Tagged Questions
2
votes
1answer
58 views
Materials for studying logic
I am looking for study and beginner material to study mathematical logic. I understand that it is a very broad topic but I would like to know what the best path there is to learning mathematical ...
0
votes
0answers
70 views
mathematical logic and valid ways of reasoning
I'm curious about what math (mathematical logic, metamath) says about the way we reason. This is going to be a vague question because I have not yet explored mathematical logic myself. My question: ...
22
votes
7answers
1k views
Does mathematics require axioms?
I just read this whole article:
http://web.maths.unsw.edu.au/~norman/papers/SetTheory.pdf
which is also discussed over here:
Infinite sets don't exist!?
However, the paragraph which I found most ...
-2
votes
1answer
103 views
What branch of mathematics improves logical thinking? [closed]
So, that's the question. I dare to generalize it even wider: what branch of mathematics improves the general thinking ability, intilligence, the way the person thinks, and makes it more logical? I'm ...
7
votes
3answers
113 views
Measure of how much information is lost in an implication
In an implication like $p \implies q$, is there some measure of how much information is lost in the implication? For example, consider the following implications, where $x \in \{0,1,\ldots,9\}$:
...
4
votes
3answers
176 views
Does learning logic and set theory before arithmetic, algebra, and geometry have an advantage?
I'd like to become conversant in a wide variety of serious mathematics, but i'm currently one of those students who did very poorly on mathematical subjects in school, never completing even basic ...
15
votes
5answers
998 views
Is 1+1 =2 a theorem?
A theorem is defined to be a mathematical statement that is proven to be true. The statement $1+1=2$ has definitely been proven in the history of mankind (Russel and Whitehead had once proven it in ...
37
votes
12answers
2k views
Is there such a thing as proof by example (not counter example)
Is there such a logical thing as proof by example?
I know many times when I am working with algebraic manipulations, I do quick tests to see if I remembered the formula right.
This works and is ...
7
votes
1answer
86 views
Independence results that cannot be established by forcing.
I read the Wikipedia article on Absoluteness recently and found mention of Shoenfield’s Absoluteness Theorem, which states that if $ \phi $ is any $ \Sigma^{1}_{2} $- or $ \Pi^{1}_{2} $-sentence of ...
2
votes
1answer
110 views
Is my book a good introductory one?
I attempting to study logic by myself, I acquired the book A mathematical introduction to logic by Herbert B. Enderton, I want to ensure that this is a good introduction so, is this a good ...
1
vote
1answer
47 views
Uniform continuity on empty set.
Let $\langle X,\rho \rangle$ be a metric space and $f:\emptyset\to X$ a function. Since $\emptyset$ is compact, I know that $f$ is uniformly continuous. But can it be proven by vacuous truth? It's the ...
1
vote
4answers
124 views
Would it also be useful to include an ordered pair function in first order logic?
Typically, first-order logic is assumed to include an equality relation $=$, even though this is "non-logical," together with some postulates about equality.
Would it also be useful to include an ...
2
votes
1answer
80 views
Successor axiom systems and sequences of axiom systems
Let $A$ denote a system of first-order axioms. Is there a canonical way to form a successor system $A'$ extending the ontology of $A$ to include all definable collections?
Edit: Importantly we want ...
1
vote
1answer
41 views
How often do incomplete types meet the hypotheses of the omitting types theorem?
I find the following formulation of the hypothesis (namely, non-isolation) for the omitting types theorem. A type $p$ over $T$ is "isolated" iff there is a formula $\phi(\vec{x})$ such that $\exists ...
8
votes
4answers
302 views
How to introduce advanced set-theoretical objects to philosophy students?
First, I apologize if MSE is a bad fit for this question. I'm going to give a course as the last course of "elementary set theory" (the previous courses were not given by me). I planed to introduce ...
