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
9
votes
2
answers
9k
views
What's the difference among the logical relations :=, =, and ≡?
I understand that ≡ is logical equivalence, "iff". '=' is a symbol for numerical equivalence. And ':=' is an identity claim. I often only see '=' and ':=' used with variables and names, ...
- 848
2
votes
4
answers
261
views
How to give proof for Q ∧ R with the premisse ¬(¬¬¬P ∨ P)?
I'm trying to use Fitch to get to an answer, but I'm really confused right now. Can someone help?
- 23
3
votes
4
answers
4k
views
Anyone can help me with proving ~(AvB) |- ~(BvA) via natural deduction?
~(AvB)
ㅡㅡㅡㅡ
~(BvA)
I have to provide a derivation to establish validation of this argument.
First of all, can I first change ~(AvB) into ~A&~B by using the De Morgan rules?
And the second is:...
- 31
2
votes
4
answers
6k
views
Conditional disjunction equivalence proof using FItch
Prove P v Q ⇔ ¬Q → P
So far I have the obvious things...
1. P v Q
_
| 2. ¬Q
| _
| 3.
| 4.
| 5.
| 6.
| 7.
| 8. P
9. ¬Q → P → Intro 2-8
I think the problem here is that I do not ...
- 347
4
votes
2
answers
167
views
help with deductive proof
∀x (Fx ∨ x=c), ¬Fb ∧ Gb |- ¬Fa → Ga
So far I don't understand how to switch variables around to prove the result.
I've got a subproof set up assuming "¬Fa" in order to derive "Ga".
In that proof I ...
- 153
1
vote
6
answers
379
views
How to prove that (P v (P ^ Q)) iff P?
How to prove (P v (P ^ Q)) ≡ P? I am not sure how to get rid of proposition Q. I am allowed to use Leibniz and apply Substitution. I already came across most calculation rules in the book: ...
- 133
4
votes
3
answers
2k
views
Disjunctive Syllogism in a Fitch Style System
I'm trying to prove an argument of the form:
B
~(C & B)
Therefore: ~C.
I can expand out ~(C & B) into ~C OR ~B, and with the premise B, it is clear that ~C is the case.
...
- 163
1
vote
3
answers
770
views
What are the rules for discharging a premise in a Zero-Premise Deduction?
If I have the problem (A → B) v (B → C), is there a way to prove this from no premises without first using Material Implication to convert the statement into ¬(A → B) → (B &...
- 11
3
votes
3
answers
4k
views
Prove P v ~P using most basic rules?
Is there a way to prove P v ~P in basic inference rules?
I can't think of where to start because nothing applies to this. I was thinking about usinig Conditional proof, but I don't know what should I ...
- 155
1
vote
5
answers
1k
views
What branch(es) of philosophy use symbolic logic as a fundamental tool?
I have been reading this book about philosophy of language by A. Miller": the discussion of Frege and Russell are excellent, using logic symbol to introduce ideas. However, the remaining chapters do ...
- 189
4
votes
2
answers
242
views
Can knowledge about argumentation be sufficient for philosophical logic without too symbolic or mathematical concepts?
The most important element for expression of truth is trough an argument, with premises and conclusion. Argumentation requires to avoid fallacies and adhere to the truth. However logic if treated as a ...
- 173
20
votes
11
answers
21k
views
What is the difference between Law of Excluded Middle and Principle of Bivalence?
Law of Excluded Middle:
In logic, the law of excluded middle (or the principle of excluded
middle) is the third of the so-called three classic laws of thought.
It states that for any proposition, ...
- 987