Questions tagged [symbolic-logic]
For questions related to symbolic logic, also known as mathematical logic. Topics might range from philosophical implications of metamathematical results to technical questions.
327
questions
3
votes
3
answers
290
views
How do you prove that a logic system is sound?
I am aware of the fact that a logic system must be sound, in order to be useful. However, I am not sure, about how, after setting up or coming up with the basic logic axioms that make up my system, I ...
0
votes
0
answers
112
views
Some Questions About A Truth Tree
The logical system used in this post is first-order logic.
I’ve been reading Introduction to Logic: Predicate Logic, 2nd edition by Howard Pospesel, and I have some questions concerning a truth tree. ...
- 53
0
votes
1
answer
187
views
Philosophy books for mathematicians
Are there any books on philosophy that make relatively heavy use of math? I'm not looking for anything on formal epistemology, logic, or philosophy of math. Two examples of books that fall in the ...
- 141
2
votes
1
answer
73
views
Sentential Interpretation in P. Suppes (1957)
Patrick Suppes gives a working definition of sentential interpretation, based on a sentence maintaining its form. By working definition, I mean an incomplete definition that is needed for someone to ...
-4
votes
1
answer
154
views
Hi! I'm 99% sure my formal argument is valid, but can you check? [closed]
I wrote this argument, and while i'm sure it is valid, it has been awhile since I've done basic logic.Thanks!
- 46
0
votes
1
answer
86
views
Question from predicate logic exam: Given model with the domain D = {a,b}, say whether the formulas listed below are true or false
I've got a logic exam coming up and one of the question types is puzzling to me. If anyone could help me by explaining what this is about to me, I would appreciate it greatly.
Note: I was unable to ...
- 1
1
vote
2
answers
203
views
When does a mathematical predicate have a truth value?
Say we have a predicate in a domain of real numbers, P(x), 2x+10=20 we know that we can existentially quantify this and say that the value x=5 makes this true, but we cannot talk about P(x) being ...
- 1,191
0
votes
0
answers
195
views
What is mathematical analysis?
Hilbert's aim to reduce all mathematics to finite logical system was shown impossible by Goedel. He did mathematical analysis of logic itself (Goedel numbering). Turing defined algorithms, and ...
- 1,139
2
votes
1
answer
268
views
Willard Van Orman Quine: Elementary Logic Exercises 1: Which of the following are statements?
I am currently self-studying formal logic via Quine's "Elementary Logic." The first exercise is to declare which of the following sentences are statements and re-write the sentences that are ...
- 21
0
votes
1
answer
66
views
Semantic consequence and Sound Argument
Is that correct to say that semantic consequence is equivalent to the concept of sound argument in classical propositional logic?
If it is the case, arguments or theories with contradictory premises ...
0
votes
1
answer
91
views
What context do quantifiers make valid expressions?
Say I have a formal language such that x is an individual constant and symbolically has a particular value (say 2) a proposition such as x+1=3 already has the value of true, and I cannot define a ...
- 1,191
2
votes
3
answers
394
views
What is the nature of the term 'variable', and is it used differently in math, computer science, and logic?
Say I'm given an expression and talk about x changing what do we really mean by this linguistically? What inferences can be drawn about the nature of variables from their practical usage?
When we talk ...
- 1,191
-1
votes
3
answers
1k
views
Proof for "⊢ (A → ¬¬A)"
I've spent 4.5 hours on this, with no exaggeration. I clearly have no idea what I'm doing here, and it's become a serious time sink. If any of you could help in proving this, I would be eternally ...
- 15
-1
votes
1
answer
111
views
Help with proving: P, ¬(Q ∧ P) ⊢ ¬Q
Here's the issue, there's no usage of derived rules allowed. So no DeMorgan's Law. All that's allowed is the basic TFL elimination/introduction rules, IP, (e)X(plosion), and ⊥. I'm absolutely lost on ...
- 15
1
vote
0
answers
130
views
Nested Quantifiers Proof - Logic
When I prove this: -∃x.P(x) ⊢ ∀x.-P(x) [True]
I did it like that:
∀x.-P(x) ⊢ ∀x.-P(x) because (negative ∃) -∃x.P(x) becomes ∀x.-P(x) so that we can say that it's true.
However, I didn't ...
- 11