New answers tagged

2

Belief in the truth of a proposition is a statement independent of it's actual truth. Consider the fact that different people can have different beliefs about B while B is either true or not, unrelated to what people believe about it. Also "Jack believes today is may the 4th" is a statement about Jack, not about today's date. To represent it ...


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Maybe you should begin by acknowledging the much that has already been done, since we are not reinventing the wheel. Relative to this, your question is not an open question as such, since the subject of category theory, usually described as the mathematics of mathematics, already exists. Firstly, I will make a point clear, that set theory is just a special ...


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The possibility that something causes itself should be excluded as a cause would need to exist first before it could cause anything. This would apply also to the notion of creation. The idea that A causes B is essentially ordinary physical causality, which is irrelevant here. Thus, the notion of cause should be further specified as A causes B to exist, i.e., ...


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The version of the Cosmological Argument you present is a caricature that no significant philosopher ever defended. This isn't your fault. The version you describe is basically the version that is presented in most modern books and classrooms; it is what most modern philosophy professors think is the cosmological argument, but it isn't a serious argument ...


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To get rid of numerous logical and semantic (meaningless) paradoxes such as Liar, modern logical positivism proposed its famous verification principle under which: The logical positivists' initial stance was that a statement is "cognitively meaningful" in terms of conveying truth value, information or factual content only if some finite procedure ...


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I know it sounds like I am being a wise guy, but what do you mean by meaningless. The statement 'If the sky is blue, then the sky is blue,' is a logical statement that does not convey any information, so I would call it meaningless. Contrast that with the statement 'If the sun rises in the North, then you owe me $100.' Statements like this are described as &...


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Existential Elimination requires that the witness (a) does not occur in the conclusion or in any undischarged assumptions. At those points, you have an undischarged assumption that includes a on line 2. Suggestion: Place the negation introduction subproofs inside each case of the v-elimination subproofs. | |_ Ex -Px | | |_ -Pa | | | |_ Pa & Qa | |...


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"Mutually exclusive" does not mean "A XOR B." It means "NOT (A AND B)" or equivalently "(NOT A) OR (NOT B)."


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"Mutually exclusive" means either one excludes the other and is synonymous with the concept of disjointness. In logic terms, "A and B are mutually exclusive" should be written as (A IMPLIES (NOT B)) AND (B IMPLIES (NOT A)). If we make a truth table for this, we see its truth value is TRUE when A = B = FALSE. If in addition to being ...


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The above answers are all good and informative, but none of them seems to answer the question--at least not the question as I understand it. Here is how logicism helped the empricists: Both rationalists and empiricists agree that deductive logic is a sound basis for reasoning about anything. Where they differ is in whether the human mind comes with a special ...


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I made a mistake. The answer I gave was for the question I asked that google directed me to this page for an answer.


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This is from the same reference as yours: It is common to divide the symbols of the alphabet into logical symbols, which always have the same meaning, and non-logical symbols, whose meaning varies by interpretation. So just like in common math, logical symbols in FOL is like universal operational math symbols like >, =, and variables which always have ...


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It literally boils down to perspective. If you say something with a specific intent and it is understood under a different context, it becomes a matter of semantics. Often times, this is brought up in argumentative scenarios because the digestion of said statement will support one side of the argument more than the other. When, at the end of the day? It can ...


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It most certainly can. It honestly depends on the specific wisdom of the person answering. You may not know anything on a specific topic but still have a firm understanding of the idea. Seems to be me in a lot of cases... I'm not "well educated". BUT I'm intelligent enough to have picked up things throughout my life that display a better ...


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I don't see how a criticism of determinism becomes a criticism of {the lack of} free will. Is anyone claiming that subatomic particles can be manipulated by conscious intent? Or even that brain physiology and neuron function is controlled at this subatomic level? If there happens to be a degree of randomness in our decision-making, then that makes free ...


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Below is from reference here: To demonstrate the important notion of the form of an argument, substitute letters for similar items throughout the sentences in the original argument. Original argument: All humans are mortal. Socrates is human. Therefore, Socrates is mortal. Argument form: All H are M. S is H. Therefore, S is M. All that has been done in ...


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Infinitary logics like L(𝜔1,𝜔) (the simplest and best-behaved of the bunch) and higher-order logics like second-order logic extend first-order logic in different directions. Infinitary logics extend first-order logic essentially by allowing "longer" formulas in controlled ways. On the other hand, roughly speaking the order of a logic refers to ...


