Questions tagged [logic]

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

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6
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7answers
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If you used intuitionistic logic in real life, would you not sound absurd?

Intuitionistic logic does not include the law of the excluded middle and double-negation elimination. I imagine a real-life conversation with an intuitionist might go like this: Amy said you didn't ...
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1answer
22 views

Is there a person in the world that is smarter than me? [closed]

So, is there? The catch is that I would not accept if a person has greater expertise in-- something. Simply knowing more about quantum mechanics, fishing and politics doesn't count as smarter.
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1answer
23 views

Instantiation and Generalisation and Formal Logic

I was wondering what generalisation and instantiation were exactly because my notes claim it to be: Generalisation: "from elementary to complex propositions" Instantiation: "from ...
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0answers
53 views

Is there a semantic version of the deductive theorem for an arbitrary logic system?

As far as I know, any logic system always defines its own semantics $\models$, but doesn't necessarily have a proof system or $\vdash$ which is complete and sound with respect to $\models$. In an ...
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2answers
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Why did the mid-19th century and earlier thinkers fixate on one-place predicates?

A book I'm reading mentions the following: A major barrier to the development of first-order logic had been the concentration on one-place predicates to the exclusion of many-place relational ...
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0answers
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What if purpose has come by the occurrence? [closed]

A question (especially from those who believe, "I exist. Therefore there has to be a purpose") I was wondering what if we are living in a multiverse, with many parallel timelines. Then this ...
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1answer
38 views

Relationship between Principle of sufficient reason and Law of identity [closed]

I have an intuition that one can derive the principle of sufficient reason from the law of identity or non-contradiction but i don't know how. If someone knows I'd like some help.
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3answers
282 views

Is it possible to define Truth?

I hope this is the right place to ask a question like this. I'm a student, I haven't studied philosophy and I'm not familiar with all of the famous philosophers, so this question probably already have ...
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1answer
46 views

How does Consequentialism handle uncertainty?

E.g. Suppose you are a Consequentialist faced with a variation of the trolley car problem. Your options are to save five people with a 20% likelihood or one person with a 100% likelihood. Which option,...
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0answers
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How does our death affect our perspective on the law of non-contradiction? [closed]

..I'm sorry if my question seems a little rough, but this has been something that has been bothering me and I don't know where to research this. Does the law of non-contradiction end when our life ...
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1answer
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How would you translate “Anything a knave claims is false” into Predicate Logic?

I am having trouble translating this sentence into Predicate Logic: "Anything a knave claims is false" (or "If x is a knave and x claims y, y is untrue.") I have pasted two ...
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0answers
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Identify the logical fallacy

I was hoping someone could identify any logical fallacies in this image. I would also appreciate it if someome could give me tips on how to find out if a logical fallacy is present and how I can find ...
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4answers
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How can we differentiate between change and progress in the area of history and natural sciences?

I'm studying a branch of philosophy that is considered with knowledge. I'm studying theory of knowledge(epistemology) and I want to use faith, reason, and memory as tools for carrying this ...
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3answers
197 views

How to reconcile the fact that mathematical proofs are logical implications with the lack of a formal calculus equivalent to the logical implication? [closed]

Theorems follow from axioms. That is, theorems are the logical consequence of axioms. Thus, mathematical proofs are essentially deductive. Proofs are all essentially logical implications. There is ...
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10answers
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What is the name of this fallacy: Is 101 binary or decimal?

A similar example would be of binary and decimal number where we are not sure about the number system or the person who proposed a number is not remotely available to disclose about number system. e....
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1answer
145 views

What are the advantages of Aristotle's term logic over predicate logic?

I have read Wikipedia's term logic entry, and the quote by Gareth Evans in the Revival section that's supposed to argue for term logic's advantages over predicate logic: "I come to semantic ...
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0answers
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Deontic Logic (resources) [closed]

Does anyone know good resources to learn or study Deontic logic? It might be books, or other resources.
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1answer
131 views

How shall I understand Wittgenstein's comment on Russell's work?

