# Questions tagged [logic]

Use this tag for general questions about logic that are not categorizable under some more specific tag, like "mathematical logic", "informal logic", "classical logic", etc.

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### Can modal logic be used to prove transitivity of equality isn't true in general?

In a related thread I argued using modal logic, that the correct form of universal instantiation is: ∀x [P(x)]; therefore P(α), where α is an arbitrary constant. Definitions C is a specific constant ...
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### What is the proper form of universal instantiation?

Definitions C is a specific constant iff ∃! x [x=C] C is a general constant iff ∀x [x=C] C is an arbitrary constant iff ∀x [x=C] ∨ ∃! x [x=C] Consider the commonly accepted form of the rule of ...
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### Is there a bright line between epistemic and necessary truths?

Given my understanding of epistemic and necessary truths it seems plausible that I can construct epistemic truths using only necessary ones, which feels contradictory. Eg 1 + 1 = 2 is a necessary ...
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### Wittgenstein and formal relations

We can speak in a certain sense of formal properties of objects and atomic facts, or of properties of the structure of facts, and in the same sense of formal relations and relations of structures. (...
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### Is Frege's axiom of unrestricted comprehension actually true after all?

Consider the following demonstration whose first line is the assumption called the axiom of unrestricted comprehension. ∀F∃y ∀x[x ∈ y iff F(x)] [OSC1] ∀F∃y [α ∈ y iff F(α)] [UI] ∃y [α ∈ y iff α ∉ α] [...
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### On the difference between a meta-variable and a propositional atom

In all of the established propositional logics that I’m aware of, a propositional atom is treated as a meta-variable. In certain first-order proof systems, this does not hold for those same logics ...
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### Nagarjuna's concept of self to logic?

I'm trying to reduce Nagarjuna's concept of self to logic. However, I'm new to logic and not an expert in Tibetean Buddhism. Is this a close fit? ∃x (S ∃¬x) I'm reading it as: If "S" ...
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### Discussion about Graham Priest's dialetheic views on Eastern and Western philosophy

Australian philosopher Graham Priest is famous for advocating Dialetheism, the view that there are true contradictions. Dialetheism goes against the law of non-contradiction. This gives rise to the ...
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### Axiomatic and formal establishment of Plato's dialectics

After years of studying Plato I have seen some attempts to formalize somehow Plato's dialectics. To be more precise, I have found writers who present Plato's dialectics (especially as it is presented ...
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### Statement Vs Proposition Vs Premise Vs Assertion

I have spent a few days running around the internet trying to find a distinct and simple explanation of how all of these terms fit together. I'm aware it is quite nuanced. Could someone help me ...
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### Can the entirety of first order logic be reduced to the propositional calculus?

I've been wondering, whether or not first order logic can be reduced to the propositional calculus. Rosser's system RS_1, described by Irving M. Copi in 'Symbolic Logic', has 5 axioms or postulates: ...
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### Why "guilty" or "not guilty" but not "guilty" or "innocent"?

Why do some courts (like those in America) decide through the dictum "guilty"(g) or "not guilty"(~g) instead of using the term "innocent"(i) for "not guilty"(~g)...
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### does Hegel's Dialectical Materialism needs justification when we re-examine the notion of "opposite" and whether that's a fact of the world?

Hegel basically says thesis-antithesis-synthesis, and this works because there are opposition of ideas or there are contradictions Derrida also uses concepts like "binary oppositions" he ...
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### Liar's paradox, dialethism and law of excluded-middle [duplicate]

I've been reading about liar's paradox and its responses. I like Graham Priest, fantastic philospher and proponent of dialethism. Graham argues that liar's paradox is solved by claiming that statement:...
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### Is Peirce’s Law seen as a principle for relevance logics?

As far as I can tell, ‘relevance’ is a bit of a nebulous term depending on which logicians you ask, but that each of them has a rigorous view of what it means. Consider the formula known as Peirce’s ...
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### Can modal logic be used to define the notion of an “arbitrary constant” in FOL?

I was wondering if first-order logic can be reduced to propositional calculus if we eliminate quantification. For example, instead of saying “for all x in a domain D, P(x)”, we could state “P(x)” for ...
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### What is the difference between a model and an interpretation in logic?

On page 319 of Irving M. Copi's 'Symbolic Logic', he states, "if we want our logical system to be applicable to any possible universe, regardless of the exact number of individuals it contains ...
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### The validity of the reasoning in Halting Theorem

Here is an example of the Halting Theorem from Wikipedia (Halting Problem) Christopher Strachey outlined a proof by contradiction that the halting problem is not solvable.The proof proceeds as ...
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### Can the Good Samaritan problem of deontic logic be resolved by reinterpreting the deontic obligatory operator as the modal necessity operator?

The Good Samaritan problem of deontic logic It seems true that the starving ought to be fed. Now if the starving are fed then there are starving people. By a standard axiom of normal deontic logic ⊢ ...
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### If some one believes that nothing really matters but he still seeks love [closed]

If someone believes that nothing really matters, but he still seeks love even though he thinks that even the love he seeks doesn't matter and doesn't have meaning, but he can not stop the urge of ...
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### The Pragmatic Maxim as a Maxim of Logic? [closed]

Why does the Wikipedia entry on the pragmatic maxim describe it as a "maxim of logic"?
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### Can we define a logical constant to be a symbol that has the same meaning in all minds? [closed]

I just looked up the definition of "logical constant" in Wikipedia, and I came across the following definition: A logical constant is a symbol in symbolic logic that has the same meaning in ...
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### What are the meanings of 'all' and 'only' in the paradox of the barber?

