# 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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### Would an erotetic operator be equivalent to its own demi-operator?

"Recap": demi-operations are e.g. "the square root of negation" in experimental(?) logic. (The association of demi-negation with using imaginary numbers as truth values is a little ...
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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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### Why not just give up on the idea of truth-functionality?

I understand that today only a minority of academics who are specialised in formal logic accept the horseshoe (aka "Classical Logic" or "First-Order Logic") as an accurate, or even ...
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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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### 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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### 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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### 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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### 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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### 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 ...
1 vote
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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 ...
1 vote
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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 ...
1 vote
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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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### 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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1 vote
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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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### If X is a statement, is the collection of all interpretations of X a set?

Let X be a statement Let SI be the predicate set of interpretations of X Let IX be the predicate interpretation of X Let NA be the predicate not contained in A ∃A∃B(SI(A)∧IX(B)∧NA(B))→∀A∃B(SI(A)→...
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### What is the significance of the Coincidence Lemma?

There is not a Wikipedia article about the coincidence lemma. I will try to explain the proof and then ask why it is important. The coincidence lemma is meant to show that the satisfaction relation ...
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### Which is correct, "the implication A → B" or "the implication ‘A → B’"?

Which is correct? The true (or false) implication A → B. The true (or false) implication ‘A → B’. What are the arguments for saying that it is wrong to say: the implication A → B and the we should ...
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### Is it possible to stick to one of these viewpoints of variables?

It has been a struggle to find a precise account of the concept of variables. There are however two viewpoints that I've seen authors convey in several logic textbooks. Variables as placeholders for ...
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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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### 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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### 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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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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### Is equality necessarily transitive?

Consider the equation b2 - 1 =0 If b is a variable, it's neither true nor false. So let the symbol b be a constant, thus the equation denotes a proposition. The symbol b is a referrer, and the ...
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