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The two negatives are negating entirely different things and so it’s incorrect to think that you can cancel them without changing the meaning of the sentence.


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Assume you have a mathematical system, powerful enough to express the sentence S: “In this mathematical system, there is no proof for the sentence S” in a strict mathematical way. Now either there is a proof for S, or there isn’t. If there is a proof for S, then S is false because it says there is no proof, so we have a proof for a false statement and this ...


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Taken literally Yoda committing a fallacy is. If you try to do something that you didn't realize is impossible, whether you end up doing or not doing is not up to you and the only way you will find out is trying. For example Hilbert (via his program) tried to establish the consistency of mathematics, but he failed because it is an unattainable goal. This ...


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Modalities in general do not commute with negation. So for (a clear) example, "agent doesn't know that X [is the case]" and "agent knows that not X [is the case]" are obviously different so we would not think to propose that K~x and ~Kx are the same/equivalent. As a TLDR summary of equivalences for the (relevant part of the) deontic logic ...


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The OP question is somewhat complicated by the imperative mood, but I do not believe that the logic of imperatives or deontic logic (see Hansen, Is there a Logic of Imperatives? for an overview) are at fault for bringing about the counterintuitive result. For the purposes of this example we can straightforwardly interpret imperatives as descriptions of a ...


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Often my manager will set a deadline for a project, and ask me if I can finish a project by that date. If I'm pretty sure I can achieve what he asks, I'll tell him "I will" or "I think so." If I think the deadline is completely unrealistic, I'll tell him I can't do it that quickly, and we can discuss changing the timeline (or he needs to ...


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Gödel's theorem is (based on) a cheap trick. But the genius of it is to see "the world in a grain of sand... and infinity in the palm of your hand." In other words, it's not the trick itself that's impressive, it's that Gödel was able to perceive the trick's implications for the foundations of mathematics and logic AND to demonstrate those ...


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Yoda's point is that like a lot of mental and physical coordination skills, it matters how you think about it. He isn't saying "don't try", he's saying "don't think of it as 'trying'", which is an entirely different statement. It's actually a very common observation when learning new skills. Initially you 'try' to do it, thinking about ...


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It's not a logical statement. It's about that mental processes that go on in your head. Trying is not the goal. If your goal is to try, you won't succeed, because it's easier to just try and then stop. Should you wake up in the morning and say to yourself "Today I am going to try to fix my car"? No! You should say "Today I am going to fix my ...


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IMO The point of this statement is to say that there is no such thing as trying. If you try you are already doing it, and either you may fail or not and you have to live with the consequences. You can not try and if it doesn't work out, you just reset and try again pretending nothing happened, because that attempt is now part of your history. So you only ...


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Steve Caballero asking himself "Do or Do not". I always remember this quote when I want to drop in with a skateboard on a very steep ramp (but still much lower than on the above picture). If I merely "try", I can be sure I won't put all my weight into the ramp, and I'll fall backwards and get badly injured. So I either : have to accept ...


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The split between Rationalism and Empiricism (note the capital letters) goes back to the 17th century. Basically, it is a dispute about the proper foundation of knowledge: Rationalism holds that knowledge is (in one of several ways) founded in our mind and in the human capacity to use reason. Empiricism holds that knowledge must (in one form or another) be ...


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This is a bit subtle. I'm guessing "case of knowledge justified through reason alone" is pointing to the Kantian conception of mathematics as synthetic a priori knowledge. Frege really wanted to be a Kantian and expressed great admiration for Kant, whom had come up with the distinction between synthetic a priori and analytic a priori knowledge. But ...


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When read as a literal statement, it would be called a fallacy. However, Yoda is not saying that "there is no such thing as trying". Suppose there is a heavy rock in front of you. You can choose to lift it, or not. "I'm going to try to lift it" is more accurately interpreted as "I'm going to undergo actions intended for lifting it, ...


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Logical positivism may not be the perfect label, actually according to Hempel who's one of its major figures during its heyday in last century, it should be more properly called logical empiricism as described here: Hempel never embraced the term "logical positivism" as an accurate description of the Vienna Circle and Berlin Group, preferring to ...


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A similar quote is used in a Karate Kid movie. That line was about walking to one side of the road or the other. Don't walk down the middle or get squished like grape. Either commit to learning Karate, or go do something else. Similarly, Yoda is telling Luke to commit to using the force. "I'll try" is often used to set up an expectation of a ...


