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Questions tagged [logic]

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

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44 views

How can many Methods of Agreement or Difference overpower 1 Joint Method?

Abbreviate Method of Agreement to MoA, Method of Difference to MoD, Joint Method to JM, Necessary Conditions to NC, and Sufficient Conditions to SC. Source: p 552, A Concise Introduction to Logic (12 ...
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How does negating an existential quantifier work?

I'm revising counterexamples for my logic exam next term, and one of them has me absolutely stumped. I have to provide a counterexample to refute the following claim: ∀x∃yPxyy v ∃x¬∃y∃zPxyz is ...
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Why must Rules of Inference be applied only to whole lines, without quantifiers?

Source: A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley [p 415:] Since, however, the first eight of these rules are applicable only to whole lines in an argument, as long as the ...
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'Any heavyweight can defeat any lightweight.' : How do you bracket the Nested Conditional?

Source: p 498, A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley Any heavyweight can defeat any lightweight. [1.] (x) [ Hx ⊃ (y) ( Ly ⊃ Dxy ) ] Even after reading this, Nested ...
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'Any heavyweight can defeat any lightweight' : Why are all the quantifiers not at the front?

Source: p 498, A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley Any heavyweight can defeat any lightweight. [1.] (x) [ Hx ⊃ (y)(Ly ⊃ Dxy) ] I bolded the only change. Why is it ...
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What are the steps and thought process behind translating Exclusive Propositions into Standard Categorical Form?

Source: p 256, A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley Many propositions that involve the words “only,” “none but,” “none except,” and “no . . . except” are exclusive ...
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How does Kant's transcendental argument show that the basis for Skepticism is unintelligible?

I understand Kant's categories, however I don't understand their value in arguing against skepticism.
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137 views

When a fallacy actually occurs

Assume a debate has occurred and a result ended the debate, but in this result a slippery slope is coming true - more specifically the contrapositive used as a basis for argument that relied on a ...
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249 views

Logical sentence… or not?

The following sentence, which is part of a presentation of the doctrine of structural holism and is translated from the french, does not seem quite to make sense to me: "each one [of the members of a ...
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How to intuit 'unless'? [closed]

I already know, and so ask NOT about, the proof of: A unless B =  A if not B =  Either A or B. Because I ask only for intuition, please do NOT prove this or use truth tables. My problem: I want to ...
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Is the logic precept that for two propositions there are four truth values ever applied to serious matters?

An elementary precept of logic says that where there are two propositions, P and Q, there are four possible "truth values", P&~Q, ~P&Q, P&Q, ~P&~Q, where ~ means "not."   Do people ...
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Logic: can I define a domain containing distinct names referring to the same object?

For example, would a domain {Eric Blair, George Orwell} contain two things, or one thing?
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Eventualities and their existence

Emmon Bach uses in "The algebra of events" the term 'eventuality' to denote states, events, processes, etc. How can their actual existence be expressed logically? For example, when I say "John came" ...
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853 views

What does Sartre mean with that existence precedes essence and how is it related to the earlier existential philosophers' thoughts?

What does Sartre mean with that existence precedes essence and how is it related to the earlier existential philosophers' thoughts? Existential philosophers like Kirkegaard, Heideggers and Friedrich ...
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How can I explain the soundness of a rule with respect to the semantics of a truth table?

The question is a mouthful but it comes from an exercise in which I was asked to explain why modus ponens is sound with respect to the semantics expressed by the truth-table. Many things are not ...
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Is arguing about “death sentence” in a dichotomic way a formal error? [closed]

Often people are trying to show that death sentence is good and useful, while some other are arguing to show the opposite. But reality is complex. If we would like to describe it with a mathematical ...
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323 views

birds of a feather flock together and guit by association

There is a saying "birds of a feather flock together" which usually boils down to People of similar character, background, or taste tend to congregate or associate with one another. Yet guilt by ...
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Did Wittgenstein say something about intuition for logic?

When one creates some logical content, like in programming, only naives think that this is a rational way of thinking. In fact, this is based on patterns and intuition. Did Wittgenstein say anything ...
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333 views

The existence of unknown propositions? [closed]

My question may seem strange and nonsensical for some, therefore I will try to explain myself to the best of my ability. So to make it clearer what I mean with my question. I will start by quoting ...
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I am trying to translate this in to English sentence. Help needed

I will notate & for "and" and v for "or" A: I got X B: I went to school. ~(A v B) = Neither I got X nor did I go to school. which is equivalent to ~A & ~B = I did not get X and I did ...
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Consciousness and its relationship to Category Theory [closed]

Since consciousness is implicitly understood/used in the use of categories , could we consider it a "fundamental" functor ? Category Theory is very general (covering/useful) to many fields now ...
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Do sentences that are “selection violations” have truth values?

Given a grammatical sentence like "Colorless green grass sleeps furiously" is it possible to assign a truth value to it?
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what types of question answer sets exist? [closed]

-let's take for example (freewill or determinism?) -is it an illogical question with no solution (no solution) -is it a logical question with a logical single correct solution (freewill) -is it a ...
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Is it opposite-day today?

