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-1

If by this you mean for example a universe with two spatial dimensions and one of time, the answer is yes- at least in the world of physics. Physicists often try to formulate their theories in spaces simpler than (three space, one time) when it isn't known yet how to do it in (3+1) space. Then they look for clues in (for example) two-space, one time ...


0

I think there is something of a general misconception about Aristotle's work on logic. Aristotle had a definite empirical outlook. For this reason, I don't believe he focused at all on his own introspective capabilities. I suspect he never considered his own logical intuition (he discussed intuition in relation to discovering scientific principles). His ...


1

You will find that there is no "law" of logic that is held universally. And to speak "of logic" confuses the issue because there isn't a single logic but rather numerous logics. Technically all you need to have a logic is a language (syntax or rules for what counts as a well formed formula), definitions of interpretation (or semantics), operators and their ...


3

If you are considering Aristotle's Syllogistic, the answer is clearly : NO. Syllogism is Monadic predicate calculus which is a subset of predicate logic. A well-know example (due to Augustus De Morgan) of valid inference that cannot be accounted for by syllogism is the following : “All horses are animals. So, all horse tails are animal tails.” Having ...


1

Player-A says p is possible, exactly when player A can see someone who raises their hand for p. That means, when player-A says p is possible, then player-A can see someone. Player A says q is necessary, exactly when everyone player-A can see raises their hand for q. Thus if player-A can see someone, then if everyone player-A can see raises their hand for ...


0

Since this question is asking whether Charles and Louis are identical given a list of properties, it may be related the identity of indiscernibles. Wikipedia describes it as The identity of indiscernibles is an ontological principle that states that there cannot be separate objects or entities that have all their properties in common. That is, entities ...


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The Organon by Aristotle is a set of six books. Here is an example of the use of "predicate" in Categories v (page 29) The species is predicated of all individual examples, the genus of these and the species....For all we affirm of the predicate will also be affirmed of the subject. In a footnote in the Prior Analytics, I. iv, the translator, Hugh ...


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From the OP: Assume player A doesn't raise his hand for Lq ->Mq, but he raises his hand for Lq but not for Mq. (emphases added). How can you raise your hand for Lq but not for Mq? By the rules, to raise your hand for Lq, every player you can see raised their hand for q. But the only scenario where you keep your hand down for Mq is if no one you can ...


2

I am aware of no standard modal logic which allows for such a derivation. What you do have in system K is □(p → q), □p ⊨ □q: In system K, we have the Axiom scheme K/Distribution axiom □(A → B) → (□A → □B) If we had □(p → q), then using distributivity we could obtain (&...


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One way to approach the question of what argument styles have only recently been labeled fallacies is to list those that are not recent. As a base-line there are 13 fallacies that can be traced to Aristotle's Sophistical Refutations. Hans Hansen lists the fallacies recorded by Aristotle: equivocation, amphiboly, combination of words, division of words, ...


-1

If you observe an event with a previously assessed zero probability, you've just proved something that was previously considered non-prove-able. Does it leads to a contradiction? Yes, and that's completely normal. Probabilities are about our predictions of the future, and the future is unknown. So, that means that in a certain point, we'll always be ...


4

As the OP and the comments note, both of the results are tautologies. Here is the truth table for the first one: Here is the truth table for the second one: As the OP notes the two sides of the biconditional are also tautologies. As to why these were marked false, perhaps the answer key was in error or the problem that was intended was misstated. Perhaps ...


0

Wikipedia describes paraconsistent logic as follows: A paraconsistent logic is a logical system that attempts to deal with contradictions in a discriminating way. Alternatively, paraconsistent logic is the subfield of logic that is concerned with studying and developing paraconsistent (or "inconsistency-tolerant") systems of logic. Max Tegmark has four ...


0

Examining Wittgenstein's Tratatus Logico-Philosophicus in both German and English, the words "synthetic(al)" and "posteriori" do not appear when I searched for them. However, "a priori" often did. The word "analytical" was mentioned in 6.11. Wittgenstein mentioned Kant once regarding the problem of the left and right hand in 6.36111. Wikipedia describes ...


1

Some general thoughts: First: The is/ought dichotomy suggests that there is no valid way to move from what is, to what ought to be. You are saying: If we can prove X, then we should do Y. You're friend is saying: Let's not do Y because we can't prove R. You've run into the is/ought dichotomy, so unless you can frame the context within an ...


1

Here's the crucial distinction: We don't know if Mr. N fathered Miss A's child, because we don't know if he's truthful. But we certainly do know he IMPLIED he fathered Miss A's child because it's a logical entailment of what he said. In my opinion we can also infer that he had an affair with Miss A, because he came right out and said so, but since no ...


2

Goedel's 1930 completeness theorem showed that first-order predicate calculus is complete in the sense that every valid formula is a theorem. There are many calculi that have as theorems all and only the tautologies, that is, the valid formulas of propositional logic, as pointed out in the answer given previously by Kjos-Hanssen. Furthermore, as stated in ...


