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Questions tagged [logic]

Logic is the study of formal systems of reasoning, especially of the deductive variety. It is one of the few fundamental philosophical subdisciplines, along with metaphysics, ontology and aesthetics. Logic has taken on considerable importance in recent mathematical developments, and one of the concerns of [tag:philosophy-of-mathematics] involves the role, extent and conceptual architecture of various kinds of logical or formal axiomatic systems.

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How much the world is logical

In her book The Art of Logic in an Illogical World, Eugenia Cheng writes:"I have already asserted the fact that nothing in the world actually behaves according to logic. So how can we use logic in the ...
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Justification of existing methods of formal logic

What is it that mathematicians, and more likely perhaps philosophers, give as an explicit justification that any method of formal logic, which is actually used by mathematicians, or even by automatic ...
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Classical logic, symbolic logic, higher-order logic, First-order logic? Learning from scratch

I'd like to ask you a question about logic. I study philosophy in a Spanish christian university. In the first year, we study logic but it's the classical one, following Aristotlé's Organon, the ...
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How would i go about using natural deduction to prove this argument is valid?

How would I use natural deduction to prove this argument is correct? It's always either night or day. There'd only be a full moon if it were night-time. So, since it's daytime, there's no full moon ...
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What irreducible functions constitute thinking?

Because all new knowledge, to be not illogical, must obey logic i.e. every thinking step must be consistent with rules of logic; so can we write an effective procedure/algorithm which may be followed ...
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Is there a natural example of a non-self-referential semantic paradox in philosophy?

A commonly studied paradox is the liar's paradox. The liar's paradox is to determine whether "this statement is false". The usual resolution is to state this the sentence is not actually a statement ...
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Validity of a modal argument?

Would you say that the following argument is valid? And if not, why exactly? For all we know, A may be the state of B; What C does is determined by the state of B; Therefore, for all ...
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What does Tarski mean when he says that truth is a property of sentences?

A fundamental statement of Tarski's Theory of Truth is that truth is a property of sentences. What does this statement mean? What kind of Truth is it referring to? What is the formal definition of '...
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Finding desirabilities and probabilities in Jeffrey's Logic of Decision

I'm trying to solve problem 16 (Ch. 5) of Jeffrey's Logic of Decision. The problem says: Suppose that A and B are pairwise incompatible propositions, and suppose that the preference ranking is as ...
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What fallacy is this?

I am curious about what fallacy the following kind of reasoning represents. Let's say we are questioning if something is true. I would argue that in order for us to question if something is true we ...
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What is the difference between depth and surface information?

I was looking for an answer to this question: Was Euclid's method of proof axiomatic? While doing so I ran across an abstract of Jaakko Hintikka for an article "What is the axiomatic method?" ...
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Descartes on Llull's logic

I recall from readng long ago that Descartes described Llull's logic as something that would allow one to speak on many subjects without knowing any of them That quote from Bonner, Art and logic ...
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How to get the refutation of (OP ⊃ OQ) ∴ O(P ⊃ Q) in Deontic Logic

In Deontic Logic, one could easily infer "If it is obligatory that P, then it is Obligatory that Q", from "It is obligatory that if P then Q" O(P ⊃ Q) ∴ (OP ⊃ OQ) Where the ⊃ is an implication (...
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Name of Principle Giving Precedence to a More General Hypothesis

As far as I know, there is a principle that gives precedence to a theory that is more general than a more specific one, i.e the more general one is more acceptable. What is the name of that principle?
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Is this an example of Denying the Antecedent?

Is this an example of Denying the Antecedent? Harry is not an inexperienced driver, and thus must not be irrational, seeing as all inexperienced drivers are irrational. At first, I thought it was ...
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Is this an example of Undistributed Middle?

Is this an example of Undistributed Middle? John is not a teenager, since all teenagers are impulsive, and John is not impulsive.
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Is deduction based on induction?

I'm wondering if deduction is in the end based on induction. The problem of induction discovered by the Scottish philosopher David Hume is quite well known. On the other hand, it's commonly supported ...
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Are there logicians who argue that knowing and believing are NOT amenable to formal study via modal logics?

Vincent Hendricks and John Symons notes the following about epistemic logic: Epistemic logic gets its start with the recognition that expressions like ‘knows that’ or ‘believes that’ have ...
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Interpretation and symbolic notations of operations in mathematics

As we know a mathematical operation is a function. And a function is a special type of relation. Ultimately a relation is a set of ordered pairs. For example, what is addition of natural numbers? At ...
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What's the fallacy of relevance here?

To know absolutely that there is no God one must have infinite knowledge. But to have infinite knowledge one would have to be God. it is impossible to be God and an atheist at the same time. Atheists ...
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How to prove : P v ( P → Q ) by Natural Deduction

Another of Tomassi's exercises I can't solve (Logic, page 109, Revision exercise III, 9) : P v ( P → Q ) I have to use natural deduction and the only rules I know are: • assumptions, • modus ...
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Is an inductive premise an empirical premise?

Is an inductive premise an empirical premise? In developing the principle of equivalence, after seeing that bodies would free fall inertially in a box in space free of gravitation (just as it would ...
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What's the difference between XY=F and XY=0 in Jeffrey's Logic of Decision?

I'm stuck solving problem 14 in Chapter 5 of Jeffrey's Logic of Decision. The first part of the problem says: Show that in presence of prob is nonnegative (prob X≥0) and prob is normalized (T=1)...
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What are the consequences of rejecting identity of indiscernibles

What kind of system are we in if we explicitly take its negation as an axiom? Here's the identity of indiscernibles. (1) ( ∀P.P(x)↔P(y) ) → x = y Here it is written in prenex normal form (2) ∀x∀y.∃...
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What is the premise and conclusion here?

