Questions tagged [proof]
For questions about the correctness of a proof or the nature of proofs in general.
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Do atheists bear the burden of proof in showing why/how the reasons presented by theists are unconvincing?
In conversations and debates between atheists and theists, is it enough for the atheist to assert that they are skeptical of theism without providing justification, or does the atheist bear the burden ...
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What is the burden of proof? Has this principle ever been challenged?
I have been surprised to find that some people doubt this principle. Onus probandi incumbit ei qui dicit, non ei qui negat - the burden of proof lies with the speaker, not with the one who negates. I ...
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Can fatalism be disproved by fate-changing magic?
In a world where magic exists, fate-spinners are people with supernatural powers that influence the chances of events happening.
Their power has been proven by countless experiments where they compare ...
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Does software exist to automatically validate an argument?
I'd like to
Derive logical arguments from English, and
test their validity using a program.
Does software exist for step 2? It would be fine if it were to give up because
The validity isn't ...
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Why not move from proof numbers to theories instead of theories to proof numbers?
In mathematics, they do this thing where they figure out what are called "proof-theoretic ordinals" (see this section of the SEP article on proof theory for background details) of theories, ...
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Is non-deterministic automated reasoning a viable strategy for solving problems in mathematical logic?
EDIT 2023/10/06
There are objections that this is too technical to be philosophy, and while I've seen questions on this forum go far beyond what I'm asking here in set theory, computability theory, ...
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Would the imaginary unit be the truth-value of sentences formed using √𝐧𝐨𝐭?
Section 4.3 of "Sentence Connectives in Formal Logic" discusses a concept of demi-negation or what is (for the sake of the text) resolved to a concept of "the square root of negation&...
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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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Proof of the existence of God?
Here it is, the long-awaited proof for the existence of God (for your consideration).
I have taken the liberty of defining discretely what God is, without which there is no question to be answered (...
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Does theism have the burden of proof?
I have heard that agnosticism seems to be the only position with respect to god that doesn’t have a burden of proof. What I find troubling about this is most people do not as a practical matter think ...
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Philosophical interpretation of the cut rule of Sequent Calculus
It seems that the cut elimination theorem of Sequent Calculus has some interesting consequences.
Quote from Alain Lecompte, La logique linéaire et la question des fondements des lois logiques (French)...
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Is there a way to confirm something material is infinite?
Mathematics is full of immaterial examples of infinities. However, is it possible to confirm or prove something material is infinite? Or, can we only conjecture they are?
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Proof for predicate logic
Prove the following formula in Fitch format:
∃x(∀y(P(y)→y=x)∧P(a)) |= ∀x∀y(¬(x=y)→(¬P(x)∨¬P(y)))
I tried to use universal introduction as my main rule but didn't know how to proceed
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Peirce cuts (mirrored) + demi-negation = demisets?
[Note: I found one essay, about Aristotle, that used the word "demiset," although at a glance it seemed like they might've been substituting this terminology for a counterpart to the subset/...
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Fitch Question Please Help Me [closed]
I'm having trouble understanding writing out a proof. The proof I'm trying to work with is :
How do I reach this goal? Which rules do I use and with which support steps to each rule (proofs to prove ...
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Is the idea of weak and strong evidence incoherent?
Hypotheses are either true or not. Justin is either a murderer or not. There is either a God or not.
If statements are either true or false, how can it be the case that certain forms of evidence ...
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Why do some proof method feel more satisfying than others?
Let's say we are asked to show that 1+2+3.. =n(n+1)/2, then a very simple way to prove this is to use induction. The proof is simple, consider P(1) and show P(n+1) from P(n). However, it feels quite ...
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In what contexts or disciplines does "One may assume X" imply "One may ignore the possibility of any statement contrary to X being true"?
In computer programming, it has become fashionable for compilers (processors of computer language) to apply the following form of reasoning:
A language standard would permit a compiler to assume that ...
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Is solipsism truly unprovable?
I know I’ve asked a lot of these but this one I’m hoping to be definitive.
I have heard pretty much everyone say that it’s unprovable, that you can’t know for sure if it’s true or not because of the ...
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How to prove ‘∃xP(x)’ from ‘¬∀x(P(x)→Q(x))’
What would a formal Fitch proof for this look like?
I am given ¬∀x(P(x)→Q(x)), and need to derive ∃xP(x) from it.
I started with this, but I don't know if I am doing the right thing, and where to go ...
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Jurisprudence and logic: Is it a necessary criterion for a claim to be declared sound that there be no evidence to the contrary as to its soundness?
So, I've been generating various arguments (such as related to the synthesis of legal arguments), and I have been doing my best to figure out how to declare that a particular claim is not sound. For ...
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Can, "This problem is unsolvable," be used to formulate the first incompleteness theorem in erotetic logic specifically?
Assumptions/definitions: the Gödel sentence is informally equivalent to, "This sentence can't be proved in system X," where X is appropriately specified. Since that sentence can itself be ...
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Does the preface paradox undermine long mathematical proofs?
Descartes, IIRC, somewhere says something about the vagaries of memory influencing our justification for believing in our memory, and thence for believing in proofs involving many steps that we have ...
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Is the debate on free will over? [closed]
I've never posted on here but I am interested in philosophy. I think a lot about free will / determinism / compatibilism. I always felt like I have some degree of free will. I know free will is ...
