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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 ...

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How should we understand different knowledge attributions? (epistemic logic)

My main motivation is in terms of epistemic logic. In epistemic logic X knows that p if p is true in all states that X sees as epistemically indistinguishable from the current state. In this sense we ...
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Is there a limit beyond which mathematics, if used correctly, cannot be applied to reality?

And if so, why, and which? Take this case: If I've two apples and I believe that with two more I'll have four apples, then I implicitly believe that summation applies to reality. Yet there are ...
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How might I notate that an entity either cannot have a quality or has all of it?

How might I notate that an entity either cannot have a quality or has all of it? I was to say that a friend, Charles, is either completely inactive, lacks the quality (property?) or action, or does ...
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How can we prove something ethical?

We as humans have ethics, giving us the ability to know what's good and evil, what's ethical what's not, yet what I consider ethical, others don't, so in theory how can we prove anything is ethical ...
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In a Descartes square are the statements just the negations of each other?

There is a decision making method based on wrapping problems into a Descartes square by answering 4 questions. I've tried to use it for my own decision process but I couldn't figure out what to place ...
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58 views

if philosophy didn't exist nor did psychology, could we prove that we think?

if philosophy and psychology didn't exist, could humans be able to prove that we think and are capable of coming up with inventions, I mean we create things because we need them(that used to be the ...
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40 views

Modus Ponens as Substitute for Syllogism

This is a pretty basic question, but I haven't been able to find a clear answer in the various sources I've looked at, including the Kneales' chapter on conditionals in 'The Development of Logic'. ...
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46 views

Could someone help me prove (P → Q) ↔ (~P ∨ Q) follows from (P ∨ Q) ↔ (~P → Q) in sentential logic?

I need to prove that (P → Q) ↔ (~P ∨ Q) follows from (P ∨ Q) ↔ (~P → Q).
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How does one judge “complexity” of assumptions for the purposes of “best explanation”?

The context for this question is from assessing theological arguments from the point of view of 'inference to the best explanation'. In philosophy (and science), we may wish to argue that some ...
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52 views

Using logic to exaggerate something

I am not sure if this is the best place for this question. Many times people in marketing or good at promoting things (and themselves) use sometimes a subset of similarities between 2 things to make ...
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71 views

Sentences and reality

Would sentences have meaning even if humans did not exist? For example, would "the earth is round" have meaning if humans did not exist? Would it be true?
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37 views

Understanding multiple values in a single cell of a truth table (P v ~Q) as (1 1 0 1) when P and Q are 1

This might seem basic to most here but I am struggling with a truth table for a disjunct. As I am looking at it further, I actually think the issue I am struggling with how to interpret truth values ...
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123 views

Could we develop a notion of conceivability that would allow us to imagine impossible/inconsistent/illogical things?

There are things that we cannot imagine because they are impossible (like a solution to Russell's set theory, since it is impossible to reach that solution because it is illogical.) Some months ago, ...
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Is Propositional Logic Sound and Complete

I hope this is not a silly question, and I am not a logician by any means; however, after reading Godel's incompleteness theorem, I wonder if there are any systems who's axioms are sound and complete. ...
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65 views

What is the relationship between “truth” and logic?

I'm fairly new to logic. What I've surmised from the book I'm reading is that Logic is the science of evaluating arguments Arguments are composed of statements Statements are sentences that can be ...
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108 views

Is a barber a barber if he doesn't get paid?

For reference: The Barber Paradox. The Barber is he who shaves all those, and only those, who doesn't shave themselves. Now the question is: Who shaves the Barber? The paradox being that if ...
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36 views

Are syllogisms independent of humans?

For example, if "All a are b" and "All b are c" then "All a are c". To make this syllogism, does a conscious being need to exist? Or is it inferred from the sentences?
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Observing a zero probability event

I am not a philosopher. Just curious. From a philosophical point of view, if one observes an event with zero probability, does this immediately lead to a contradiction? For example, if you have a ...
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74 views

Why does one negative premise suffice to imply a negative conclusion?

Capaldi PhD Columbia, Smit PhD Catholic University of Leuven. The Art of Deception (2007). Why's 2 true please? I can't intuit why, because 3 outwardly contradicts it. I prefer an intuitive ...
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2answers
58 views

In categorical logic, why must any argument with two negative premises be invalid?

Capaldi PhD Columbia, Smit PhD Catholic University of Leuven. The Art of Deception (2007). Why's 1 true please? I prefer an intuitive explanation, not one with Truth Tables or Formal Deduction.
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34 views

Implication in sentences

What implications do we get when we use the past tense? For example, if I say that when I was younger, I used to play football, does this imply that now I don't?
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54 views

Can the principle of sufficient reason be applied to the whole of existence?

Many philosophers (Leibniz and Heidegger, to name but two) consider "Why is there something rather than nothing" the most difficult and important question. Given that "nothing" is a possibility among ...
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How to prove ¬(p→q) ⊢ p &¬q

This is the first time I have posted anything on this forum. I am using Tomassi's Logic. Unfortunately I have been unable to solve some of the problems. One I can't solve is this one: ¬(p → q) ⊢ p &...
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160 views

Consciousness doesn't need your body - a thought experiment

1) During a deep sleep, your consciousness deactivates to reactivate upon awakening 2) During a deep sleep, you are narcotized and killed, to be replaced instantly by an identical copy, which wakes ...
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Do premises need to be valid conclusions themselves?

I'm pretty new to logic. I recently purchased "A Concise Introduction to Logic" by Patrick Hurley based on reviews. So far I'm liking the book. I'm really focusing hard on the first chapter to get a ...
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Do logic and reasoning need to be validated by an ultimate authority?

