New answers tagged

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You need to resolve each of the cases into the term you want to proof to be able to use a disjunction elimination, like so:


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Since they are mutually exclusive we can't write so using equality sign. Also, since equality sign is illogical here I need not explain whether it is sensible to use the reverse notation. All of us know that murder is a terrible crime. When we say "suicide is a murder", there is a great chance of creating awareness among people about a terrible ...


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From a logical point of view, if we define murder as the "killing of another person" and suicide as the "killing of oneself", then the two actions are mutually exclusive. If instead we agree on a revised definition of murder as "killing of some person", then we may consistently assert that suicide is a particular case of murder. ...


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Short Answer The answer is yes and no. Philosophical theory itself does not because philosophical texts are largely exercises in defeasible reason conducted in natural language which is far more syntactically and semantically complex than artificial language. However, formal logic, like problems conducted in Fitch, can have trivial solutions. Long Answer The ...


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Logic itself might be thought of as having levels, and then there is type theory. But perhaps philosophy itself is this higher/deeper thing? At least, logic mostly concerns inferences to conclusions, that we assert through our very act of arguing, and erotetic or imperative logic would "conclude" in other questions or imperatives instead. (Strictly,...


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Yes and no, depending on what you mean by "being part of". Logic is part of philosophy, but can be applied to various disciplines. When you find logic in philosophy of mathematics, that's just an application of logic, and does not mean that logic is subordinated to that particular discipline. In fact, one may even argue that mathematics itself is ...


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As pointed out by Noah Schweber, since LEM holds for decidable statements, we need something suitably complex to get a good example. A good starting point are existentially quantified statements. Asserting that ∃x P(x) in intuitionistic logic means being able to actually provide a witness. On the other hand, ¬∃x P(x) means being able to derive a ...


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This academic paper is absolutely critical and vital to understanding my answer:-- (https://link.springer.com/chapter/10.1007%2F978-3-642-12821-9_2) This paper very much links formal logic with many forms of phenomenon. I repeat: This paper is very important. The keyword here is "fundamental." If fundamental simply means "most important,"...


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Here's a discussion that might help: Boss: EMPLOYEE! Did you complete that very important assignment I told you to do yesterday? Employee: What? You didn't give me a new assignment yesterday! In fact, you weren't even in town.. you were still on vacation, right? Boss: Look, either you completed the assigned task or you failed to complete the assigned ...


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Simple answer, although it's for you to decide whether this sidesteps the question you actually wanted to ask: Amy could be lying but also have incorrectly modelled the world. She may have lied that you didn't go to school, but maybe she only thought you went to school when in fact you didn't. Then she is still lying (that is, she said something she believed ...


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Propositions in intuitionistic logic are probably best understood as statements about provability. P ʌ Q means that you can prove P and prove Q, ¬P means that from P you can derive a contradiction, ∃x.P(x) means that you can exhibit a particular x and a proof of P(x) for that x, and so on. There is a law of noncontradiction because there can't be a proof of ...


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There are ways we could apply normal propositional logic that might seem insane. We might utter a contradiction (any contradiction), look our interlocutor squarely in the eye, and then confidently state, "Therefore, a cedar tree draped with polkadot cloth strips ought to be the first democratically elected leader of [insert country name]," or any ...


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You give the example: Amy said you didn't go to school yesterday. She lied about it though! So you did go to school? What makes you say that? The issue here is that typically you would not say that Amy lied unless you knew that what she said was false, and the implicature would be that you know what she said was false because you know you ...


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As Conifold comments, a real-life intuitionist would not shy away from assuming LEM ... when appropriate. Intuitionism merely permits the failure of LEM, it doesn't assert that it always occurs. For example, consider equality: in intuitionistic mathematics, equality is decidable (= subject to LEM) in the context of the natural numbers but usually not in the ...


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Nope. If it's not an ability to understand a subject to a deeper or shallower extent, then there is no such thing as being smart or not smart. At least, that's what comes to mind at first.


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I agree with @SonOfThought's initial statement that, Progress means: Movement to an improved or more developed state, or to a forward position. From this definition we can easily understand that since there is movement, 'Progress' is a subset of 'Change'. That means, for 'Progress' there must always be a 'Change'. To the extent that I believe 'progress' is ...


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Think of it this way. Where abduction ends with a possible explanation, IBE (allegedly) gives you the actual explanation: Abduction 1. E is the case, 2. and H explains E; 3. hence, there is a reason to believe H. IBE 1. E is the case, 2. H explains E, 3. H is the best explanation for E; 4. hence, H is true. An additional premise makes all the ...