Ludwig Wittgenstein said Russell’s books should be bound in two colours…those dealing with mathematical logic in red – and all students of philosophy should read them; those dealing with ethics and ...
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1answer
39 views

How to prove that the axiom H is valid in the following frame

To prove incompleteness of KH, I have to prove that the axiom H is valid on the following frame: Axiom H goes as follows: □(□p↔p)→□p I don't know how to prove this, but here's one idea that's half ...
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0answers
34 views

Alessio Moretti's graphs

Moretti and his colleagues are at the head of a school of logic focused on the tradition of the Square of Opposition and similar graphs/diagrams. Besides a strong thesis of logical form depending on/...
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2answers
135 views

A case of vacuous truth : Have you taken part in your department's open discussion session already?

Today I encountered a vacuously true case. But I am not so sure, so please help examine it. It was from a question form that asks: Have you taken part in your department's open discussion session ...
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1answer
64 views

What is this snippet from Frege's Begriffsschrift saying?

I have no background knowledge in logic so I am a little lost about where to begin. This is the photo I am trying to learn about and it is from Frege’s Begriffsschrift.
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0answers
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Computing Premises from Consequence

We write 'If A, then B' to mean that if A is true, then B must be true because B is a logical consequence of A i.e. it is impossible for A to be true but B to be false. Let us consider one such ...
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5answers
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What separates mathematics from logic? Can “mathematical” operations be applied to logical systems?

In my 'Introduction to Logic' class, my professor told us that half of the class will be based on "mathematical" operations withing logic. After looking through the textbook, I realized that ...
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3answers
103 views

Can classical logic hold without causality?

Consider a universe where causality failed to hold. Would that universe be described by classical/standard logic? Or would we have to use a radically different logic where causality was not necessary? ...
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1answer
42 views

Logic question about the sum of one's free choices

If each moral choice a person makes is free (as in free will) it seems to follow that the sum or totality of all those choices is also free. In other words, if each individual sin can be avoided, then ...
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1answer
55 views

What are some of the struggles that come with teaching formal logic? [closed]

I'm currently an undergraduate student who wants to do research on the pedagogy of formal logic. As a result, I wanted to know what are some challenges that instructors (or even students for that ...
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1answer
41 views

Where in Aristotle's Topics did he say there's no exact/clear way to distinguish two concepts?

I've heard that Aristotle supposed in his Topics that there's no exact/clear way to distinguish two concepts. What exactly did he say?
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1answer
138 views

Is it true that if an argument is invalid, any argument of that logical form must be invalid?

I am stuck over whether these statements are true: First: "If an argument is invalid, any argument of that logical form must be invalid." Second: "There may be invalid argument with ...
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0answers
95 views

how to translate the following sentence

Either it is not the case that Gonzolo play music and does not go to concert,or it is not the case that he does not read book and does not play football. P:Gonzolo play music , Q: Gonzolo go to ...
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1answer
32 views

if [if (if P then Q) then (if P then R)] then [if P then (if Q then R)]

i am new in logic course, i saw an question in my book. it says that show the following argument is valid by using natural derivation rules. if [if (if P then Q) then (if P then R)] then [if P then (...
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1answer
54 views

Why Frege thinks geometry is synthetic?

Frege believes that arithmetic is analytical. Why not Frege thinks geometry can be reduced to arithmetic by coordinate system or something else?
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0answers
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Why is a material condition true if its antecedent is false? [duplicate]

So I ran into the "drinker's paradox" the other day, which compelled me to learn about the nature of the logical material conditional. But when I studied the truth table (below) I got pretty ...
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1answer
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Can you give other examples of skeptical hypotheses that haven't been mentioned yet?

