Questions tagged [logic]

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

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14
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12answers
11k views

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.
2
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1answer
13 views

When to use logic symbol variants?

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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6answers
3k views

Gödel's theorem and God

I have seen it argued that Gödel's Incompleteness Theorems have implications regarding the existence of God. Arguments for the existence of God run mostly along the lines: "Because of Gödel's Theorem, ...
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1answer
128 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 ...
2
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1answer
30 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, ...
12
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8answers
3k views

Why did we define vacuous statements as true rather than false?

I have been trying to understand why implications about the empty set are treated as "true". It seems to me intuitively that vacuous statements should be false. For example consider the sentence: ...
4
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5answers
82 views

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 ...
2
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3answers
81 views

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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1answer
61 views

Is this a fallacy, and if so which?

Recently, I had this conversation at the workplace: me: I'm calling you because John needs access to this resource. I have access already and we need it to complete our work. her: Why do you have ...
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3answers
103 views

The concept of infinite past [closed]

Is it possible to give an a priori answer to whether or not an infinite past is possible?
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1answer
55 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&...
0
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1answer
36 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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3answers
168 views

Lists and predicates on lists in classical first order logic

I have to express some basic Prolog code in classical first order logic (FOL). In Prolog i use lists, together with member/2 and append/3 a lot. Could you give me some tips for writing clauses like ...
10
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1answer
1k views

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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0answers
51 views

Is it possible for there to be a function that is monotonically increasing while remaining infinitely low? [closed]

In trying to formalize an argument, I arrived at two claims: f'(x) > 0 for all x, y where x and y are real numbers, f(x) < y Is this a contradiction?
0
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1answer
26 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
95 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. ...
1
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3answers
162 views

Infinity - Sizes vs Types

Suppose there is a line, infinitely long in both directions. Make arbitrarily "uniform" cuts or "integers". Obviously there are infinitely many of these. And there are arbitrary "lengths" BETWEEN ...
0
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1answer
25 views

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
34 views

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
2
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3answers
115 views

Does anyone have an example where a sufficient condition comes first?

Example: Sufficient Condition of A+ MUST MEAN Necessary Condition of Studying occurred Temporally speaking, either condition can occur first, or the two conditions can occur at the same time. In our ...
10
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4answers
1k views

Was Kant anticipating Gödel's incompleteness in his antinomies?

Kant's attempts to prove that there's a limit to pure reason based on the existence of antinomies, i.e. pairs of propositions where each one is rational, but the propositions contradict each other. ...
1
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1answer
253 views

Omnipotence Paradox Defense and Meinongianism/Neo-Meinongianism

I was considering a solution to the omnipotence paradox in which excluding logical impossibilities from the definition of omnipotence is justified as follows. Consider the proposition, "God could ...
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1answer
71 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 &...
16
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13answers
5k views

When can we call an explanation “rational”?

There are a lot of questions involving rational judgment, rational choice, rational explanation, etc... And at the same time, it seems that "being rational" is a guiding principle for a lot of people. ...
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2answers
96 views

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: 1.(A ∨ B) ⊃ (C ∨ D) C ⊃ E C ∨ ~F A ● ~E F ∨ (D ⊃ Z) .: Z KEY: Tilde (~) forms negations (“...
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1answer
57 views

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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0answers
46 views

Baconian Logical Fallacy

I have been reading about logical fallacies lately, and I saw the Baconian fallacy listed here (of course on everyone's favorite site, Wikipedia). The description provided reads: "using pieces of ...
0
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2answers
46 views

What is the difference between these 2 sentences with quantifiers?

I'm practicing writing FOL sentences and I have the following sentences. The first sentence is the solution I provided and the second is the correct solution ( per the solutions manual).The difference ...
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1answer
53 views

Counterfactuals in Premises for Arguments

Can counterfactuals in premises make an argument sound and valid? I understand that soundness requires both validity and true premises whilst validity requires the premises to follow to the conclusion....
3
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3answers
158 views

How do we know certain things to be “obvious”, in general?

Sometimes while discussing things, we might come across statements which are pretty obvious to us. And, in English, sometimes we use statements such as -- "It's pretty obvious". But without ...
6
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3answers
161 views

Formal systems and interpretations for numbers

In my book (Hodel's Intro To Mathematical Logic), we are given several examples of formalized mathematical theories such as group theory, Peano arithmetic, etc. But I've had this ongoing confusion: ...
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3answers
135 views

How to contradict a general statement?

