Questions tagged [logic]

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

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Cogito corollaries and meaning

Doubt implies thought. I'm doubting. So I'm thinking. [(d→t) ∧ d]→t Thought implies existence. I'm thinking. So I exist. [(t→e) ∧ t]→e d→t; ¬t→¬d; [¬t ∧ (d→t)]→¬d t→e; ¬e→¬t; [¬e ∧ (t→e)]→¬t [(d→...
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Did we give up on Euclid's method? [on hold]

Most people seem to regard attempts at Euclid's method in philosophy as failures. Example: Spinoza's Ethics Some of them then say that because Spinoza failed, any modern attempt is futile. But I ...
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Formalism in (math) vs. (philosophy) [on hold]

What's the difference between formalism in math and formalism in philosophy?
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Trouble with cookies [on hold]

Matter cannot be created. Cookies are matter. So cookies cannot be created. I know this seems absurd but I'm using this to make an important point about arguments. The argument appears to be valid ...
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139 views

Does the Universe make sense? [on hold]

When faced with a paradox, we say: well this can't be because it doesn't make sense. p = "x doesn't make sense" q = "x doesn't exist" The contrapositive preserves validity: p implies q (not q) ...
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The enunciation clause (Lyotard & Levinas)

As kind of introductory remark, let me state that I'm not academically-trained in philosophy, so my apologies if this comes up as a rather simple question. I was reading Logique de Levinas by JF ...
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Why doesn't philosophy have higher standards for its arguments?

Mathematical systems are an excellent model for organizing and conducting thought: A conjecture is an unproven claim, while a theorem is a proven claim. A corollary is a claim that follows from ...
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234 views

Can someone explain this logical statement?

I have been trying to teach myself philosophical logic, but my mind is completely stuck. I cannot seem to understand the abstractions, which is unusual for me given that I have taken very advanced ...
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Why is there an O type conclusion in modus celaront

Modus celaront is type logical syllogism. No reptiles have fur. (MeP) All snakes are reptiles. (SaM) ∴ Some snakes have no fur. (SoP) The conclusion is of a O type(Some .. are not ...). Why is ...
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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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Did anyone argue against the possibility of a perfect prediction from within a system?

Did anyone offer an argument against the possibility of a perfect and complete prediction about a system from within that system along the following lines: Let's imagine a machine (like a desktop ...
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186 views

What is the difference between logical consistency and logical entailment in deductive logic?

I am having a little trouble sorting out two definitions from the first chapter in my logic textbook, The Logic Book by Bergmann, Moor and Nelson. I am under the impression that a set in a sentence ...
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Incorrect statement in Suppes' Introduction to Logic

Chapter 2 of Suppes' develops the notion of sentential inference and how to construct rules of inference. However, there is one part in his development that seems incorrect no matter how I look at it. ...
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61 views

Negation of a relational quantified term?

Formally, when you negate a quantified term which is attached to a relation, is a distributed term always made undistributed and vice-versa? For example, consider this statement : Anyone who assists ...
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84 views

Wittgenstein's solipsist, from Tractatus?

According to the early Wittgenstein of the Tractatus, the solipsist is one and one and the same with the world. He then makes the claim that solipsism coincides with realism. 5.64, Wittgenstein ...
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Using solipsism's incoherence with doubt as proof of the external world?

I have the following rough outline of utilizing solipsism as a proof by contradiction to the goal of asserting an epistemological proof of the external world. A solipsist (Wittgenstian) lives in a ...
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1answer
225 views

Does this argument make sense?

Consider the following argument: (A) Either sales or expenses will go up. (B) If sales go up, then the boss will be happy. (C) If expenses go up, then the boss will be unhappy. (D) ...
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156 views

Who first studied asymmetric relations qua relation?

Who first asymmetric relations qua relation, viz., the fact that A relates to B by some relation does not always/necessarily imply that B relates to A by the same relation. ?
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Who first studied “logical (ir)reversibility”?

Who first studied "logical (ir)reversibility" philosophically? By "logical (ir)reversibility" I mean questions like:Why is it easier to multiply large numbers than to factorize them? understand a ...
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54 views

Can paraconsistent logic be translated to Aristotelian logic? [closed]

Maybe if you split sentences in parts you could translate in atomic ideas and translate paraconsistent logic to Aristotelian logic.
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Quick question on validity of arguments across propositional and predicate logic

Could someone clarify a quick question regarding the following please? From the text: Assume Γ ⊭ ϕ. Then there is an L2-structure A such that all members of Γ are true in A and ϕ is false in A. ...
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Quick question on discharging assumptions

Could someone explain conceptually what the consequences are of assumptions NOT being discharged in a natural deduction ? Suppose the objective is to establish a claim of the form : 'If A,then B.' ...
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What should be the correct form for this particular argument?

Thank you for reading my concern and providing your precious time. I am writing this question to highlight the difficulty in solving the problem due to wrong punctuation and sentence construction. ...
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What does « answering a question » mean? [migrated]

Since StackExchange is about asking and answering questions, I came up with this problem : what is the criterion of a valid answer ? I suppose it is a matter of the type of question you are asking, i....
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Unproven premises leading to true conclusion imply valid premises

Suppose that we have a bunch of premises which are unproven but lead to a valid conclusion, how much of a leap of faith it is to assert that the premises can now be seen as valid? I have said "a ...
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What is the meaning of “object of” in this context?