0

I don't think this is really a philosophical question, but I'll weigh in anyway... This is like asking "What can I deduce about a person from his fingernails." Answer: The person has fingers. Back to your question, they may be speaking out of selfishness, empathy, a combination of both or none of the above. Comforting someone who has suffered a major loss ...


2

As the comments note there is an error in the problem. To check the problem, one can use truth tables. Here is a truth table for the original claim: (A ∪ B)′ ∩ C = (C ∩ A′) ∪ (C ∩ B′) Here is a truth table for the modified claim: (A ∪ B)′ ∩ C = (C ∩ A′) ∩ (C ∩ B′) Michael Rieppel. Truth Table Generator. Generated on May 12, 2019 at https://mrieppel....


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Bo Bennett's site Logically Fallacious provides dialogues for arguments that Bennett considers to be legitimate fallacies and not pseudo-fallacies. Here are two examples he provides for the Ad Hominem logical fallacy: My opponent suggests that lowering taxes will be a good idea -- this is coming from a woman who eats a pint of Ben and Jerry’s each night! ...


1

The question is: So is the answer just simply B)? I am not sure why the question mentioned without knowing whether Mr. N is truthful in answering these questions. Does that have an impact in our deductively inferring of Mr N's answers? Construct the following symbolization key based on Conifold's suggestion: A: Mr. N had an affair with Miss A. F: Mr. N ...


0

Essentialism 'Christianity' is a porous term. We can't define necessary and sufficient conditions for a set of beliefs or practices to be Christian. Christianity is an essentially contested concept. Any nuclear, essentialist approach is bound to fail. Following this line of thought, which does full justice to the history of religious ideas, we can't say ...


-1

I don't think so. The subject of [formal proofs of mathematical logic] is 'formal proofs' or 'proofs'. The subject of [sound deductive inference] is 'sound deductive inference' or 'inference'. The subject of 'formal systems that have [deductively sound formal proofs of mathematical logic]' appears to be 'formal systems'. An inference is, among other ...


0

The issues of generality, self-reference and a hierarchy of languages would likely not be a solution to Wittgenstein's mysticism. As Russell suggests (Tractatus, page 23) Wittgenstein would of course reply that his whole theory is applicable unchanged to the totality of such languages. G. E. M. Anscombe illustrates Wittgenstein's position by quoting 6.52 ...


0

What is a repetition? Popular examples so far include numbers and physical objects being counted, but it is all fraught with space-time conceptions. A fraction of a number carrying on infinitely is not infinity. Supposing that 1 unit may be added or subtracted infinitely is not infinity. When defining infinity, why believe that we can apply space-time ...


1

The notion of infinity boggles the mind, but maybe that is because our minds are conditioned by a temporal component since birth. Consider how the earth's rotation and revolution would instill in all earthly beings some concept of time. We observe time, or at least perceive that we do, all around us, always. We think, speak, and behave in coordination with ...


1

If you are a part of the mainstream of the Christian religion, then yes, you accept that Jesus could, and did, suspend what we call "scientific law." It's an important part of orthodox (small "o") Christian belief that Jesus' divine nature granted command over the realities of the universe; a power that Jesus wielded, not indiscriminately, but as an ...


1

Everything is possible if and only if the rules stay the same in whatever universe we are in. E.g. if we say that 2 = 2, then this rule holds. If we change the rule to 2 = 3, then 2 = 2 no longer holds. Saying that 2 = 2 and at the same time 2 = 3 could be allowed in some notations but not in the functional notation [for every input value (domain), a ...


2

There are two questions: Does believing in Christianity imply believing in miracles? Is this belief in miracles consistent with believing in laws of nature? Answers to the first question depend on what a particular Christian means by Christianity. To avoid setting up a straw man, I will quote an influential Christian writer, C. S. Lewis, who takes a ...


3

A set Γ entails the statement P if and only if there is no truth-value assignment in which every member of Γ is true and P false. This is a standard def of entailment, check any textbook on formal logic. I would include a reference but that might be a product endorsement? A simple truth table will show a row where α is true and β is false so ~( α|= β) and ...


1

There are many problems with your statements : 1°) syntax What is a sentence? Is it just a sequence of words or does it follow rules of construction? 2°) semantic What means 'x is true' ? How do you determine the truth value of a sentence? This looks dumb but the truth of the statement "x is false" might not imply that x is indeed false. For example, the ...


2

A → (B → C) is basically another way to write (A ∧ B) → C. So B → (A → B) is better not described as every fact deductively follows from every other, but every fact deductively follows from itself and every other. It is tautology, as the "every other" part is redundant. The original statement would be wrong if you mean every statement follows from every ...


0

The question is how to understand why (A → B) v (B → A) is always true even when A and B are sentences that have nothing to do with each other. The reason is that the truth values for the conditional (→) and the disjunction (v) are defined to be true for three out of the four possible sets of valuations of A and B in such a way that their combination always ...