I need some help with my philosophy homework. We were told to formulate our own skeptical hypothesis and use it as part of a radical skeptical argument, and that the skeptical hypothesis needs to be ...
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0answers
43 views

How should I think about the probability of a causal effect? [closed]

This is a burning question that I've always had. In particular I would love to learn more about uncertainty and non repeatable events. Especially whenever you can't use complicated math and run ...
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1answer
38 views

When to use logic symbol variants? [closed]

Many logical operators seem to have multiple variants: Material implication: ⇒, →, ⊃ Negation: ¬, ~, ! Conjunction: ∧, ·, & Disjunction: ∨, +, ∥ etc. Are there differences in their usage (e.g., ...
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1answer
237 views

What fallacy is this? Ignoring rate of change

What is this fallacy? "I threw a ball onto the roof. Which way did gravity pull it? Well obviously because the ball started on the ground level and ended up on the roof then gravity must have ...
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1answer
52 views

What is the literal meaning of “The only thing that I know is that I know nothing”? (Is not knowing anything a knowledge?)

If a person says, "The only thing that I know is that I know nothing." What exactly does that mean (not metaphorically), literally? If the only thing they know is that they know nothing, ...
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1answer
63 views

Choice and action

Moore highlighted the connection between asserting and believing by making note of how odd, "It's raining but I don't believe it" (as if to say "I don't believe it's raining but it is&...
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3answers
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Are There Finitary Logical Constraints on Converting Recursive Syntax to Semantics?

From the logical standpoint can we continue these series on and on and still be able to make sense of it? 1. I know <--- no problem 2. I know ...
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12answers
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Why is it that the statement “All goblins are yellow” does not contradict the statement “All goblins are pink?”

From what I know, I think it has something to do with vacuous truths, but my understanding is not quite there yet.
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1answer
42 views

Why is ∃x∈A P(x) equivalent to ∃x(x∈A /\ P(x)), but ∀x∈A P(x) is not equivalent to ∀x(x∈A /\ P(x))?

I know that ∀x∈A P(x) is only equivalent to ∀x(x∈A -> P(x)), but why isn't it equivalent to ∀x(x∈A /\ P(x))? I can use the laws in logic to compare the two, but I want an intuitive reason as to why ...
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5answers
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Intuitively, why does the disjunction equivalent of the conditional statement “If you study hard, then you'll pass the test” make sense?

This is of the form P -> Q, which is equivalent to ~P \/ Q. The equivalent statement would be the following: "Either you don't study hard, or you'll pass the test." My question is, why ...
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1answer
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How do you differentiate between At least one X and Exactly one X in predicate logic?

Here are the following two sentences. At least one person speaks English. ∃𝑥E(x) Exactly one person speaks English. Instead of ∃𝑥E(x), what do I write?
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1answer
29 views

How to read modal logic's countermodels?

I'm new to Modal Logic and currently playing a tree proof generator just to see how some stuff work, but I can't read the countermodels that the algorithm gives me when my proposition is invalid. I (...
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3answers
118 views

can an argument containing a contradiction be valid argument

I know that validity has nothing with truth of the conclusion or with how good argument is in general, and an argument is valid iff the truth of its premises guarantees the truth of its conclusion. ...
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1answer
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Is my interpretation of “and” correct in these statements?

Let A mean "Equation A has a solution" and B mean "Equation B has no solution." I am a little confused, so I wrote down some possibilities and I wish to see if my interpretation of ...
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2answers
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Question about fitch 6.19 proving A or C from premises A or B and -B or C

How to prove A or C from premises A or B and -B or C. Am using fitch and have been stuck on this for an hour
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1answer
87 views

Does the truth value of a material conditional depend on context?

Suppose the following material conditional "If 1+1=2 then Moon is made of cheese". The antecedent refers to the context of mathematics. In that context "1+1=2" is true. Whereas &...
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1answer
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Requesting help with designing curriculum (Logic)

I am currently a math major in university who wants to design my own area of study/major, specifically in Logic. I was wondering if I could get some help on how Logic sets itself apart from philosophy?...

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