Barber's Paradox In a certain town there is a barber who shaves all those who don't shave themselves, and only those who don't shave themselves. Who shaves the barber? Let b denote the barber. Let x-...
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### Negating the verb and negating the subject 's property

What is the strict and exact relation (implication, equivalence etc.) between these two sentences?: I. Alcibiades is not wise. (Negating the subject 's property) II. Alcibiades is not (=isn 't) wise. (...
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### What is the reason behind the fourth axiom in Gödel's ontological proof?

In Gödel's ontological proof, axiom 4 goes like this: And I'm not sure about what it means. If that P(φ) is true, then isn't it necessarily true as well? There's some basic concept about modal logic ...
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### What does it mean to say that two theorems (provable statements) are 'equivalent'?

sometimes one sees/reads assertions such as "[the bounded inverse theorem] is equivalent to both the open mapping theorem and the closed graph theorem", but taken formally and literally this ...
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### How can you derive Conjunction if your only underived rule of inference is modus ponens? [closed]

Suppose you are working with a logistic system for the propositional calculus that only has one underived rule of inference, namely Modus Ponens. How can you derive Conjunction in it? Rule 1: A, if A ...
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### Why should I not believe there are true contradictions?

Kane Baker has a YouTube video in which he introduces the word 'wulture'. 'Wulture' applies to all things that are vultures, and excludes all things which are white. Delia is a white vulture. He asks: ...
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### Can assumption in Hilbert style proof system be contradictory?

⊢（¬A→A）→A I don't know how to solve this proof with the Axiom, Theorem and Inference rule in Hilbert-style proof system so I ask my classmate and he show me his answer. After viewing his proof, I was ...
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### Vacuous truth in non-classical logics

Does the notion of a vacuous truth exist in non-classical logics as well? I'm thinking of logics inspired by intuitionism, which assign great importance to constructive proofs.
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### Relationship between Structural Contraction and the Absorption theorem?

Edit: Originally I called the absorption theorem “contraction theorem” which makes everything needlessly wordy and confusing. I will call the left structural contraction rule simply LSC rule, and the “...
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### Can Frege's axiom of unrestricted comprehension be slightly modified to avoid the Russell paradox?

Russell showed that Frege's axiom 5, the principle of unrestricted comprehension is false, by considering the set of all and only sets that aren't elements of themselves. It's my suspicion that that ...
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### How do complex propositions and Aristotle's logic work?

Is it allowed to create a syllogism with complex propositions? Here is my example where P is a sequence of actions and M is a final cause. S = "Cake maker" P = "Finding of ingredients, ...
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### Help with a derivation problem

I am having trouble with this derivation. if anyone could help me that would be great ~T->(~P → ~R). (R → (~T → P)) → (~Q → ~S). ~S → (~Q → S) therefore Q
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### Is this Barbara syllogism of a final cause right?

Hi i'm trying to learn how to make an explanation of a final cause in the form of a Barbara syllogism but I don't know if I have the terms in the right order. The Barbara definition I'm using is from ...
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### Logical form, Wittgenstein

The question is going to be about TLP, not Philosophical investigations. I know that a logical form of a proposition can't be represented in the proposition itself. But can it be represented by the ...
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### Did God "design" logic? [closed]

Note, this question doesn't require belief in God, but it helps me formulate the question. Is the following statement a possible truth: He decided that 2 + 2 = 4*. He could have made it so that 2 + 2 ...
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### Wittgenstein and the possibility of expressing a logical form

Why did Wittgenstein in TLP considered the "logic of facts" and a logical form inexpressible? If I'm not mistaken, he himself a lot of times was trying to describe a logical form in his work....
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### Are all languages universal?

I am reading the book titled 'A Companion to Philosophical Logic,' where I gained insight into how logic serves as a tool for representing our thoughts, which are expressed in natural language. In my ...
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### Is there a set theory which implies the interval [0, 1] but no more?

A deductive system (as a collection of judgments and rules of inference) can be used to describe something commonly called a “set theory”. We can imagine a priori there are certain properties we would ...
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### Theory build on the top of a Logic

Could somebody elaborate the meaning of following statement from wikipedia concerning intrinsical differences between set theory and type theory: Unlike set theories, type theories are not built on ...
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### Can a function have a set as its value? [closed]

In relation to his possible worlds analysis of natural language conditionals (e.g. 1975 Indicative Conditionals) Robert Stalnaker posited a function which takes an antecedent proposition and a ...
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### The logic of facts

The possibility of propositions is based upon the principle of the representation of objects by signs. My fundamental thought is that the “logical constants” do not represent. That the logic of the ...
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### Is there a limited number of 'pragmatic' logic rules?

What you have cited is a pragmatic limit, as you have not seen logic systems with more than 8 or so precepts. IF there were such a limit to precept quantity, then YES there would be a limit to the ...
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### Is there an infinite number of logic systems?

Is there an infinite number of logic systems? To answer that question you need to determine what the lego blocks are. To my knowledge, the only lego blocks that exist that make up logic systems are ...
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### What does "free" mean in "free logic"?

An anonymous person and I are debating how we should translate "free logic" into Korean. They suggested "자유 논리(自由論理)" and I suggested "빈 논리(빈論理)." The noun "논리(論理)&...
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### Wittgenstein on sense

What's sense according to Wittgenstein? I think I might have missed the definition in TLP, but I can't find it anywhere. From the context it's obvious that Wittgenstein's sense isn't that of Frege. ...
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### Bayesian conditional probability and material implication

I was reading E. T. Jaynes' Confidence Intervals vs Bayesian Intervals (available here), and I came across this statement regarding Boole's The Laws of Thought: Boole's own work on probability theory....
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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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