Questions tagged [logic]

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

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13
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12answers
15k views

Are omniscience and omnipotence mutually inconsistent?

I see this in The God Delusion by Richard Dawkins: If God is omniscient, he must already know how he is going to intervene to change the course of history using his omnipotence. But that means ...
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10answers
3k views

Is the universe isomorphic to a universal turing machine?

I often think about problems that require an understanding of the very essence of computation and its inherent limitations. So, my questions are as followed: Is the universe isomorphic to a universal ...
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6answers
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Does Gödel's argument that minds are more powerful than computers have the inconsistency loophole?

In "Raatikainen, P., 2005, “On the Philosophical Relevance of Gödel's Incompleteness Theorems,” , the author argues that Penrose's and others use of Gödel's theorem as an argument against mechanism (...
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2answers
2k views

What are the truth-values of intuitionistic logic?

Classical propositional logic is bivalent, that is its set of truth-values has cardinality 2 (True & False). Intuitionistic logic drops the law of the excluded middle; does it have the same set of ...
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3answers
7k views

Can there be a valid argument which has a tautology as a conclusion?

Given this definition: A deduction is valid if and only if its conclusion is true whenever all of its hypotheses are true. Can an argument be valid if it has a tautology as a conclusion? An ...
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3answers
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Does a philosopher need much knowledge of mathematical/formal logic?

I am not a philosopher but I would like to ask this question. I know that there are philosophers like Hobbes, Locke or Foucault, who excel in the areas of ethics, political philosophy and aesthetics. ...
12
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9answers
4k 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. ...
8
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4answers
8k views

How does one prove De Morgan's laws for quantifiers?

One of De Morgan's laws state that ¬∃x P(x) is equivalent to ∀x ¬P(x), but how would one go about formally proving this? Numerous attempts to find a solution have been futile, even proofwiki.org ...
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3answers
194 views

What justifications have been given for using particular systems of logical calculus?

I think that using any particular system of logical calculus should be properly justified. This justification should be seen as particularly important and pressing in science and technology, and ...
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5answers
5k views

What's the difference between “not all” and “some” in logic?

We have, not all represented by ~(x) and some represented (∃x) For example if I say, Not all are animals. Some are animals. Because we aren't considering all the animal nor we are disregarding all ...
9
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2answers
663 views

Is there a deduction analog to the problem of induction?

Aren't deductive and inductive reasoning equally unjustified? So, inductive reasoning is going from specifics to general, whilst deductive reasoning is going from general to specific. But in deductive ...
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3answers
542 views

What are the arguments for and against “one true arithmetic”?

This question was born out of a discussion Is the real number structure unique? on Math SE, but since it is more philosophical than mathematical I decided to ask here. From Gödel completeness and ...
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9answers
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“This sentence is true”. Is there a word for this class of statement?

Is there a term that means "A self referential statement which is true if (and because) it is true and false if (and because) it is false"? "This sentence is a lie" is a paradox in the sense of "...
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1answer
223 views

Is the problem of logical omniscience intractable?

Vincent Hendricks and John Symons notes the following about epistemic logic: Epistemic logic gets its start with the recognition that expressions like ‘knows that’ or ‘believes that’ have ...
10
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1answer
857 views

Do Western logicians have a term for “the five crafts” (الصناعات الخمس)?

My only formal exposure to Logic is from an Arabic text book, where five methods for proving and/or convincing an opponent of your argument was described. These methods are termed "the five crafts" ...
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4answers
521 views

Can something “count” as TRUE without support by logic and empirical data?

I was in an online debate and had this statement presented to me. I would note further that your apparent positivism rests on what is logically a faith claim - specifically, the unproveble claim ...
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6answers
6k views

Do humans make decisions based on logic or emotions?

I often hear that we are emotional beings, that we make decisions based on our feelings, mood and emotions. These decisions may not be logical and serve us best. On the other hand some argue that we ...
4
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2answers
805 views

First book to self-learn logic, mainly to improve reading comprehension?

