Questions tagged [logic]

For questions about logic, whether it concerns syllogistic logic, mathematical logic or the nature of logic itself.

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Hi! I'm 99% sure my formal argument is valid, but can you check?

I wrote this argument, and while i'm sure it is valid, it has been awhile since I've done basic logic.Thanks!
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Proving the Conclusion

Derivations Prove that the following arguments are valid.ANSWSER IS POSTED (Q → ¬P), (¬Q → ¬P) ⊢ ¬P notes: ⊢ stands for the conclusion. so basically, I am trying to prove how -P is a true/proper ...
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Is there such a thing as N-valued logic?

Is there such a thing as N-valued logic, N being above 5 since there exist 3-valued and 4-valued logic. I am asking, because after true, false and neither, the additional truth value basically don't ...
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The working of Laws of logic on informal reasoning

As a mathematics learner, I can connect the laws of logic with the deductive type (formal logic) of reasoning, but I cannot sink those fundamental laws with the informal sense; however, induction and ...
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What could be some general unifying principles to guide what a philosophical reflection/enquiry might look like?

The notions of logical consistency, pertinence and possibly relevance seem important for a philosophical inquiry on some matter to be fruitful and interesting. Other notions once considered important, ...
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Can hatred and retribution be justified and rationalized without free will?

Without free will, our behaviour would be no different from any other natural phenomenon, Sam Harris and other determinists claim: https://imgur.com/bIrWOJI “Compare the response to Hurricane Katrina,...
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Looking for help understanding modal logic and graph structure

I'm a novice to modal logic and only have a passing familiarity with classical logic. I started reading 'Modal Logic for Open Minds'. It is very readable, but then on page 16 the author introduces a ...
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Quantifying the value of a life

Recently, I was presented with the problem of whether I would rather kill a 30 year old man in a third-world country, or a 30 year old man in a first world country. I said that the three factors ...
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1 answer
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Who are some key modern philosophers who have addressed the paradoxes of parts and wholes (mereology)?

I've read Graham Priest's book One (2014). Where he offers a what he calls "gluon" theory of parts and wholes. (These are metaphysical gluons which are not related to gluons from particle ...
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I might have found a fundamental problem with Novikov's Self-Consistency Solution principle?

I was thinking over Novikov's principle, trying to explain it to some younger people interested in the topic when I had a realisation. This is probably easily explained, but its stuck in my head now ...
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Which practical applications of the fourth figure of syllogism exist?

There are four figures of simple categorical syllogism, well-known since Aristotles. I started to wonder about practical applications of each figure, so I've addressed different literature, obtaining ...
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What is the "metaphysical status" of vacuous truth?

Consider the set "of objects on the table" and suppose that the table is empty. Point of view 1: the elements of the set have the same properties the any other real objects on the table ...
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How is it possible to explain a logical language through a natural one?

Suppose we are to learn a subject like mathematics, then for it's precision and rigor, the topics discussed are described in terms of theories of logic. Suppose a student wishes to learn mathematics, ...
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Does causation exist?

It is often claimed that radioactivity, virtual particles popping in and out of existence, quantum mechanics, etc have no causes. That at the level of fundamental physics, causes and effects are ...
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◇(p ∨ q) → (◇p ∨ ◇q) in Modal Logic K [closed]

I would really appreciate a full proof of this theorem. I need to prove ◇(p ∨ q) → (◇p ∨ ◇q) in Modal Logic K. (◇p ∨ ◇q) → ◇(p ∨ q) example I started with ¬(p ∨ q) → ¬p and ¬(p ∨ q) → ¬q. ◻¬(p ∨ q) → ...
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Can something be assumed impossible until proven otherwise in philosophy?

I only see people assuming that something is possible until proven that it's impossible when there is no evidence. Is there a philosophy that assumes something is impossible until proven that it's ...
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Help needed with predicate interpretations- Wilfrid Hodges logic

I was going through Hodges' Introduction to Elementary Logic and was rather puzzled by a section where one is asked to translate an argument into a predicate interpretation. The entire thing reads: ...
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What are borderline cases?

What is a borderline case, and its relationship with vagueness? I have googled a lot but didn't quite find anything that suits my understanding.
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Ex contradictione quodlibet and Contradiction elimination

Are "Ex contradictione quodlibet" and "Contradiction elimination" two different names for the same rule in classical logic? Or are there differences between them? E.g.: P (...
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What is the negation of this predicate?

I have a predicate T(x,y) where x is in the set of humans and y is in the set of statements. T(x,y) means "x knows y is true". My question is: is the proper negation of T(x,y) "x doesn'...
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What is the difference between a Belief and Truth

I was interested in the definition of truth, i followed this post What is the difference between Fact and Truth? what I understood is that truth is anything I believe in or appears to be accurate ...
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Is there a term that means "soft validity?"

By "soft validity" I mean this: The formal definition of validity is that if the premises are true, the conclusion must be true. I will call this "hard validity." "Soft ...
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Difference between Truth and Fact [duplicate]

I was interested in the difference between truth and fact. For me, truth is a belief that appears to be from a perspective. and a fact is an undeniable reality. Is this way of thinking correct? How ...
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Are multiple anecdotes still logically unsound?

We know that arguing from one anecdote is fallacious. What about multiple anecdotes describing the same phenomenon? For example, using customer reviews to buy a product. Would this still be considered ...
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1 answer
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An argument against a creation ex nihilo

I wanna know the crucial points in this argument that just came to my mind to prove that nothing can come from nothing is logically true. We define nothingness as the absence of anything bar logical ...
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Help with Predicate calculus [duplicate]

I need to prove this theorm ∃y(Fy → ∀xFx). meaning i need to arrive at this result based on no assumptions. help?
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Why do we prohibit consensual incestuous relationships?