A lot of presuppositional appologists argue that the Abrahamic God is real because the Bible is self validating and that everyone "knows" God (except you have to presuppose sense perception and that ...
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28 views

Verum or T in dynamic epistemic logic models

I've been reading a paper on dynamic epistemic logic where they use T in a way that I'm not really familar with. The paper is here by Wesley Holliday, page 16: https://pdfs.semanticscholar.org/dae6/...
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How does philosophy advance despite irreconcilable background assumptions (“positions”) on every topic?

In philosophy there are always, and on almost everything, many "positions", many different possibilities to choose from, and there isn't mainly some decisive conclusion between positions as to what's "...
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86 views

Is logic logic because God defined it as such?

A popular argument that comes, by some theists, for attributes of God is: The argument that some of God's attributes, such as Omnipotence, are illogical cannot restrict God from having them since ...
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720 views

Given p ⇒ q and m ⇒ p ∨ q, use the Fitch System to prove m ⇒ q

I have spent about 6 hours now trying to prove this using the Fitch system and I just keep going in circles! Attached is one of the 500 attempts :) I have a feeling it's done fairly simply and ...
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32 views

Online (pdf) resources on doxastic logic

I would be interested in learning more about doxastic logic. The wiki entry is rather detailed but still obviously very summarised and references therein are either papers with a paywall or books ...
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Is causality a type of necessary and sufficient condition?

Does 'A caused B' mean that A is a necessary and sufficient condition for B? Imagine that we go to a shop and buy two items with a total cost 40 dollars (30 for 1st item and 10 for the 2nd). Is the ...
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Is calling an argument a fallacy, or is the notion of informal fallacy, just a method of manipulation?

Indeed, there are ways of thought which are not consistent with logic. I am not talking about such fallacies here. All of formal fallacies, statistical fallacies or fallacies of relevance (e.g. ad ...
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Why is faulty generalization called an informal fallacy?

According to wikipedia faulty generalization belongs to the class of informal fallacies. Also, a fallacy is called informal if it originates in a reasoning error other than a flaw in the logical ...
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Can you divide the natural numbers in half sequentially? [closed]

My brief stint on SE has been quite interesting because it forced me to make the premises of my inquiry more explicit. I resisted this initially simply for reasons of economy, but economy proved to be ...
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Does believing in a Christian God logically imply believing in miracles?

Assume you are a Christian and you believe that the descriptions of the life of Jesus are facts. Things like turning water into wine magically, walking on water and other miracles seem to be ...
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how do people pick the letters for syllogistic logic problems?

I encountered the following argument while I was studying syllogistic logic from a book: All red cars kill papers, (premise) All cars that kill papers are beautiful, (premise) All red ...
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Does the value of truth have an approximation threshold?

In other words, a truth value in a mathematical sense is binary, but human communication is fallible and runs the risk of fallacy, error, and distortion. The idea of being "close enough" to the truth ...
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What are the logical fallacies of this argument?

SCIENTIFIC FACT: Nothing in the universe, ceases to exist, it just appears in some other form. LOGICAL FACT: We can be absolutely sure that what we experience right now, exists. Let's mark ...
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How to show that (P & Q) v (~P v ~ Q) is a theorem in SD

I’m working on a practice question on my logic textbook. And I’m stuck at this question. This is what I have so far: 1. ~(P & Q) Assumption/ Negated Eelimination 2. P Assumption/...
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Learning Peano's notation

This is more a request than a question. I would like to read Russell's The Logic of Relations in which he uses Peano's notation. I'm looking for a text available online which would explain thoroughly ...
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Are arguments claiming the impossibility to prove or disprove anything themselves impossible to prove? [duplicate]

Could arguments claiming the impossibility to prove or disprove anything be flawed because if they were sound they would also be impossible to prove? Or could you just assume they must be right ...
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Defining 2 words with respect to each other

I apologize if this is in the wrong forum. I listen to a radio show where the host talks a lot about love & hate. He defines love as 'the absence of hate' and he says that hate is 'the absence of ...
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What's wrong with the following argument regarding temporal limits?

Let us suppose there is a limit: you cannot buy something after 10:00PM. From the position of law, of course "cannot" must be taken directly. But from the position of common thinking, people are less ...
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Why are conditionals and disjunctions “consistent with more possibilities than categorical propositions”?

From: Philip Johnson-Laird BA PhD Psychology (UCL), Stuart Professor of Psychology Emeritus at Princeton. (Author isn't a logician.) How We Reason (1st edn 2008). p. 344.   A similar effect ...
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73 views

If-then syllogisms

We have a sentence like this: If you are right above 85/100 then you can enter a university. Does this sentence presuppose that a university exists in order for it to be true?
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Does the principle of explosion prove the laws of logic are independent of the mind? [closed]

A friend said that if the universe does not adhere to the laws of logic, then under principle of explosion anything is possible. Is he wrong? If not how does that work?
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88 views

Philosophical feminism and logic

Are there any resources to study about academic works on philosophical feminism and logic?
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221 views

What logic does Fitch's paradox use?

So I have been looking into Modal Logic as well as epistemic logic (and its dynamic versions) with the hopes of studying their applications to Fitch's paradox. Fitches paradox refers to the proof ...
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Without truth tables, how can I deduce that P → Q ≡ ¬P ∨ Q? [duplicate]

From: Philip Johnson-Laird BA PhD Psychology (UCL), Stuart Professor of Psychology Emeritus at Princeton. (Author isn't a logician.) How We Reason (1st edn 2008). p. 108. I changed the ...