I read this and ask.metafilter.com, but desire to focus on improving comprehension of difficult writing. I never studied logic and prefer a textbook with practice problems with full detailed ...
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4answers
6k views

Argument “a is b” but “b is not a” valid?

Is it true that in logic "a is b" but "b is not a"? Does it work one way or both ways? For example: a is b Therefore, b is not a If this is valid, How can you prove?
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2answers
482 views

Can there be true conclusions without assumptions?

I was thinking of the sentence "I think therefore I am", which I had for a long time considered indisputable because it's self-evident. Then I considered the hypothetical situation where my ...
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3answers
309 views

Can all mathematical reasoning be translated into traditional logic?

Can all mathematical reasoning be translated into traditional (Aristotelian, syllogistic) logic? It would seem not ∵ one cannot syllogistically establish the validity of the reasoning in the ...
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1answer
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How does Kant derive the categories of the understanding from the logical forms of judgment in the Critique of Pure Reason?

I didn't arrive at any cogent and clear conception of the exact relation between Kant's logical forms of judgment and his categories, and most importantly, how he derives the latter from the former. ...
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1answer
376 views

What did Wittgenstein (mean to) achieve in the Tractatus?

I read the Tractatus about a decade ago, and was impressed, both by it and I suppose myself! But suddenly I'm seriously wondering what the book has or could achieve. Not so much how it changed ...
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0answers
73 views

Can hypercomputation compute the impossible?

There are things which are illogical/logically impossible (like saying that 2+2=4 and 2+2=5. Without changing anything in the axioms of mathematics or logic, this would be a contradiction and would be ...
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2answers
263 views

'I flunked every thing, but you have to let me pass.' How is this an Appeal to Pity?

[Source:] I know I flunked every exam, but if I don't pass this course, I'll have to retake it in summer school. You have to let me pass! Why is this a fallacy? I agree that the speaker desires ...
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8answers
11k views

Is Kurt Gödel's Incompleteness Theorem a “cheap trick”?

I found a throw-away critique of Kurt Gödel's Incompleteness Theorem in an essay about Deconstruction: The basic enterprise of contemporary literary criticism is actually quite simple. It is based on ...
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9answers
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What fallacy in Pascal's Wager allows replacing God with the devil?

I wanted to know the name of the fallacy or fallacies the Pascal's Wager in the sense that it can be applied to motivate one's belief in many things. A similar argument to the original Wager can be ...
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4answers
33k views

What is the difference between a statement and a proposition?

I'm doing a MOOC on mathematical philosophy and the lecturer drew a distinction between a proposition and a statement. This is very puzzling to me. My background is in math and I regard those two ...
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1answer
11k views

How do quantifiers work in predicate logic?

Predicate logic is somewhat like propositional logic, except that where propositional logic only works on the level of whole sentences (e.g. A = "Socrates is mortal", B = "All ...
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4answers
4k views

Where is the weakness in the ontological proof for God's existence?

I read the ontological proof for God's existence. As much as I understood, it says that if you consider that existence is part of essence, then the most complete essence should also exist. Now, I see ...
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2answers
5k views

Semantic vs syntactic consequence

I see that the double turnstile ⊨ denotes the semantic consequence of some sentence of logic, and single turnstile ⊢ denotes the syntactic consequence of some model. This seems equivalent to me. Why ...
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3answers
1k views

What are the major research programmes in contemporary logic?

As an interested outsider who is prone to reading about different formulations of logic, I've become interested in better understanding the big picture of what people are trying to accomplish as they ...
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4answers
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Why is Modus Ponens valid?

I am having trouble understanding what defines Entailment operator. On Mathoverflow I posted this question on what I perceive to be paradox of entailment. Consider: Modus Ponens: P therefore Q P ...
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9answers
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Do the laws of logic exist independently of human or animal consciousness?

Are the laws of mathematics and logic, such as if a=b, and b=c, then a=c just constructs of the human mind, or does the universe hold an innate logical structure to it, which the physical part of the ...
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3answers
570 views

Introductory book on philosophy of logic?