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Does this proof of God I made work? [closed]
I worked up this proof of God, and I want to know if the proof works. Here is the proof:
Something which is unlimited is limited by not having limits. If limits were to be imposed on something which ...
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Proof for the absence of free will?
EDIT (17/08/2022): I have answered this question with an evolution of the argument. See accepted answer below.
There are a number of arguments which aim to prove the impossibility of free will.
The ...
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Is the Categorical Imperative Simply Bad Math? :)
The title is clickbait, but the question is not.
First, The Categorical Imperative:
Act only according to that maxim whereby you can, at the same time, will that it should become a universal law.
...
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Is game-theoretic semantics in logic more consonant with LEM than ~LEM?
When someone plays a game, they are minded to try, at least, to score points in the game (even if there is no final score but one can simply try for a higher score each time one plays), and often ...
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Is it possible to show that something does not exist?
I am aware that I could show that something does not exist with the knowledge of an implication.
If B is true if A exists, then A does not exist if B is false
But if we have no implications, is it ...
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Why is Diogenes the Cynic's solution to Zeno's Dichotomy Paradox insufficient?
According to Wikipedia's discussion of Zeno's Dichotomy paradox (emphasis mine),
According to Simplicius, Diogenes the Cynic said nothing upon hearing Zeno's arguments, but stood up and walked, in ...
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Proving God and believing only provable things
This question has two, related, parts.
Part 1.
I recently have been on some discussions regarding proving God exists and proving that Jesus is really the son of God; intertwined with that, there was a ...
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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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I need help using the rules of implication/inference to construct a proof for the following argument: [closed]
I need help using the rules of implication/inference to construct a proof for the following argument:
A ⊃ C
D
~C
~A ● D
KEY:
Tilde (~) forms negations (“not,” “it is not the case that”).
Dot (●)...
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Can someone formulate John Pollack's argument in understandable terms for laymen?
http://www.strongatheism.net/library/atheology/ontological_argument_for_nonexistence/
By the way, I am not asking whether this argument is sound or not. I just want to have it formulated in ...
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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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Fitch Proof Help, Conclude ~B from ~(A > B) [closed]
I'm in the process of learning fitch proofs and I've come across one I'm having trouble setting up.
Premise: ~(A > B)
Goal: (A & ~B)
In other words, it looks something like this:
1 | ~(A > B)...
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Is there anyway to prove things happen/exist if I'm not aware of them?
I don't even know how to properly ask this, but how can one prove things happen without them knowing?
Things only exist for me when I'm aware of them, either by direct contact (I see it, I feel it etc....
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Does predicate logic have truth tables?
As I recall in propositional logic, it was possible to draw truth tables for the arguments such as for:
(P ∨ R) [I live in Paris or I live in Rome]
Therefore, (~P ⊃ R) [If I don't live in Paris ...
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How to argue statistics using logic?
Typically in logic, we have the axioms as facts which are 100% true but in statistics we have things which are true sometimes. For example, "the coin is heads" is true 50% of the time when ...
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Underlying logical structure behind Descartes' Ontological argument?
Quoting SEP:
Version A:
Whatever I clearly and distinctly perceive to be contained in the
idea of something is true of that thing.
I clearly and distinctly perceive that necessary ...
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How should we characterize the logical structure of wishes?
The motivation for this question is extraordinarily stupid, but it requires just enough thought and specific knowledge of formal logic that I think it still falls within the broad scope of "...
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Can we doubt all knowledge?
Can we doubt all knowledge from all sources (perception, reports, and reason)?
Regarding doubting reason, reason can't be proven, it is preceived and judged instantly by our logic, but what if our ...
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What is the relationship between algorithms and logic?
Is an algorithm (cooking a dish, Grover's/Shor algorithm, etc.) a form of deductive reasoning or inductive reasoning, and if not what exactly is the relationship between an alogorithm and logic?
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What, if any, are the most important claims to be considered proven in the absence of observation; ie: claims derived from logic alone?
This question arose during contemplation of whether free will and/or moral responsibility might ever be proven real or illusory.
Galen Strawson has proposed a proof for the impossibility of moral ...
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Gödel’s Incompleteness Theorem: How can truth go deeper than proof?
My current understanding:
Math starts with a set of basic (purportedly self-evident) statements that are taken as a given without the need to prove them true, like e.g., a + b = b + a etc. Such ...
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Is a game player winning against very long odds being a cheat, an example of the logical fallacy of personal incredulity?
There's this Minecraft speed-runner called Dream who has been accused of cheating due to his drop luck (ie receiving useful things in the game). A moderator team has calculated that the p-value of the ...
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How to prove you are an atheist?
I've been reading a conversation between two individuals - A claiming to be atheist and B asking him to prove it, since B does not believe that A is saying the truth and can't be sure if A is really ...
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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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Does Gödel’s findings boil down to part of classical mathematics (as opposed to computation) is flawed?
According to artificial intelligence researcher Joscha Bach, only classical mathematics is affected by Gödel’s incompleteness theorem however not computation where calculations are performed in a step-...
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is there such a thing as non-constructive computational “proof”?
For the problems which can’t modified into a constructive proof, is there some useful notion of proving them to some computational approximation?
I’m referencing:
“Interpretations come at a cost: for ...
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