When talking about sexual relationships between brothers and sisters, our initial intuition might be, “Well that’s just wrong. There’s something immoral about that”. Now, to examine the logic, I ...
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A Logical conundrum

"No one tells the truth all the time" is this statement true or false? If it's true did you say the truth this time or not? It seems adding temporal predicate makes things even worse... :-D
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2 votes
2 answers
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Does logic give us a single definitive and universal answer for comparing the odds of unlikely events?

As an amateur who has interest in logic and mathematics I've been reading about the concept of different probability perceptions. I'd like to have your opinions over the subject below. When it comes ...
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How could second-order logic satisfy (neo) Fregean's epistemic goal?

Recently I've been reading Shapiro's Higher Order Logic in The Oxford Handbook of Philosophy of Mathematics and Logic, Chapter 25. There are some paragraphs confusing me:  One traditional goal of ...
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1 answer
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Why can't Aristotelian logic account for deductions which rely on propositional logic, or express relationships between two or more objects?

This is a summary from absurdbeing.com: Unfortunately, as mentioned, Aristotle’s system of logic (based entirely on the deductive syllogism) was incomplete in at least three ways: first, it didn’t ...
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Why do we call logical concepts abstract when logic is specific to the situation?

Things like propositions and predicates, which are specific to certain logics. Example: If only classical logic applied, not everything would be possible. (LEM, etc). Many logicians say classical ...
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Philosophy book written using logic statements

I would like to translate a philosophy text into logic axioms and propositions. Then, I would like to use prolog to check if the text is logically consistent. However, I find it difficult to translate ...
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3 votes
4 answers
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Finding a fallacy in a comedic dialogue

In one of the Abbot & Costello show episode the following dialogue goes: Abbot: Is it not true that you are a servant of the public? Officer: Yes, I am servant of the public. Abbot: I happen to ...
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I've been working on this for way too long :/

I've made a lot of progress on the proof below, but I am stuck on the last steps where I need to add existential quantifiers back in: ¬∃x ∃y Smaller(x,y) For context, I'm a logic novice, but I'm ...
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2 answers
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Does the principle of explosion contain all analytic knowledge?

“From falsehood or contradiction anything follows”. Is this the “multiverse” or pluralism in which set theory, all logics, etc are a small portion? Every finite list of axioms and theorems would have ...
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Constructing natural numbers from nothing

I found that many of us (mathematicians) try to construct natural numbers defined from the intuitive concept 'size of the set'. They take ϕ, the empty set, as the starting point, then define and ...
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Assume: (C∧D)∨(¬C∧D); Prove: C↔D

Is it possible to prove this formally in fitch? I found that when C is false and D is true the conclusion is false while the premise is true.
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Can predicates and statements function as singular terms?

My main goal in this post is just to see whether my intuition on predicates and statements is correct when it comes to classical logic. What I want to know is whether a predicate can function as a ...
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Question from predicate logic exam: Given model with the domain D = {a,b}, say whether the formulas listed below are true or false

I've got a logic exam coming up and one of the question types is puzzling to me. If anyone could help me by explaining what this is about to me, I would appreciate it greatly. Note: I was unable to ...
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1 vote
5 answers
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When does something cease to exist?

For humans, legally speaking, someone who's "brain dead" is confirmed to have ceased to exist. But what about philosophically speaking? What makes someone who they are? If we are our bodies, ...
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When does a mathematical predicate have a truth value?

Say we have a predicate in a domain of real numbers, P(x), 2x+10=20 we know that we can existentially quantify this and say that the value x=5 makes this true, but we cannot talk about P(x) being ...
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'for some x' statements [duplicate]

What is the correct understanding of the phrase 'for some x' in logical definitions? For example sometimes I've seen it as 'for some (values of) x' and others in uses such as 'there exists some x such ...
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Understanding 'Assignment'

I wonder why we use 'assignment' the way that we do? When we state with a definition expression that some variable takes some value, what does this mean? Is there a sense of time in the frame of ...
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If the Continuum's cardinality could physically change because of a physical manifestation of forcing

Suppose that the Continuum has a specific cardinality assigned to it when it exists "in" a physical universe. (This, or a similar-sounding supposition, occurs frequently enough in the ...
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The absorption of parathetic sentences into the One True Fact

Two assumptions At least "hypothetically" or "for the sake of argument," I would like to use the slingshot argument to compare and contrast various sentence-types. So for now, ...
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1 answer
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Are Gödel's Incompleteness Theorems a refutation of Rationalism?

According to Putnam, Gödel's theorems show that the set of truths in Number Theory (i.e., true propositions involving natural numbers and their properties) is not recursively enumerable, whereas all ...
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Can dysfunctional objects preserve their identities?

There is a claim that dysfunctional objects no longer belong to a specific category. For instance: eyes are pairs of globular organs of sight. An eye is an object that sees. An eye that ceases to be ...
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What are the philosophical solutions to "ship of Theseus" problem of identity?

Ship of Theseus is a thought experiment in which every piece of a ship kept in a harbor is replaced one at a time. The questions are: would the end result be the same ship or a new ship? If it is not ...
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Can categories be objective rather than socially constructed?

There are claims that categories are socially constructed and subjective. For example: "there's no such thing as specie or life. They are socially constructed"* Are there philosophies in ...
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