Questions tagged [logic]

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

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12
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3answers
498 views

What is the telos of a proposition?

Whitehead contends in Process and Reality that propositions are “hybrid entities” which act as “lures for feeling.” The famous co-author of Principia Mathematica scolds the traditional conventions of ...
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7answers
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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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6answers
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Quantum Mechanics and Logic [closed]

I heard several times that the results of quantum mechanics (double-slit experiment for instance ) challenge our logic. One example of that is the famous physicist Lawrence Krauss. He keeps ...
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16answers
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Does the notion of an all-powerful God conflict with the idea of free will?

In Abrahamic religions, God is often believed to be wholly omnipotent. People also seem to believe that humans have "free will", especially insofar that they feel they are in control of their own ...
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9answers
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what is the truth value of a sarcastic statement?

In light of Donald Trump's many statements (and then retractions of said statements) it is very difficult to decide whether what he is saying is true or false. Many attempts at fact-checking often ...
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4answers
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Logic, Russell, joke [closed]

There is a Russell impression with a joke on youtube, in which Russell puts the following questions to G. E. Moore: Do you have any apples in that basket? Do you have some apples in that basket? Do ...
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6answers
931 views

Are there degrees of truth ?

I do not assume bivalence - that every proposition or declarative statement - is either true or false but not both. I do not raise the issue of 3-valued logics or offer or invite any theory of truth. ...
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5answers
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Intuitively, why is ¬(P ↔ Q) ≡ P ↔ ¬Q?

Source: p 77. Sweet Reason: A Field Guide to Modern Logic (2010 2 ed) by Henle, Garfield, Tymoczko. I pursue only intuition; please do not answer with formal proofs or Truth Tables. I already ...
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2answers
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What's the relevance of falsifiability in regards to logical arguments?

Is it reasonable to classify logical propositions that rely on deduction and are non-falsifiable as being inherently not worthy pursuing or does this just applies to inductive reasoning?
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What is the fallacy in comparing evolution to a fairy tale?

I found the following statement on this Creationist site. If a fair maiden kisses a frog which instantly changes into a handsome prince we would call it a fairy tale. But if the frog takes 40 ...
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7answers
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How can I develop my critical thinking skills?

I am a freshman engineering student going to college. I want to learn how to think critically and to become a critical thinker and a sharp arguer. I am interested in philosophy, because I am curious ...
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3answers
463 views

Do all epistemologies suffer from the “regress of justifications” problem?

Aristotle describes the regress problem in his logical work Posterior Analytics I.2: b5. Some hold that, owing to the necessity of knowing the primary premisses, there is no scientific knowledge. ...
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2answers
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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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4answers
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How do I check if two logical expressions are equivalent?

For example: Is (A ∨ B ∨ C) ∧ (D ∨ E ∨ F) the same as (A ∧ D) ∨ (A ∧ E) ∨ (A ∧ F) ∨ (B ∧ D) ∨ (B ∧ E) ∨ ( B ∧ F) ∨ (C ∧ D) ∨ (C &...
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Is the notion in Hume that you cannot deduce an “ought” from “is” related to his assertion that reason must be the servant of the passions?

I hear it asserted that David Hume said one cannot deduce an "ought" from an "is". I also find it asserted that he said reason must be only the servant of the passions. I had long uncritically ...
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2answers
563 views

Is reductionism the primary means of logical analysis in analytic philosophy?

I was reading a philosophical article about analytic philosophy and I saw the claim: Russell and many philosophers influenced by him asserted that complex statements can be reduced to simple ...
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2answers
397 views

What are the dialetheist semantics for logical negation?

This question is in a sense a follow-up, or elaboration, of the question "What are the motivations for Dialetheism?". Reflecting on the way I phrased that question, and the way I remarked on answers, ...
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8answers
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What is the truth value of the proposition 'All unicorns are beautiful'?

If we let Fx denotes that which has the property of being a unicorn, and Gx denotes that which has the property of being beautiful, then this proposition would be signified by the following: ∀x(Fx→Gx)...
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9answers
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How to prove (A v B), (A → C), (B → D) therefore (C v D)

Obviously since A → C and B → D then if A v B one of C or D must be true. My only idea is v must be introduced, but how would I use subproofs to show one of A /\ C or B /\ D is never false if A v B?
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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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7answers
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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: ...
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Does philosophy belong to empirical science or formal science?

According to Wikipedia, science can be divided into empirical science (such as natural science and social science) and formal science (such as mathematics, logic, statistics). I was wondering if ...
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5answers
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What's an intuition for material implication?

The paradoxes of material implication show that the usual interpretation of implication as "if ... then" statements leads to counter-intuitive results. For example, from (P & Q) -> R we can ...
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3answers
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When is pointing out a person's hypocrisy not considered to be a logical fallacy?