"Half of the American population believes that the universe is 6000 years old. They are wrong about this. Declaring them so is not 'irreligious intolerance'. It is intellectual honesty." -Excerpt ...
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how do I input these statements into a truth table generator?

I am in rush to finish this homework and have tried inputting my problems into several truth table solvers. I keep getting error messages, which solver should I use and how do I change my statements ...
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How do pragmatists avoid this modal argument against their view of truth?

I am reading Harry Gensler's Introduction to Logic (Routledge, 2002) and doing exercise 1 of 7.3b in the "Basic Modal Logic" chapter. I think I follow the steps. The answer is in the book. My ...
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Does anyone know how to prove ~ ∀x (Ax→Bx) from Ǝx(Ax & ~Bx)?

Ǝx(Ax & ~Bx) Premise SHOW: ~ ∀x (Ax→Bx) I really appreciate anyone who could help The instructions for the homework were to Prove that the obverse of a particular ...
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Has there been any philosophical guidance regarding when to use logic vs empirical testing?

One obvious disadvantage of testing a given claim with scientific constraints is that one may never know the number of possible constraints to try, in which combinations, and in which order to modify ...
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Does Reflective Set Theory “RfST” fulfill the requirements of founding Category Theory and Mathematics?

On mathoverflow I've posed the question in the title in connection to Muller's 2001 criteria for a founding theory of mathematics, which largely raised in connection to Category theory [see here]. ...
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Is using analogies a bad logic reasoning?

When discussing with someone, I like to take the argument they use and put it in another context, to see if it works, and if it doesn't, ask why the argument should be valid in one context but not in ...
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Is it scientific or a logical error to claim something is true because I can't think of another explanation

The situation Let's say, someone is wrong on the internet. She says The forums on that newspaper article is closed. Apparently the newspaper want to suppress public debate. I reply: That's ...
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How to prove (PvQ) & (RvS) : ((P&R) v (P&S)) v ((Q&R) v (Q&S)) by Natural deduction

Another of Tomassi's exercises I can't solve (Logic, page 109, Revision exercise III, 3) (P v Q) & (R v S) : ((P & R) v (P & S)) v ((Q & R) v (Q & S)) I have to use natural ...
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What's the fallacy when someone asks a question and then answers it themselves?

Example: "Why didn't you compete in the annual sports event? It was because you knew that you'd lose anyway!" Or, "How did he run that fast? he must've taken steroids" It falls under unwarranted ...
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Generating false statements in propositional calculus

Let p stand for the sentence "George is 6ft tall". Let q stand for "George is 5ft tall". Statement 1: ~(p → q) It is false that if George is 6ft tall, George is 5ft tall. It seems pretty obvious ...
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Your irreducible ground truth [closed]

What is the ground you build your arguments on? By this I mean something that would be the ultimate base for your reasoning, something irreducible, a (self) evident and therefore unprovable fact, an ...
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When are Accessibility Relations satisfied?

We can only "measure" (quantify) counterfactuals by an accessibility relation to our own world. Therefore how can we assert something as necessarily true in all possible world's if quantification of ...
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Existential Quantifiers and Modal Logic

I have a question about predicate logic and modal logic. Namely, do any of them overlap with one another? To give an example, does existential quantification apply to counterfactual statements? A ...
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What is actual is a metaphysical necessity?

You look out of the window and it's raining. You grab a bottle and pour some water into a glass. You probably don't consider these events as necessary: it could have been a sunny day and you were free ...
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Are there any techniques for dealing with an arguer who continually denies facts?

Inspired by this question where individuals can't imagine something being possible, and somewhat similar to this. I've recently been in a debate where the debater had the very annoying habit of just ...
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Are there useful logics that reject disjunction introduction?

Are there logics with fairly natural semantics that don't have disjunction introduction? Is there a good way of thinking about what "flavor of system" you're in when you don't take disjunction ...
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Is “I cannot imagine a mechanism for X to happen, so X can never happen” a named logical fallacy?

I have encountered this reasoning quite frequently: Somebody posits the hypothesis that an event X can happpen. A recent example I encountered was "vinegar and salt in the boiling water make eggs ...
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John Earman and Time Travel

Time travel and grandfather paradox: Earman suggests in his 1995 paper that physical possibility should be considered similarly with the laws of nature (i.e. logical possibility). Does this mean that ...
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Logic and resolving a modus tollens

Wasserman presents a common argument against time travel: (P1) If backward time travel were possible, it would be possible to perform a self-defeating act. (P2) It is impossible to perform a self-...
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Justification for axiom OB-RE in deontic logic

Let OB p denote "p is obligatory". Axiom OB-RE is (p ↔ q) → (OB p ↔ OB q). This axiom seems false to me (under the interpretation of obligation). For example, let p denote "don't lie to me" and q ...
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Grandfather Paradox and Causal Loop

How does the grandfather paradox cause a causal loop (and therefore a bootstrap paradox)? https://en.wikipedia.org/wiki/Grandfather_paradox
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Is Ross' paradox really a paradox?

Consider the following disjunction introduction: Your room is clean. Therefore, your room is clean or your house is burnt down. Ross' paradox allegedly arises when applying this inference to ...
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Is there anything wrong with this argument?

The Constitution of the Russian Federation says, in Chapter 1, Article 1: The Russian Federation - Russia is a democratic federal law-bound State with a republican form of government. The ...
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proof for relational predicate logic

I have been working on this problem for over an hour and I think I have simply missed something. I need some help. The rules I am allowed to use are the Basic Inference rules (MP, MT, HS, Simp, Conj, ...
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Why can't existence be expressed in linear temporal logic?

In some circumstances, existence cannot be expressed in linear temporal logic. I don't understand why it can't be constructed with negations and global quantifiers. For example, the wikipedia page (...