New answers tagged

1

Everything for daily life can be understood as a matter of patterns. All kinds, species, ideas, or races of things. All those terms mean the same thing, I see a stone, another, a third, and understand a pattern or idea. In extremis the sciences contrast this with measurement. Measurement means, in the terms of daily life, comparing one thing to another. ...


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The categories or predicables are part of the syllogistic "logic." Which was not yet strictly a closed logic in Aristotle, but only became so with the Stoics. With Aristotle the research was still more open, and the distinction between formal rules of inference, and general reasoning about the world, was not yet arrived at in the authoritative form which it ...


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Meaning can be found in action -- therefore if you find meaning in life (whatever that means for you) but you die sometime, your meaning likely dies with you. In such an event I'd say that life has no meaning unless it's always existing -- namely because "the meaning of life" is multifaceted and could mean various things. You can't reasonably argue of "...


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Logic means or is understood in a great variety of ways; often it is simply used as synonymous with reason in the sense that in daily life reason is distinguished from emotion. The most common technical sense of the word in the history of the West, from crica 300 BC until 1900 or so, was the syllogism. In syllogistic logic all the weight is on what happens ...


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What you're suggesting is that we can slice an infinite real line up into chunks. We number them "chunk 1", "chunk 2" and so on to create a countable representation of the real number line that completely covers it. Huzzah, the real line is "countable". However, because we're talking about the Real number line, you can use a kind of Epsilon-Delta move to ...


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This seems like a useful opportunity to suggest a technical but valuable distinction between different applications of logic. While it's a bit of a broad brush, logic might be held as the study of the relationships between statements. Classes and sets of statements are related to each other in many different ways; for example, we might understand how the ...


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Spinoza’s Ethics might be very close to what you are looking for — it employs a quasi-proof-oriented “geometric” technique elaborating what some would call the god of the philosophers; a “pantheistic”, arguably even atheistic conception of immanent divinity, worked out in syllogistic form, ostensibly deriving the downstream results from a handful of axioms.


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Validity and truth Do you regard these as separate notions ? In a deductively valid argument, the conclusion cannot be false if the premises are true. However, a valid argument can have a false conclusion : (a) All cats are white; (b) X is a cat; therefore (c) X is white. This is a deductively valid argument. If (a) and (b) are true, then (c) must be true. ...


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Have you seen the video Shapiro's Excluded Middle? I don't think it includes any actual footage of Ben Shapiro talking. However, it gives some specific examples, with quite a bit of detail.


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Wikipedia provides a valuable summary of necessary and sufficient conditions and their use in natural language. Here is an overview: In logic, necessity and sufficiency are terms used to describe a conditional or implicational relationship between statements. For example, in the conditional statement: "If P then Q", Q is necessary for P, because P cannot ...


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Would you be able to do it if I rewrote the problem in arithmetic language? De Morgan's Laws are just the distributive property. (a+b+c)(d+e+f) a(d+e+f)+b(d+e+f)+c(d+e+f) ad+ae+af+bd+be+bf+cd+ce+cf ∎


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The question is how one can check in general whether two propositional logic formulas are equivalent. There are multiple ways to do this. I will outline four methods: truth table, tree proof, natural deduction and equivalence relations. Truth Table To use a truth table generator connect both formulas with a biconditional and see if the column under the ...


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One tool you might find useful as guidance is this tree proof generator. Here is the output for reflexive and transitive accessibility: Here is a countermodel if the accessibility relation is only reflexive: Tree Proof Generator. https://www.umsu.de/trees/


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If you have De Morgan's laws (DeM) as inference rules you might be able to do something like the following: Note that I cannot immediately derive the goal given the rules in the proof checker I am using. First I have to derive line 2, but that has double negatives in front of the A and the B. To remove them I have to use conjunction elimination (∧E) to ...


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You are given the premise (P > Q) > R. Since you want to show a conditional, P > (Q > R), assume as you attempted the antecedent, P. Then you need to derive the consequent, Q > R. However, that consequent is also a conditional. So start another subproof within the first subproof by assuming the antecedent Q. Now the goal is to derive R. At this point you ...


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Your setup and experiment are analogous to the following more general scenario: Suppose you want to provide evidence for the claim that all As are Bs. To do so, you design an experiment that only ever looks at Bs, and willfully ignores anything that isn't a B. If you find a B that isn't an A, no big deal; this doesn't contradict your hypothesis that all As ...


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What is the justification for the claim that observing something that is neither a raven nor black increases the likelihood that all ravens are black? This isn't a formal answer, but it might help understand the reasoning behind the apparent paradox. Suppose you have a box that contains N birds, R of which are ravens, and B of which are black. You don't ...


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The question is given a positive, odd integer n can we check two things n is a raven number based on some effective method run by a machine n + 1 is a black number based on another effective method run by a machine and then claim, based on empirical testing of positive, odd integers up to 10 decimal digits, that the following is true for every positive, ...


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As Mauro ALLEGRANZA notes in an answer, it is possible that the argument is not valid. This answer will provide two ways to check if that is the case. First note that although the argument uses predicates of an object b there are no existential or universal quantifiers. We may think of each of these predicates as propositions. This will allow us to simplify ...


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Hint See page 174 : "In each of the following exercises, you should assess whether the argument is valid. " Use truth table with the following truth-assignment : v(M)=TRUE and v(D)=FALSE.


