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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10k views

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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3answers
641 views

How is Wittgenstein’s “notorious paragraph” about the Gödel's Theorem not obviously correct?

Timm Lampert quotes from Wittgenstein's "notorious paragraph" (§8 of Remarks on the Foundations of Mathematics, Appendix 3) in http://wab.uib.no/agora/tools/alws/collection-6-issue-1-article-6....
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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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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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74 views

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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2answers
137 views

Would logic be respected if we assume that the God's omniscience includes the ability to DIRECTLY OBSERVE future events?

If we assume that God knows the future, we think that the only possible way He could do that would be if He knew all possible states of the system. He could thus "compute" that future. But this "...
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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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1answer
88 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 ...
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3answers
138 views

Concerning the definition of “valid”

I studying graduate math (not very far into it) and I realized that some of the higher level math texts I would like to read are hard to access without a strong basis in logic. Now I've taken ...
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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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2answers
71 views

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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References for the Realism/Anti-Realism debate in Logic

The concept of anti-realism in logic seems to be an interesting and growing idea. I'm looking for references (papers, books, authors...) regarding the debate between realism and anti-realism but ...
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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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3answers
251 views

Understanding the simulation argument

I came across Nick Bostrom's paper called Are You Living in a Computer Simulation?. The paper argues that at least one of the following propositions is true: The human species is likely to go extinct ...
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2answers
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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55 views

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 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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Can there be cause and effect without time?

Our usual understanding of cause and effect operates tensely; that is in time. But consider a basic statement in some generic computer language: if x then y Is this in time? Well an actually ...
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Trying to decide if the terms “proper education”, “real world education”, “successful life” are vague or ambiguous?

I feel that all three of these terms can have different meanings, but are they all vague as well? For example, proper education could mean a university education/college education/education in the ...
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60 views

A question about possibility

If A, then B ~ A So, possible that B Valid or not? My take: Not valid. Reason: Valid means if all the premises are true, the conclusion must be true That means adding new information should not ...
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4answers
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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2answers
167 views

Why do we need Aristotle's theory of predication?

My question is about Aristotle's theory of predication. Why do we need it at all? I know it's intuitive to pick up something and say something about it like "S is P", but doesn't this lead us to ...
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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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2answers
80 views

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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1answer
84 views

Proof from tree to steps

I'm able to get the proof in a tree form (it's invalid). Is there a method where I can transform it to steps method indicating the rules of inference and replacement?
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2answers
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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4answers
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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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2answers
221 views

Has anyone developed a “restricted English” notation for logic (first-order or otherwise)?

I ask because Kleene mentions the possibility in Mathematical Logic, but I am not sure if he meant this as something he's aware of, or as a hypothetical possibility. I also enjoy the first part of ...
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96 views

Logical Necessity

Logical necessity is that which is necessary by definition. Otherwise it is sometimes considered to be that which cannot possibly be false, or cannot be otherwise metaphysically. The usual example is ...
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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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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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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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105 views

De Morgan for Quantifiers Formal Proof: Inhabitance Question

I have a problem reading existing question's answers. I've successfully encoded the proof of one of De Morgan's Laws, ¬∃x P(x) → ∀x ¬P(x), for Quantifiers formally via cubicaltt type-checker via Curry-...
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1answer
177 views

De Morgan for Quantifiers Formal Proof: ∀∃-intro and -elim Questions

I have a problem reading existing question's answers. I've successfully encoded the proof of one of De Morgan's Laws, ¬∃x P(x) → ∀x ¬P(x), for Quantifiers formally via cubicaltt type-checker via Curry-...
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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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Having trouble starting a proof

I am given the following premise: ( Q --> R ) and the following conclusion (( ~ Q --> ~ P ) --> ( P --> R )) I am allowed to use Modus Pollens, Modus Tollens, Hypothetical Syllogism, ...
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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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305 views

How to derive: F(xy)→∼F(yx) ∴ ∼F(xx)

This is from Logic 2010, Derivation 4.021: F(xy)→∼F(yx) ∴ ∼F(xx). The book we use is Parsons', but I cannot even make sense of these symbols stand-alone F(xx) without any quantifier. This problem ...
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1answer
96 views

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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3answers
101 views

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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1answer
45 views

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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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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1answer
206 views

If metaphysical grounding of beliefs is not necessary what is to logically compel one to believe anything?

'Grounding' is the notion that 'because of X, Y', X being the reason one can accept Y beyond pragmatic considerations. In this way, X and Y are analogous to cause and effect respectively. If it is ...
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47 views

Fitch Proof Help

I'm having some trouble solving this proof in Fitch. How do the universals switch place from the premise to the goal? There is no negation in the goal so negation introduction is not the way to go, I ...
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176 views

Does anyone know of a philosophy which rectifies or considers the following question?

Let's imagine that I began to doubt the validity of one of my arguments, which leads me to question my ability to make rational arguments. And so begin to distrust my intuitive ideas about logic, then ...
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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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1answer
27 views

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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621 views

Can a sentence without a truth value be true?

I was doing some very, super, light reading on self reference. It seems to me that the statement nothing that I say is true both: cannot be understood with the T-schema; is self referential. - ...