I know that there are quite a few questions like this here already, but I haven't yet found an answer that would satisfy me. I'm looking for an introductory logic book. My main goal is to work ...
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7answers
3k views

Are all paradoxes reducible to one “fundamental” paradox?

I may need to refine this question, since I am mostly grappling with a murky intuition and haven't yet done the real work. When I encounter many of the well-known paradoxes, such as Zeno's dichotomy, ...
8
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1answer
297 views

Are there different levels/categories of falsehood?

Consider the following sentences: The current president of the United States has 2 daughters. The current president of the United States has 5 sons. The current emperor of the United States has 12 ...
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7answers
5k views

Selection of logical connectives {¬,∨,∧,⇒,⇔} in set theory?

Nearly every treatment of set theory, whether Paul Halmos' Naive Set Theory, Herbert Enderton's Elements of Set Theory, Patrick Suppes' Axiomatic Set Theory, etc. introduce a common set of logical ...
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2answers
1k views

Is “propositions of logic are tautologies” (Wittgenstein) literal or mystical?

At 6.1 in the Tractatus, Wittgenstein says, "The propositions of logic are tautologies." When he says this, is he referring to the fact that the axioms of propositional logic as presented, for ...
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14answers
999 views

Why should I believe my own conclusions?

Consider the metaphysical question of whether God exists (just as an example). There are, and have been throughout history, billions of atheists, billions of Christians, and billions of people with ...
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11answers
1k views

Proof Universe Came From Nothing?

Consider the following proof: (1) Let the Universe be defined as the set of all things. (2) It is impossible for a thing to come from itself. (You can't be your own parent) (3) 2 implies a set of ...
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10answers
4k views

Is it a fallacy to say that a sane person cannot apply rational thought to the motivations of the insane?

A common argument in today's news is that: Someone commits a heinous crime by shooting a bunch of people. Anyone who commits a heinous crime must be insane. Sane people cannot apply rational thought ...
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1answer
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Should Wittgenstein be given some credit for Godel's incompleteness theorem?

Is there a connection between Wittgenstein's argument against the "Theory of Types" and the proof of Godel's Incompleteness Theorem? Being only semi-knowledgeable, I will draw the connection of which ...
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6answers
2k views

What fallacy dismisses criticism of a bad law with “just don't break it”?

Let's say someone is criticizing the government for instituting some draconian policy, and/or for persecuting people for doing something minor. And the response is:"Just don't do it and you'll be fine"...
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4answers
631 views

“→” is the symbol for material implication. Is there such a thing as “immaterial implication”?

Why do we qualify "implication" with "material"? This seems to imply that there are other kinds of implication.
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2answers
14k views

How do I use the “Barbara, Celarent, … etc.” mnemonic?

Medieval logicians memorized this most famous logic mnemonic: Barbara, Celarent, Darii, Ferio ← direct first figure Baralipton, Celantes, Dabitis, Fapesmo, Frisesomorum ← indirect first figure Cesare,...
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3answers
2k views

What's the difference between Aristotle's logic and Frege's logic especially with regard to predicates?

I'm reading a book and the author introduced Aristotelian logic and then he provided an overview of Frege's development of logic, but I don't understand what the difference is between Aristotle's ...
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1answer
303 views

Making 'sense' of Wittgenstein's senselessness / nonsense distinction in the Tractatus

For this question I'm just considering Wittgenstein's theory at the time of the Tractatus. As far as I know, for Wittgenstein: Meaning - The object denoted by a word (i.e. referent). Sense - The ...
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3answers
189 views

Once it happened, an event was necessary?

What would happen to an event in the past, if time itself ceases to exist? Without time, has what existed (such as the writing of this sentence) never happened? A total disappearance of space-time ...
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2answers
542 views

In logic, do propositions default to true or false when objects in them do not exist?

In this hypothetical: Firefighters always tell the truth, while politicians always tell lies. Suppose three people, who are either a mix of firefighters and politicians, all politicians, or all ...