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
0
votes
0
answers
46
views
How would demi-conditionals work?
Let 𝒜 = an actuality operator and √→ be demi-if. Which, if any, of the following conversions would go through?
𝒜A √→ 𝒜B = √𝒜A → √𝒜B
𝒜A √→ 𝒜B = √𝒜A → 𝒜B
𝒜A √→ 𝒜B = 𝒜A → √𝒜B
𝒜A √→ 𝒜B = √�...
- 16.7k
0
votes
1
answer
66
views
Correct way to write statement using symbols?
I would like to write the following using logic symbols but am unfamiliar with the practice. Here is the statement:
If it is accepted that life will arise from matter given the right conditions
and if ...
user63267
2
votes
0
answers
23
views
Does a function assigning any sentence to some 𝘢th-order logic exist?
I feel like I'm just reinventing Tarski's wheel with this idea, or maybe I'm even remembering what I've looked over with respect to Tarski's undefinability thesis and phrasing it in a way that ...
- 16.7k
3
votes
1
answer
155
views
Modal system K - prove ⊢ (□p ∨ □q) → □(p ∨ q)
I am trying to prove the following:
⊢ (□p ∨ □q) → □(p ∨ q)
However, I think that I am lacking the knowledge of a tautology in classical logic that would help me prove this.
I tried something, but it ...
- 133
0
votes
2
answers
112
views
Axiomatically prove □(A ∨ ¬B), ¬□A, ⊢ ◇¬B in modal system K
This time I have a more "complex" problem at first glance. I need to create a direct proof using the axioms of system K and rules of inference, but I have been unable to do so.
□(A ∨ ¬B), ¬��...
- 133
3
votes
2
answers
333
views
Proof of □P ⊢ □¬¬P in modal logic system K
I need to prove the aforementioned formula in modal logic system K, which I am having trouble to do.
Of course, this should be easy to prove if I had access to axiom T, but since it's system K, we can ...
- 133
1
vote
0
answers
58
views
Is Nozick's Experience Machine self-defeating?
Nozick's experience machine is usually described as able to bring about any desired experience. If it can't do that, then it's not a suitable object for the thought experiments Nozick and others build ...
- 1,586
3
votes
1
answer
136
views
What are the arguments of philosophers against the reasoning which justifies the horseshoe from truth-functionality?
There is a reasoning in mathematical logic which is meant to prove that the horseshoe is the only logical operation which fits our notion of conditional.
The reasoning starts from the idea that the ...
- 8,363
1
vote
3
answers
118
views
From English Sentence to Symbolic Logic: "The Happiest Person is not named John"
Suppose that x is over the domain of all things and I have the following predicates:
H(x) = x is a person, J(x) = x is named John, F(x,y) = x is happier than y, a = John Smith
My interpretation of ...
2
votes
1
answer
41
views
Question regarding the stipulated 'domain of discourse' for models of first-order sentences
Assume 'S' is a first-order sentence about a subject 'Z'.
When one stipulates a Model for 'S' with a domain 'D' does one always assume that the domain will contain all the objects within the subject '...
- 79
1
vote
0
answers
40
views
Zero-one laws Model Logic, question regarding significance of domain size
Wikipedia informs me that:
Essentially (correct me if I'm wrong) the result states that as the domain of objects (domain of discourse) grows (n->inf), a static first order sentence (S) will be ...
- 79
10
votes
7
answers
3k
views
What did Russell mean when he wrote that the null-class, the class having no members, did not exist?
I am not quite sure I interpret the following sentence correctly in Bertrand Russell's paper on existential import:
and among classes there is just one which does not exist, namely, the class having ...
- 8,363
2
votes
0
answers
72
views
Questions about Feature Placing Languages/Predicate Functor Logic
About a year and nine months ago, I poses a question here about Quine's predicate functor logic and ontological nihilism. I'm still having trouble wrapping my head around these ideas. I hope someone ...
- 384
3
votes
3
answers
101
views
Is it a rule of formal languages that all occurences of a symbol must 'refer' to the same object?
A rule of subsitution is that we replace all free occurences of a symbol x with free occurences of a symbol y to subsitute y for x in a formula φ.
Hence the sentence 'x=x' is inherently true for all x ...
- 1,191
1
vote
1
answer
101
views
How can I formalize the argument that morality cannot exist, in FOL?
I am trying to formalize the following argument:
Every moral theory is equally valid.
One can always get a new moral theory from another one.
For something to be metaphysically real or to exist, it ...
- 115