This is the context: ...object of self-reference: 1) a sentence that negates its own truth. 2) an event that negates its own existence... The topic is about the concept of self-reference in ...
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How to translate “No dolphin sings unless it jumps” into predicate logic?

i have a silly logic question again. How would you translate the following sentence into predicate logic? No dolphin sings unless it jumps. My guess is that it is an E-sentence of the form "no A ...
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How to translate “Only dogs and dolphins jump if petted” into predicate logic?

The Logic2010 software provides exercises for the symbolization of English sentences. But i'm stuck with one symbolization, which closely resembles another one I solved correctly. The first one ...
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2answers
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Is there any difference between declarative sentences and statements?

I was reading about propositions and statements and the differences between them and saw this: What is the difference between a statement and a proposition? and the answer that one of the users ...
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1answer
92 views

Measuring a Person's Aesthetic Sense

Can we measure or evaluate the aesthetic sense of a person? Like, can we statistically say that Person A has a superior aesthetic sense to Person B? Since beauty is relative, can we truly 'grade' ...
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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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4answers
106 views

What is an argument with necessarily true conclusion?

I cannot understand what an argument is with a necessarily true conclusion. Could you explain to me what it is and write here some examples? Moreover, what is the meaning of “necessarily true” and “...
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Language Proof and Logic 15.16 [duplicate]

This problem concerns the practice problem 15.16 of the textbook Language, Proof and Logic. So I saw a similar post here, which gave most of the correct answer (Language proof and logic Chapter 15 ...
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1answer
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Is an argument valid if one of the premises don't affect the conclusion?

Let's say I have an argument with premises P, Q and R, with a conclusion S. But let's also say that Q and R are sufficient to conclude S. But having P as a premise doesn't affect the argument in any ...
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68 views

Which philosophers proposed theories containing a performative contradiction?

Socrates was blamed of this by being wrongly interpreted of saying: "I know that I don't Know." or other variants. What he really said was: "I neither know nor think that I know." Source: https://en....
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Book Introduction to Logic. Patrick Suppes-Section 2.1-Excercise 4

Anybody can help me with the solution of this exercise? Construct a (non valid) rule of inference which by itself will satisfy Criterion II but violates Criterion I? Thank you in advance. Diego.
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What falls under Hegel's concept of “absolute knowledge”: does that include deductive logic and scientific explanation?

In the wikipedia page for Hegel's Science of Logic, it states: According to Hegel, logic is the form taken by the science of thinking in general. He thought that, as it had hitherto been ...
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What is the meaning of free variables?

In some books I see something like: phi(x1,...,xn) with free variables among x1,...,xn. An example of this is on 2nd paragraph, page 25 of the book Knowledge in Action. I have included a snapshot of ...
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Could the link between virtues and pleasures and pains in the third chapter of Nicomachean Ethics' book II be considered a hypothetical syllogism?

In the chapter 3 of Nicomachean Ethics' book II, Aristotle says: Again, if the virtues are concerned with actions and passions, and every passion and every action is accompanied by pleasure and ...
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Is is logically inconsistent to say that male on female violence is wrong? (Compared to vice versa)

I have always believed that the reason it is more wrong for a man to hit a woman than vice versa is mainly because women tend to be physically weaker then men, and that even if a women initiated ...
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Logical, semantic and self-referential paradoxes: The Truth teller and the Liar (draft) can an expert on the matter give feedback?

Title: Logical semantic and self-referential paradoxes: The Truthteller and the Liar (draft, informal) (major) assumption: A statement is either true or not true (law of excluded middle, classical ...
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Fitch Proof - Arrow's logic of preferences

I've been stumped on this one question in particular for several days now and I'm hoping to get some help on where I'm going wrong. Given the following premises: ∀x∀y(StrongPref(x,y)→ ¬StrongPref(y,...
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Can anyone tell which one of these sentences are materially implies(implication) and logically implies(implication)?

these are the contexts: 1): If the number 0 has a certain property, and any natural number a has the property implies that a +1 also has the property, then every natural number has the ...
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Why does one need to specify that the language is “well-orderable” for first order logic to be complete?

While reading Wikipedia I noticed the phrase "well-ordered language" in the following related to Gödel's completeness theorem: The completeness theorem then says that for any first-order theory T ...
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60 views

What are the types of non-deductive arguments?

I've been looking for it, but Google leads the search to multiple sort of pages that, although they talk about logic, explain the subject very differently from each other and they don't fix a list ...
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What are the conditions needed for a good argument in the field of informal logic?

I'm trying to get the difference between the concept of argument in the field of formal and informal logic and I'm still a little bit confused by how. Are true premises and non-false conclusions ...
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Is the doomsday argument flawed?

Through the doomsday argument people try to calculate the number of humans that will ever live based only on the number of humans that have lived until now. To me this arguments seems very flawed, but ...
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Fitch Arrow Proofs [closed]

Using the FITCH program and the FITCH derivation rules you should make a proof or derivation of C10 from P5 through P11. P5: ∀x∀y(StrongPref(x,y)→ ¬StrongPref(y,x)) P6: ∀x∀y∀z((StrongPref(x,y)∧...
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A question about material implication

I have a question about reading material implications. I know this read as "if p then q". like: if the moon is made of green cheese then the earth is round. but I can't read it in this sentence: ...
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Which solution is better for this predicate?

We have this predicate: Prime(x) ≡ x>1 ∧(∀y)(Divide(y,x) → (y=1 ∨ y=x)). Now I have to turn this into an English sentence. I've come up with three answers: x is a prime number if x is greater ...