there's a section on numbers and set theory. But there's not deeper hint on why it's important to philosophy. I guess that in mathematics we ...
6
votes
3answers
212 views

Does Poppers theory of Falsification apply to mathematics?

Mathematics is generally & popularly judged a science in the basic duality: science - humanities. As enemies and collaborationists. The border heavily & fiercely policed. However, it seems to ...
3
votes
1answer
80 views

Is there a theory with only observable quantities?

In Nitzens & Bichlers Capital as Power, they quote from Weinbergs Dreams of a Final Theory: I pointed out [to Einstein] that we cannot, in fact, observe such a path [of an electron in an ...
-1
votes
1answer
66 views

Equality Awareness (for minorities, LGBT, women, etc.)

Recently there has been a facebook campaign to raise awareness of the struggle for LGBT equality, whereby facebook users change their profile pictures to an "equal" sign. This campaign seems to be ...
0
votes
0answers
53 views

Was Deleuzes understanding of the infinitesimal calculus primitive?

According to the SEP: Deleuze was one of the targets of the polemic in Sokal and Bricmont 1999. As much of their chapter on Deleuze consists of exasperated exclamations of incomprehension, it is ...
1
vote
0answers
43 views

Are Axiomatic systems derived from Law?

Axiomatic systems arose in Greece & India in Geometry and Language, the exemplary texts being Euclids Elements and Paninis Ashtadyayi (grammar). Now, when one considers the idea of Law: Law ...