Imagine, we had a very well-known day called opposite day, where everything is negated. Also imagine that you are walking along the street and someone asks you: "Is it opposite-day today?" What ...
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About considering two constants when using Herbrand's universe

Excuse the poor wording if the question wasn't so clear or misleading, tried to word it to the best of my abilities.If it's worded incorrectly please don't hesitate to tell me the correct question or ...
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117 views

Does this proposition prove anything? [closed]

Consider the proposition "absolute truth does not exist". One can look at two cases: 1.This proposition is true This case leads to a contradiction: if the proposition "absolute truth does not exist" ...
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What are some tools for overcoming bias within a participant when engaged in a Socratic debate? [closed]

Given that bias is not easy to argue with and an embedded unconscious obstacle to critical and logical debate. What tools are there to overcome bias in a Socratic debate?
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What is the argument in this Paragraph

What is the argument in this Paragraph (Aquinas's Five Ways): The fifth way is taken from the governance of the world. We see that things which lack intelligence, such as natural bodies, act for an ...
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177 views

Is there a notion of 'objective' in Hegelian Theory?

According to the wikipedia entry on Categorical Logic: Lawvere's writings, sometimes couched in a philosophical jargon, isolated some of the basic concepts as adjoint functors (which he explained as '...
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Modal logic and set theory question [closed]

So if n is a member of the set of natural numbers, such that n is greater than 1 and lesser than 3, then n=2 necessarily?
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Conditional statements truth table [duplicate]

Possible Duplicate: How can we reason about “if P then Q” or “P only if Q” statements in propositional logic? I have read in quite a few books that the proposition 'p->q' can be read as either '...
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What form of logic is necessary for practical philosophy?

Logic is broad and concerns different fields, so to be more specific with the purpose of logic what is the most important form of which required for practical philosophy?
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What is the name of the argument that disallows the current state or condition of things as it is independent of reason?

I remember a few years ago I came across a description of a framework of argument that disallowed the use of the current (or any other) state in the argument given that the state is independent of how ...
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202 views

Language as barrier to concepts [closed]

Can the limitations of language be considered a barrier in conveying a philosophical concept? How can an idea that resists linguistic formulation be conveyed without losing the essence? Is there a ...
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37 views

Possible worlds and accessibility relations [on hold]

Is there anything preventing possible worlds from meeting one another in a plane of existence that intersects both possible worlds? And if not, how would you describe such a plane that intersects ...
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Logic Philosophy question [duplicate]

I am looking for help in answering the full question with a full conditional proof (cp). This will help me understand this question and others that I am trying to understand. Thank you. Would ...
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26 views

Is There a Maximally Consistent Set That is Not $\omega$-complete? [closed]

I was going back through Mates 2nd edition Elementary Logic and am having a bit of trouble on one of the exercises; it says, "Find a counter example to the following assertion: for any set of ...
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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 ...
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Was Russell's purpose in Principia Mathematica to formalize all the possible constructions of logic?

In writing Principia Mathematica, was one Russell's purposes to formally describe all the possible variations of logical concepts and reasoning that can be used in mathematics? For example, suppose ...
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51 views

How to derive P > (Q > R) from (P > Q) > R in Fitch?

I am having a little bit of difficulty coming up with a Fitch-style natural deduction proof. Presumably, I need to use a few conditional introduction rules, but I am not sure what I can get out of ...
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How would I go about proving P>Q from the premise (notP v Q)? [duplicate]

A similar question had already been asked, but the solution involves steps I am unfamiliar with. in class, we have only been exposed to intro and elim rules, as well as contradiction rules. Here is ...
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Fitch Proof - Logic LPL 6.31

I am trying to complete the following proof in Fitch but am completely clueless on how to approach it. Any help would be appreciated! Thanks
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123 views

To connect or to disconnect mathematics and platonism?

How [do philosophers] strongly support or refute the view that: mathematics is a bag of tricks for real-world problem solving; undecidable statements are an irrelevant and harmless side-effect of an ...
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Complement of “at least two people share the same birthday”

Suppose a room contains 𝑛 people. What is the probability that at least two people share the same birthday? So this is actually a question on probability, but I'm really confused in the logic and ...
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Is every reason reducible to a sequence of tautological statements? [closed]

I think of tautological statements as those statements which when explained should repeat themselves, and should intuitively explain the reason. For example, A = A because 'A is equal to A'; Dog is ...
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Logic Question in a fitch style system - disjunction elimination

I am having difficulty in formally proving two arguments. Firstly, given the premises A ∨ (B∧C) ¬B∨¬C∨ D derive A v D. I can see why it has to be either A or D, because if it's B and C, ...
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What is an example of a true contradiction in a paraconsistent logic?

While reading the Wikipedia article on trivialism I noticed the following: In classical logic, trivialism is in direct violation of Aristotle's law of noncontradiction. In philosophy, trivialism is ...
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Clarifications on 1) Modus Ponens, 2) Modus Tollens, 3) Inductive, 4) Incomplete based on examples

My second lecture on Hypothetico-Deductive methods (based on Popper's falsification theory). In the class, we were given the following examples. We had to classify which examples belong to 1) Modus ...
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Does Barrow and Tipler's “anthropic principle-multiverse” entail the existence of all logically possible universes?

I've read several texts that indicate that the anthropic principle (applied to cosmology, and more specifically, to the multiverse) yields the existence of all logically possible universes (most like ...
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An erotetic argument about the liar paradox

I noticed something about the liar paradox, when the liar sentences are taken as questions. Let’s start with the liar index, “This sentence is false.” Allow this to be questioned: “Is this sentence ...