0

It is a tautology. •If B is true, then A->B is true. Then B->(A->B) is B->T. B->T is T. •If B is false, then B->(A->B) is F->(A->B). F-> Something is always True. That's why B->(A->B) is true.


4

I take a statement to be ridiculous iff it contains or implies a contradiction. That being said, B --> (A-->B) is not ridiculous, but it is a tautology, which makes it vacuous. I feel the previous answers over complicated things, but here are two short arguments showing that it is a tautology. 1. B --> (A --> B) Assumption 2. B --> (~A v B)...


8

The topic you want to research is 'paradoxes of material implication.' That is, you are right to think there's something odd about this formula. But it does not mean that every fact deductively follows from every other. Consider your target string: B-->(A-->B) Now note that the convention is to define the connectives such that the conditional 'P-->Q' is ...


6

When proving a conditional one assumes the antecedent, B. The goal is not to derive this, but from this assumption to derive the consequent which happens to be A > B. But A > B is another conditional. Since it is a conditional one derives that in the same way. First assume the antecedent, A. Can one derive B? Yes, one can, because in this derivation we ...


0

Classification can be taken in two ways: the simple act of dividing a subject into its main divisions, which anyone can do after memorizing a Ramean tree for the subject; or a second more comprehensive meaning which encompasses the "understanding" aspect of the subject, by defining classification not simply as a static Ramean tree, but as a process of ...


0

The main problem with the argument is in the first line: So if we have two mutually exclusive and jointly exhaustive hypotheses, with equal prior probabilities, say, evolution and creation ("E" and "C"), and a observation, say, homologies (H) if one of the hypotheses entails the observation, that hypothesis is more likely, given the observation, than the ...


1

The result desired is one of the De Morgan rules. One way to show this is to use the law of the excluded middle on A. That is, A or ¬A is true. This involves considering two cases, A and ¬A. In both cases we need to reach the conclusion, ¬A ∨ ¬B. The easy case is ¬A. Use disjunction introduction to derive the desired result: ¬A ∨ ¬B The more difficult ...


1

Actually I think i figured out the solution...


0

This is an alternate proof to the one provided by Eliran. As Eliran mentioned, To prove the equivalence P = Q we must prove P > Q and Q > P. To prove P ↔ Q, that is (P = Q), from the three premises, I first show that Q → P on lines 4 to 8. I had to take a detour with a subproof on lines 5 to 6 since I do not have a double-negation introduction rule in ...


0

Wikipedia defines a probability space as follows: The probability measure P is a function returning an event's probability. A probability is a real number between zero (impossible events have probability zero, though probability-zero events are not necessarily impossible) and one (the event happens almost surely, with almost total certainty). [my emphasis]...


1

The propositions you're describing fit under the broad category of modal logic. According to the Stanford Encyclopaedia of Philosophy, A modal is an expression (like ‘necessarily’ or ‘possibly’) that is used to qualify the truth of a judgement. Modal logic is, strictly speaking, the study of the deductive behavior of the expressions ‘it is necessary that’ ...


0

I am trying to get this proof to work out and so far I feel like I have the first part right but I'm stuck on how to get the A→B part. Begin by assuming A → B, then state LEM as a Tautological Consequence to use disjunction elimination to derive ¬A ˅ B. Also, your attempt needs to be tidied up, you have a few unecsessary steps and you seem to forget that ...


1

Here is a very similar question with three answers: Prove (¬P ∨ Q) ↔ (P → Q) Your question seems to be focused on the Fitch system and your approach to the problem seems to be different. I will only address how you might proceed without considering how you might do this in the Fitch system. You are attempting to use disjunction elimination with the ...


0

1) The burden of proof is borne by whoever makes the claim that is easiest to prove. Absolute non existence of something is impossible to prove, but please notice how your rephrasing into : "There exists at least one universe in which Object A does not exist." also narrowed the conditions. If you were to narrow it further into: "A glass of water does not ...


1

Since one has to prove ¬E one place to start might be E as an assumption. The strategy is to derive a contradiction somewhere after that assumption and then derive ¬E which is the goal. The rest of the steps I think you are aware of. I am including the results of the proof checker. The proof checker you are using is likely different and you will need to ...


1

It's invalid. When there can be a world in which the premises are true and the conclusion is false, the argument is invalid. So if you wanted to use Tarsky's World as tool, you would need to use block language. So lets make: P = Tet(a) Q = Small(a) R = Cube(b) S = Large(b) (these are just random predicates that don't change the meaning of the argument) If ...


1

By using a truth table generator one can show that one of the set of valuations for the sentence letters leads to the result being false. To see this, use this input ((P=>Q)&&(R&&S))=>(~P=>(Q&&R)) in the Stanford Truth Table Tool. When P and Q are false and R and S are true then the conditional with the conjunction of the premises ...


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