People keep using the word "whataboutism" and it seems people don't really know what it means, and I don't see how it's a logical fallacy if it's a very good argument. For instance, if the U.S. says ...
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572 views

Shouldn't statements be considered equivalent based on their meaning rather than truth tables?

Consider the following truth table, which serves to define the logical connective ⇔, P | Q || P⇔Q T | T || T T | F || F F | T || F F | F || T According to the above truth table, the logical ...
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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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4answers
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How do we separate rules of logic from non-logical constraints?

I think that very often the idea of 'constraint' appears in mathematics. For example, when a triangle is considered, 3 points are constrained not to be co-linear, and then we try to discover the ...
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514 views

What are the critiques of the “we might as well assume it” solution to the problem of induction?

I'm curious whether the following proposed solution to the problem of induction has ever been discussed in the literature: Either the future resembles the past or it does not resemble the past. If it ...
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1answer
869 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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How can we justify the use of logic?

I would like to hear some philosophical arguments which justify the use of logic. Additionally, if a justification of logic takes the form of an inference, is it a problem if this inference itself ...
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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 ...
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1answer
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What is the axiom of reducibility? And what philosophical controversies did it incite?

Trying to come to terms with basics concerning philosophy of logic, and wish to ask about some particular issue: What is in simple words the axiom of reducibility put forward by Russell? And what is ...
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3answers
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Are there rules for dealing with self-reference “paradoxes” in logic?

My favorite paradox that leads to an endless regress, and also leads to a question: The sentence after this is true. The sentence before this is false. When contradictions appear in proofs, ...
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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?
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Can a “real” paradox exist?

Given a statement, S: "S is not true." We arrive at a paradoxical solution whether or not we assume S to be true or false. Does this automatically imply that we have made an error in logic, ...
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1answer
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What is Kant's argument about the relationship between logic and reason?

At Wikipedia, I read: Logic arose (see below) from a concern with correctness of argumentation. Modern logicians usually wish to ensure that logic studies just those arguments that arise from ...
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1answer
248 views

Is there a sheaf-theoretic description of para-consistent logics?

Paraconsistent logics drop the notion of global consistency, instead they have a notion of local consistency. In sheaf-theory, or categorical logic, as in topos theory, there is a notion of local ...
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Can one still derive paradoxes from the amended version of Naive Set theory given by Cantor in a letter to Dedekind?

Consider the following definition of set given by Cantor in a letter to Dedekind: If on the other hand the totality of the elements of a multiplicity can be thought of without contradiction as '...
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1answer
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How does Robert Nozick explain the Gettier problem?

Nozick agrees that the Gettier counterexamples to the JTB analysis of knowledge are cases where someone has a JTB but does not know. What is his explanation of what has gone wrong in those cases? ...
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7answers
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Has quantum mechanics destroyed the fundaments of logical reasoning?

In quantum mechanics it is thought to be possible that something could be at two places at the same time. But if that is really the case then perhaps law of non-contradiction is no longer valid. So ...
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15answers
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If logic is based on human reasoning, how can most people be so incoherent?

I believe that our understanding of formal logic is to formalize how a human brain is supposed to work. And this also makes sense when we think of mathematical problems that we only should get the ...
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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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4answers
446 views

Is there a logic that takes time into account?

I hope this is neither too simple nor off-topic; I apologize if so. I have just noticed that standard sentence logic seems to make assumptions about time in determining the truth/falsity of a ...
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3answers
849 views

Are there any resources for teaching young children philosophy and logic?

My oldest child is nearly six years old and will be starting his first level of formal schooling in a few weeks. I don't believe he will be taught philosophy and logic in the classroom, so I would ...
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5answers
472 views

Why would definition not be proposition?

I've read in one mathematics book that any definition is not a proposition. Why is it so? What definition of proposition makes the former into the latter? EDIT: There is well-known analytic-syntactic ...
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Is the argument that a claim is “too strange to be made up” an appeal to logos or pathos?

When someone tries to persuade you of the truth of something they said and they use the argument that it is too strange to be made up (or any variations of this, such as "too complicated to be fiction"...
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7answers
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How is (A → B) → C different from A → (B → C)?

This question derives from p 322, A Concise Introduction to Logic (12 Ed, 2014), by Patrick Hurley, but I do not quote it because its example presumes knowledge of pharmaceuticals and is too esoteric. ...
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2answers
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What exactly is informal logic and is this what I'm looking for?

I've been reading and researching about formal and symbolic logic for some time now, mainly out of interest in rationality. But I've come to a point where the various logical systems seem more like ...
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5answers
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Asking a genie for more wishes [closed]

I just saw this SMBC comic. The second picture looked really promising, but as far as I see it, this attorney screwed up. With his second wish it doesn't matter whether you say wish or splork, so ...
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2answers
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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,...