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I think there is a deeper philosophical point here... the nature of "willing" or "attempting" isn't all that clear. What exactly does it mean to "will" my hand to move? It would be clearer if there were two separate entities... 1) the trying to move my hand. 2) the hand moving. But for moving my hand... or for breathing... or ...


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There is no fallacy, there's a misinterpretation of the situation. There are situations where trying and failing isn't particularly bad. There are situations where trying and failing is extremely bad. Say someone points a gun at you and demands your wallet. You can "do" (grab the gun and smack him offer the head with it), good result. You can "...


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The argument you're trying to formulate (as a rebuttal to Yoda) is this: do successfully IMPLIES try fail to do IMPLIES try THEREFORE (do successfully OR fail to do) IMPLIES try However, this critically misses the point. Your argument is uncontroversial, it matches the way Luke (along with most of the rest of us) sees the world. But the entire purpose of ...


0

The statement God exists is logical. But it is not necessarily true. You are confusing logic with truth. Logic is like mathematics: it is just a set of rules. It doesn't presuppose a truth value for x or y. x=3 could be true or false. It does not depend on logic. Logic is just a method of reasoning regarding truthfulness and falsehood. But logic does not ...


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For me, the ambiguity comes from "being perfectly frank". Who is perfectly frank ? If it is the person talking, then the sentence is grammatically incorrect as the subject of the second proposition should also be the person speaking, i.e. me/I, and not you. However, when we first read this part of the sentence, we may expect that the person giving ...


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In the book, amphiboly is defined as "when an ambiguous statement serves as a premise with the interpretation that makes it true and a conclusion is drawn from it on an interpretation that makes the premise false". The fallacy always applies to an argument. An ambiguous statement is not amphiboly. There has to be a conclusion resulting from the ...


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Since its truth value depends on the personal opinions and so it can not be a logical statement( therefore different persons give different truth values based on their opinions. ) Please give a clear answer. There are some layers of confusion in this question, so (despite the request) the answer isn't exactly simple. Given the context provided in the ...


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The site Logically Fallacious defines the ambiguity fallacy as follows, and includes amphiboly in the definition: When an unclear phrase with multiple definitions is used within the argument; therefore, does not support the conclusion. Some will say single words count for the ambiguity fallacy, which is really a specific form of a fallacy known as ...


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Well, amphiboly is grammatical ambiguity where a sentence could be read multiple ways. Perhaps it's about to whom the phrase "being perfectly frank" refers - the speaker or the person to whom he's speaking. Is there any additional context for this sentence?


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Second Order Logic has much stronger expressive power. Many propositions can be formalized in second order language, but can't be expressed in first order language. For example:


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You can still praise God by stating "God is not limited by anything other than God" i may call "God is Almighty" but then don't be overwhelming by saying God unlimited can be impossible. This concept of "infinity" must be understood properly. On real life we can say infinite, unlimited as "Unreachable All at Once" It's ...


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You can translate the following proof into natural deduction.


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Regarding your: Why is an argument of the form (‘A=B’, ‘B=C’, therefore ‘A=C’) non-syllogistic? This inference is from basic math arithmetic properties, or more strictly speaking from set-theoretic definition of Equivalence class, which transitivity in this definition plays a central to arrive at your conclusion A=C. So apparently, this is not exactly the ...


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For the first question, it depends exactly how one defines syllogism; see this other question for variations. Presumably Kenny means to exclude reasoning "modulo equational theories", e.g. using first-order logic with equality from his idea/definition of syllogism. This is fair as Aristotle, whose ideas still dominated logic at the time, didn't ...


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An economist would say that this a fallacy of composition but this is more or less in the sense that Conifold spoke of equivocation around "good". Basically alcohol has some good and some bad properties. One can form a similar one-sided argument for the bad properties Drinking alcohol makes me drive poorly. Driving poorly is bad for me (because e....


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As Tetlock says, having skin in the game is facilitative: more specifically, it adds a sense of salience and urgency. If someone has to decide whether to take a business trip, they will be more focused, attentive, and judicious with the question if they have to pay for the trip themselves than if the company pays for it. But like anything else, perspective ...


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There is no infinite, there is no "unlimited". There is only "not limited by something" Infinite asserts thing can exceed beyond itself without additional assertion from outside which is impossible. It's the way old philosophers trying to praise God is unwittingly trapped by impossibilities that injure the understanding of God's self. Any ...


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