Question posted on May 22, 2014; 3 responses 
In writing mathematical proofs, I've been struck that direct proofs often seem to offer a kind of explanation for the theorem in question; an answer the question, "Why is this true?", as it were. By contrast, proofs by contradiction or... 
Mathematics 

Question posted on May 8, 2014; 1 response 
Hello philosophers,
I have yet another question. This time it's on the fundamental foundations of mathematics. I would like to know what Gödel's incompleteness theorem and inconsistency theorem actually stated. Intuitively, math seems logical, in the physical world, if you... 
Mathematics 

Question posted on April 25, 2014; 1 response 
One of the obvious ways computers are limited is in their representation of numbers. Since computers represent numbers as bit strings of finite length, they can only represent finitely many, and to a finite degree of precision.
Is it a mistake... 
Mathematics 

Question posted on February 23, 2014; 1 response 
Imagine that a Greek philosopher promised to his queen that he would determine the greatest prime number. He failed. Do you think that the mathematical fact that primes are infinite was a cause of his failure? I'm asking this because... 
Mathematics 

Question posted on December 12, 2013; 1 response 
My understanding is that we can use systems like Peano Arithmetic to prove the seemingly basic truth that 1+1=2. Do such proofs actually give us reasons to believe that 1+1=2 that we didn't have before? Are they more fundamental or... 
Mathematics 

Question posted on October 17, 2013; 1 response 
I am interested in how mathematical propositions relate to objects in the world; that is, how math and its concepts somehow correspond to the physical world. I have thought a bit about the issue, and realize that what happens, say,... 
Mathematics 

Question posted on September 25, 2013; 1 response 
Does the fact that our perceptions can be represented geometrically and that geometry consists of eternal truths independent of the mind prove that an external reality underlies our perceptions?... 
Mathematics, Perception 

Question posted on August 15, 2013; 1 response 
Is it ethical for game theory to be applied to conflicts which may involve mass human deaths for nondefensive wars?... 
Ethics, Mathematics 

Question posted on August 1, 2013; 1 response 
Are dimensions exceeding 3 actually comceivable or are they purely intellectual constructs? Is this even debated in philosophy?... 
Mathematics, Physics 

Question posted on June 20, 2013; 1 response 
I have a question. Years ago me and two friends got into a debate about a riddle. The riddle goes like this:
A train starts from point A and is travelling towards point B. A wasp is travelling in the opposite... 
Mathematics 

Question posted on June 13, 2013; 1 response 
Is 0 really a fraction? Because some do not agree that it is not a fraction. But I have a thought
Fraction=no. of equal parts considered/total no. of parts
So if I divide a chocolate in 4 parts and eat no... 
Mathematics 

Question posted on June 7, 2013; 1 response 
In mathematics numbers are abstract notions. But when we divide number say we do 1 divided by 2 i.e. ˝ does this mean abstract notions are divisible. It gives me a feeling like abstract notions have magnitude but then it... 
Mathematics 

Question posted on May 9, 2013; 2 responses 
How would a philosopher of math describe what happened when ancient mathematicians discovered (?) the number zero?... 
Mathematics 

Question posted on May 9, 2013; 1 response 
Does a point in geometry (cartesian and euclidean) occupy space or have volume (if we consider 3D geometry)? And is a line segment always perpendicular to its point of origin? Or can we frame this as, is a line perpendicular... 
Mathematics 

Question posted on May 2, 2013; 1 response 
What does it mean when a certain axiom is neither provable nor deniable?
Does it imply that such axiom is selfevident and can't be doubted?
I don't think that "real skeptics"(a skeptic who is so deep in doubt that he... 
Mathematics 

Question posted on April 11, 2013; 1 response 
Are mathematical truths such as 2+2 =4 arguable exceptions to the correspondence theory of truth? I mean is 2+2=4 a truth that corresponds to "the world"?... 
Mathematics 

Question posted on April 4, 2013; 1 response 
Hi, I love your website and I have enjoyed reading the articles.
Please could you help me with a question?
I would like to ask the question regarding 'negative numbers'. Can there be such a thing as a negative? Please allow me... 
Mathematics 

Question posted on March 21, 2013; 2 responses 
Are 3 and √9 the same mathematical object (in light of the fact that they have the same numerical value), or are they distinct mathematical objects?
In other words, are the expressions '3' and '√9' coreferential names (both referring to the... 
Mathematics 

Question posted on March 15, 2013; 1 response 
Dear philosophers,
I really appreciate your website, which I just discovered!
I'd like to make one comment regarding the recent questions about infinite sets on March 7 and March 14. In your responses (Allen Stairs and Richard Heck on March 14), you... 
Mathematics 

Question posted on March 14, 2013; 3 responses 
Hi, I was hoping for some clarification from Professor Maitzen about his comments on infinite sets (on March 7).
The fact that every natural number has a successor is only true for the natural numbers so far encountered (and... 
Mathematics 