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I'll take a stab at this. Let's take it from the bottom up and see what sense we can make of it. Deduction: We can think of deduction in terms of the classical Greek conception of the syllogism. Though the point is often lost on people, syllogisms are mainly a teaching tool for the foundations of logic: they show correct (and incorrect) ways of extending the ...


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An n-ary relation gives rise to parameterized unary predicates if one fixes n-1 arguments. Wilfrid Hodges argues that this is what logicians did before the nineteenth century. (There may be other works of his that better explain this.) More concretely, they would re-write the relevant statements by using natural language reasoning so that all relations are ...


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Instantiation: from a general statement to an individual case. Example: "Every human being is a Philosopher"; therefore "Socrates is a Philosopher". Generalization: the "inverse" inference. From an "generic" individual case to a general statement. Example: "A human being is a Philosopher"; therefore "...


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Because there was a calculus for one-place predicates, Aristotle's syllogistic, roughly equivalent to monadic predicate calculus. Aristotle does discuss "relatives" in Categories, which refer to multi-place relations, or rather to objects entering them. What will later be called oblique syllogisms involving relatives is mentioned in passing in ...


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Regarding change: Although change seems an exceptional behavior in nature, while statism is the rule, the fact is that change is permanent and statism is not even possible in nature. Change is the subjective perception of difference. It is perception that makes something static, whilst such is just an illusion. Seeing the same river as before (or the same ...


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Maybe, but then only trivially. One could argue that the Law of Identity is that for every A, A → A. One could also argue that the Principle of Sufficient Reason is that for every B, there is an A such that A → B. And then, for any given A, "For every B, there is an A such that A → B" reduces to "For every A, there is an A such that A → A"...


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Russell's preferred example of what he means by a "simple particular" is a sense-datum (an object of sensory experience), but it could apply to any object of awareness that is the sort of thing having properties. Importantly, what we often intend to call "particular" are not really particulars: they are in fact more complex. This includes ...


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All logical truths share one vital set of elements, they are tautalogical, symbolic, null and meaningless. Opposed to this is metaphysical truth, where metaphysical means, that which is real or actual. Whether this type of truth, as J D has mentioned elsewhere, is part of an endless controversy and can only be resolved by one individual's belief in its ...


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The word "truth" could be defined at will, but are you looking for an explanation of the disquotational scheme? So to say, if "S is P" is true iff S is P, then are we saying that "S is P" corresponds to S being P (when S is P), or perhaps "S is P" coheres with other truth iff S is P (this seems peculiar)? Now, "...


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See this Stanford Encyclopedia of Philosophy entry about Tarski's Theory of Truth. Also this Internet Encyclopedia of Philosophy entry. I hope you find them helpful.


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I always thought Chalmers but then I saw a video of Daniel Dennett claiming he was first. Said he called it the Hard Question


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Iirc the typical immediate solution is to divide good and duty, so that utilitarians can say that a choice can be descriptively best without being what we choose based on imperfect/incomplete application of the utility principle. Whether this defeats the point of this utilitarianism is another question, concerning for instance the strength of the ...


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I can see at least two interpretations for this question: Someone might assume "101" is necessarily either binary or decimal. Someone might assert "101 is a binary number" without considering the alternatives. So in both cases the fallacy consists in "forgetting" about some of the logical possibilities. As pointed out before, ...


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There is some need for clarification here. Nobody claims that material implication is the same as logical implication. Material implication, or the material conditional, is an object-language propositional connective. It is the same kind of thing as ⋀ and ⋁ - its job is simply to take two truth values as arguments and return a truth value as a result. It can ...


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It is unusual to use a predicate such as U to indicate untrue. In classical logic a proposition is untrue if and only if its negation is true. So, unless you are trying to do something cute with the semantics of truth and falsehood, it would be better to replace Uy with ¬y. That said, both your formulations are correct. However, there is another issue. Your ...


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This is an example of: False Premise Technically, false premises are not fallacies (not even informal ones), but rather errors in observation or in the interpretation/translation of observations into logical premises (i.e., statements of fact). In this case the facts being claimed are clearly not justified by the actual observations. It is possible to claim ...