Consider the statement, "All the geometrical shapes on the screen have radius equal to 6". Suppose on the screen we have 6 circles with radius equal to 6 and also 1 triangle. In order to ...
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0answers
85 views

Is logic part of Philosophy or Mathematics?

Is logic part of Philosophy or Mathematics? I asked this question "Does programming use logic more or mathematics more" and users on some site insisted that logic was part of mathematics, I ...
2
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3answers
134 views

What is the definition of intension?

I have read in philosophy books about intension. But no one has defined it rigorously. What does it actually mean? I asked in a previous question about identity of intension. If this question is ...
0
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1answer
42 views

Are actions self-referential?

Someone recently told me that "actions are self-referential" (which means that we do not have to specify a particular actor to know whether an action is possible or not). He made it sound as ...
0
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2answers
52 views

Is a vacuously true argument a valid argument? [duplicate]

From what I know, given some argument, the argument is valid when it has true premises that lead to a true conclusion. Now, what if the premises were false? I mean, the conclusion would be vacuously ...
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1answer
42 views

Does “business logic” mean formulation of business by logic? [closed]

I have heard that ethics can be formulated by logic. So I guess there are many things which can be formulated by logic. Is it the same case for business? Does "business logic" mean ...
1
vote
2answers
66 views

Does the universal quantifier express existence? [duplicate]

Does the universal quantifier express existence? If I say "All dogs are cute", does the truth of that proposition require at least one existent dog? My question is different from the ...
11
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3answers
20k views

The difference between soundness and completeness

Is anyone able to articulate the difference between the properties of soundness and completeness insofar as they relate to the validity of the tree test?
0
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1answer
28 views

Intro Natural Deduction Problem: Given premise (p -> q) -> p show p using deduction

This is from the Daniel Bonevac Deduction text, page 122 #12. Given premise (p -> q) -> p show p using deduction. I can do this using made up rules on steps 4+5, not given in the book. The other ...
4
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1answer
78 views

Are there famous unsolved problems in logic akin to the Millenium Prize problems?

Are there major theorems that logicians have yet to tackle? And I don't mean any problems that pertain to the philosophy of logic (i.e. logical pluralism, the nature of logical consequence, etc), but ...
0
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1answer
38 views

Negation of the Rule of Implication proof

tried forever to figure out a solution to this problem. It's based on the rule of Material Implication with a negation in front of both sides. Namely the premise is ~(A>B) with the goal solution ...
0
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1answer
29 views

Having trouble paraphrasing sentence

F: French wins gold medal G: Germans win gold medal D: Danish win gold medal I have to use truth connectives to paraphrase: They will not all win gold medals I am thinking when paraphrasing it , one ...
4
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3answers
102 views

A possible formal failure made by Kripke?

In Kripke 's Naming and Necessity, there is a footnote says that "Lewis's elegant paper also suffers from a purely formal difficulty: on his interpretation of quantified modality, the familiar ...
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2answers
71 views

What's the name of this kind of fallacious proof to refute an idea?

In an argumentation where speaker A suggests an idea, we sometimes encounter this kind of fallacious proof from speaker B that speaker A's idea is bad (a very common form is known as passive-agressive ...
5
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1answer
131 views

How were formal systems and notion syntactic consequence (proof) developed?

I've looked at several resources to learn about logic and metalogic, and they first present syntactic consequence and semantic consequence as separate things and then try to show how each implies the ...
0
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0answers
70 views

Are axioms more important than definitions?

To prove a theorem in mathematics we usually use our axioms, definitions and other already proved theorems. Suppose we wante to prove a specific theorem and we haven't prove any other theorem and also ...
3
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1answer
126 views

Why did Hilary Putnam change of opinion towards Quantum Logic?

Hilary Putnam is known for having proposed a radical change in our thinking about the physical universe: He proposed that the universe was fundamentally based on Quantum Logic, and not in Classical ...
1
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1answer
111 views

Do mathematical objects exist after their definition? [duplicate]

Suppose we have a system with a set of axioms. Now we begined to define new terms. E.g. in maths we have a particular set of axioms and then we define what a function is. But do all the functions ...

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