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.
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Does quantifier dependence involve putting ∃ before ∀ (or vice versa)?
I don't know why I'm having such trouble getting the gist of the SEP article on independence-friendly logic, but I am. I also remain perplexed about a comment I received on the MathOverflow about the ...
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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 ...
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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 ...
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Help with formalization of argument (ignore premises) in FOL
I am trying to formalize the following argument:
Every Moral theory is equally valid.
There always can get a new moral theory from another one.
For something to be metaphysically real/exists it must ...
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What is 'expendable' in logic and how to explain 'tautology' given this image?
This image is from http://www.nfillion.com/index.php/teaching/9-logic-112. According to this, a proposition can have 4 basic properties: (1) necessarily, (2) not possibly, (3) missing, and (4) ...
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Is there a symbolic formulation of modal realism?
Is there a symbolic formulation of modal realism, i.e. the doctrines of modal realism captured in some formal system?
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Are "A ∧ A" and "A ∨ A" degenerate expressions?
Although some time ago I had become somewhat familiarized with the notion of degeneracy in mathematics and physics, in my musings on the trivial/nontrivial distinction I found that both Wikipedia and ...
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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 ...
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How can sequences/expressions occur in other sequences/expressions?
I know I specifically wrote a question about Wetzel, however I do not want to invalidate previous answers.
In Quine's 'Mathematical Logic' he discusses occurences of 'expressions' in other '...
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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 ...
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Is there a non-transitive frame in which schema 4 is true? Or an irreflexive frame in which schema T is true?
So, I know that I can construct a frame {W, R, I} which is not transitive and in which schema 4 is not true (more specifically, Axiom Schema K and Axiom Schema 4 are not both true). I also know that I ...
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fitch proof. P v Q, Q→ ¬ R, ¬ P, ¬ R → ¬ S GOAL: ¬ S
Need help exercise using the FITCH program format. I'm stuck on where to start. The following 4 steps must be used to prove the goal.
P v Q
Q→ ¬ R
¬ P
¬ R → ¬ S
GOAL: ¬ S
Now I know: ¬ P and P v Q ...
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Is there a semantically complete system of direct-method natural deduction/sequent calculus?
Does anybody know of a system of direct-method natural deduction/sequent calculus, in other words, a system that does not require (or even incorporate) conditional (and indirect) proof method(s) and ...
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Semantic expressiveness of modal logic
I am wondering how much of the semantic of basic philosophical questions can be expressed by formal arguments in modal logic. Here is one argument I formalised myself:
P1 ◇ ∀a, ∃x // GNB(x, a) ∧ C(a)...
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What does philosophy say about the normativity of simulated thought within the analytical tradition?
Given the coherence theory of truth, new propositions must observe previous theory and logic (i.e. every thinking step must be consistent with rules of logic); many analytic philosophies believe it is ...
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Recommendation: Second Order Logic textbook
I'm looking into Universalist Realism, Nominalism, Trope theory and the application of Second Order logic to each of them, however I have little/no experience with Second Order logic. Please let me ...
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How did Fitch's opposition to the Russell-Whitehead theory of types turn out since the 1950's?
In a footnote to Appendix C of Frederic Fitch's Symbolic Logic (page 217), Fitch writes about his article, "Self-Reference in Philosophy":
It is reprinted here in order to indicate more fully my ...
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What is (∃!e) in Davidson 1967?
Davidson proposes a causal law for singular event causation. Here is one example of a backward-looking part of such a law (changed slightly for clarity and to avoid copyright infringement):
(e)(u)((...
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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 = √�...
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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 ...
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Are there only two levels in languages, meaning and symbols?
Say in my language I have a 'variable x', in my language the symbol x represents a (variable) number, so at a level of meaning it is an object, and at a level of symbols 'x' is simply a set of lines ...
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Need help with this Symbolic Logic Proof please
I am having trouble solving this proof. Line 5 is wrong, I know it's Demorgan's Law, but the proof machine doesn't accept that as an answer. I think it only accepts ~Elim, vElim, vIntro, ~Intro, &...
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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. ...
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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 ...
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Proving validity/invalidity of a modal argument
□(A v B) → (□A v □B) ...(1)
This symbolic argument is intuitively invalid. In (1), if we replace B with ~A, then we see that though the antecedent is necessary, the consequent is a contradiction since ...
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How to represent "apart from" formally?
While working on an argument over the last few days, I came to a point where I needed to formally render an "even if" sentence. Here and here, I found some good options, but I'm not sure I ...
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how to translate the following sentence
Either it is not the case that Gonzolo play music and does not go to concert,or it is not the case that he does not read book and does not play football.
P:Gonzolo play music , Q: Gonzolo go to ...
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Truth function question
Is there a truth function connective for the phrase “after all”
I know “all” can be done in finite cases
I am using the Logic Book 4th ed
I am trying to find a paraphrase for it.
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Alphabetic Substitution, Barcan, and Strict Implication
Context: I'm stuck on Axiom 8 from the introduction to Barcan 1946, "A Functional Calculus of First Order Based on Strict Implication." My instinct is that I'm missing a basic, perhaps obvious concept-...
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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 ...
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How to define a new logical language
There are a number of logical languages defined that are so called flavors of a certain logic (for example, flavors of First Order Logic). Such new logical languages sometimes extend or restrict the ...
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Help with natural deduction by introduction and elimination rules
This is where I’ve gotten so far. I’ve proven it from left to right but I’m getting some trouble proving it from right to left. I’m trying to reach the conclusion by double negation.
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Predicate logic proof solve
Provide a proof for the following using FOL in forallx
Use the natural deduction system and proof strategies in forallx to provide a formal proof for the following . Please provide a picture of your ...
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Fitch proofs help?
I'm new to logic and can see how to write these out informally, but need some help seeing how they should be translated into formal proofs in Fitch.
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A question about possibility
If A, then B
~ A
So, possible that B
Valid or not?
My take: Not valid.
Reason:
Valid means if all the premises are true, the conclusion must be true
That means adding new information should not ...
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Formal Proof with Quantifiers
∀x ((Cube(x) ∧ Large(x)) ∨ (Tet(x) ∧ Small(x)))
∀x (Tet(x) → BackOf(x, c))
∀x ¬(Small(x) ∧ Large(x))
goal: ∀x (Small(x) → BackOf(x, c))
How would one prove ∀x (Small(x) → BackOf(x, c)) in a formal ...
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Is Classical Logic the proper model of the deductive logic of human reasoning?
Which mathematicians and philosophers unambiguously claimed that Classical Logic was the proper model of the deductive logic of human reasoning, and when did they say it?
The expression "Classical ...
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