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No, it cannot. Logic itself can "rationalize" any belief. But "proof," in any scientific or juridical sense, entails empirical evidence to support the reasoning. A great deal in the evolution of philosophy addressed this very issue. The Platonic dialogues concern the evils of specious reasoning by the Sophists and Rhetoricians, who taught ...


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Frame challenge Is 101 decimal? [T/F] or Is 101 binary? [T/F]? A question cannot be True or False. Only a statement can be True or False. A question can be answered with Yes or No. Example 101 is decimal. True or False? The first part of the above is a statement and the second part is a question about the statement. We don't need to answer the statement - ...


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Progress means: Movement to an improved or more developed state, or to a forward position. From this definition we can easily understand that since there is movement, 'Progress' is a subset of 'Change'. That means, for 'Progress' there must always be a 'Change'. And 'History' is (The study of or a record of) past events considered together, especially ...


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Another strange example of something being both empirical and a priori would be the existence of time itself. Human Beings, perhaps not very well and strongly, do indeed have an "internal clock" built-in. The observer can tell that time has passed very roughly, even when deprived of the traditional senses. At the same time, if you leave an apple ...


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So, the question is confusing two different things. The question "Is 101 decimal or binary?" is a false dichotomy or false dilemma as 101 could be a representation in any number base > 1 since 1 and 0 are valid symbols. However, the cartoon of two people with conflicting perspectives is not a false dichotomy. If anything, it's potentially an ...


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I would say that Change is a very broad word, but any change that happens produces information in a universal system which means that the system as a whole is progressing. Progress in other hand is more appropriate in this because in a human society (cultural perspective) we could have destructive changes but not destructive progress. When we say ethics ...


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The name for this is Paradox. No-No Paradox And the only way to solve this paradox is when all the players recognize that they are in a paradox and need to understand that both are talking about the same thing in different perspectives. If one player cannot agree, he is trapped in the Dogma (in-the-box mindset)


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I am going to attempt to answer the intention of the question, which was around a seemly subjective assessment of fact with TWO viable conclusions. I don't believe the OP is posing a false dilemma scenario. This is a case of Affirming the Consequent Decimal 101 looks like "101". It looks like "101". Therefore it is decimal 101. (?!) ...


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I'd argue that the statement/question itself is perfectly fine, and in no way fallacious. But it may be used as trick question to make a joke at the cost of the answerer. The English question "A or B?" is somewhat ambiguous since it does not specifiy whether the or is inclusive or exclusive: or is by default inclusive, but questions of this pattern ...


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False dilemma is indeed a good term for this example. However because only two options are presented the term false dichotomy could also be used in this case.


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I add my answer there following comments where I think this is not a fallacy, but only an ambiguous statement or a lack of context. The false dilemna would apply if in your context you would be forced to choose. We could also dig towards the confirmation bias where one or many people only read what they goes towards their own opinion.


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Long comment You can take a look at a simple piece of "real mathematics" and consider how much "formal logic" is implicit in that three lines theorem. A lot of "classical" propositional logic is implicit in it, without strictly formal propositional calculus at all. See David Hilbert's The Foundations of Geometry (1899), English ...


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(This could be better suited as a comment, but my reputation score is too low to add comments) It might help if you make clearer what you mean by "logical implication": do you refer to another formalization of some rules of logic, or to the inner activity of the mathematician? Although when you say most theorems are not even proved formally, since ...


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EDITED 9/11/2020 What is the name of this fallacy: Is 101 binary or decimal? I prefer to call it the either-or fallacy, but it is also known as false dilemma among others. The idea is that a choice is given that constrains to two or perhaps a few options when a much broader reading of responses is both possible and warranted. In your example, 101 is a ...


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Gareth Evans is arguing that Aristotelean logic is closer to natural language usage and as such introduces fewer unfamiliar logical devices and has fewer counterintuitive features. This is true, but the vast majority of logicians consider this to be a price worth paying to have a much more powerful and expressive logic. Natural languages such as English have ...


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H is invalid in this frame. Let's take p as false throughout N*, and p as true throughout N. That makes H false in any world in N*. Instead of proving H to be valid in the frame, which it isn't, the correct method is to prove that every substitution instance of H is valid in the model based on this frame in which V(p,0*)=1 for every propositional variable. ...


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The philosophical works of Russell, Wittgenstein, and others in the Analytic Philosophy tradition of that era are still of great importance. Their ideal may have failed — they never managed to bridge the philosophical gap between logic and the objective world to produce the fully 'scientific' logic they had desired — but there is no denying that they made ...


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