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Consider the following example: "Let x=0 if the Goldbach conjecture is true and let x=1 if the Goldbach conjecture is false." We know that x is either 0 or 1, but we don't know which (yet!). That's exactly what's going on here. Given a structure S, let Th(S) be the set of sentences true in S. For each sentence p, either p is true in S and hence Th(S)-...


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The following from Wikipedia's sequent calculus article may be similar to what you are looking for: The standard semantics of a judgment in natural deduction is that it asserts that whenever A1, A2, etc., are all true, B will also be true. The judgments A1,...,An ⊢ B and ⊢ (A1 ∧ ⋯ ∧ An) → B are equivalent in the strong ...


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This is not a single logically coherent view, its a collection of views that have little to do with one another, other than being condescending toward mathematics as it is practiced. Some of them are contentious, some have followings and others appear to matter to a few individuals, some seem obvious to me, some are clear to no one. None of them are ...


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If Hume claims that the only vice is murder, then he can restrict the discussion to murder. However, if Hume is making a claim about vice in general, and Hume acknowledges that there are actions other than murder than are correctly classified as vices, then we are free to consider other examples of vices. Consider the example of cheating in a sporting ...


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If you are able to use modus tollens, then the result would follow quickly. Here is an example of that using a different proof checker: However, if you have to derive this using introduction and elimination rules, the following might work using a proof provided by the authors of forallx (page 170): Kevin Klement's JavaScript/PHP Fitch-style natural ...


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The complement of "at least two" is not "at most two" but "at most one" (in general the complement of "at least N" is "at most N-1"), because "at least two" and "at most two" could be true at the same time. But to say that "at most one person shares the same birthday with themself" is to say that no two different people do. So it is correct to say that the ...


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There's The Logic of Reliable Inquiry by Kevin Kelly, which develops a formal learning theory framework to address philosophical problems about scientific inquiry.


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The best way to do that would be to do what philosophers of the mind do, and reject historical forms of realism like objective reality, and Cartesian duality. Gilbert Ryle in his The Concept of Mind attacks Cartesian rationalism, and purports to show that the mind-body duality is a category mistake. In philosophy, the position that defends that psychology is ...


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Karl Popper - The logic of scientific discovery - it is a classic book about methodology and Philosophy of science. The concept of falsiability is crucial to understand modern epistemological debates.


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This is a good question. There are multiple sorts of tautologies, each with a different purpose. One is the Law of Identity which is phrased as "A is A", and is essentially an axiom in reasoning. For instance, in mathematics, an equation like x+y+z=5 may eventually result in a statement such as 0=0 in which the mathematician can be assured that he has ...


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This is just plain rubbish as pointed out by the mathematician David Hilbert in his book, Geometry and the Imagination - he did not call it 'Geometry and the Tautology'. In fact, he spends a great deal of time and trouble in the early part of the book giving mathematicians who fetishise the tautology a good kicking. In fact, it's deductive thinking that he ...


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Your scepticism of Dennett is well-grounded. Claims similar to Dennetts were given by Skinner under the rubric of behavioral psychology where one supposed thinking things (res cogitans) were merely things, that is automatons, and one was not supposed to ask a man about his inner self, his telos or his intentions, or indeed how things were going with him, as ...


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When I run across problematic statements of this sort, I always prefer to follow Wittgenstein and look for the error in language that lies behind it. This is precisely the kind of 'philosophy' he thought needed therapy more than analysis. The first step in that Wittgensteinian therapy is to step back and consider what purpose this claim has in Dennett's ...


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I just wish to add a few thoughts and conceptualizations that came to my mind: As others have highlighted, there is a long debate (a) about determinism, and (b) about the definition of free will, and (c) if free will is compatible with determinism (this position being called 'compatibilism'). (a): Some answers here mentioned that at the micro-level ...


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Your question is formulated from a quite narrow point of view: you assume that everything in nature works according to rules of the macroscopic universe ("chemically", "If any input causes with 0 uncertainty", "system"...). Following such fallacious assumption you consider that everything is predefined. So, you are minimally falling in the fallacies of ...


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Because we ignore to what extent we are deterministically programmed to take certain actions and we ignore to what extent consciousness plays a role in the plasticity of the brain. eg. "somebody with anger management issues decides to use therapy to shape their emotional responses. Somebody else with the same issues decides to kill people." ...


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If we accept that neuro-chemistry largely explains cognitive function, deterministically, how can we be accountable? Thats a very big if and given the prevalence of law-courts, judging and judgements in our world and of freedom and liberty it might be better to to ask how can determinism exist. But of course that is just as silly a question as the first. ...


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Here is the question about the law of the excluded middle (LEM) and the principle of bivalence (PB): I don't understand precisely in which situations one or the other principle are at play, it seems that they may appear together, but not necessarily. Can someone give me examples and help me clarify the differences? Andrea Iacona in her article "Future ...


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From Google: il·lu·sion noun a thing that is or is likely to be wrongly perceived or interpreted by the senses a deceptive appearance or impression a false idea or belief. Daniel Dennett in Consciousness Explained lays out his argument for how consciousness is illusory by starting with debunking Cartesian duality and concluding ...


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Reasoning and perception We need to draw distinctions. Can any moral reasoning be perceptual ('how can "moral reasoning" ...be construed as the act of perceiving?) and Is all moral reasoning perceptual ('to consider the whole of "moral reasoning" as a perception sounds like nonsense to me'). Whatever the relations between them, these questions are not the ...


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There isn't any difficulty with the truth or falsehood of statements about future events. Consider the two following statements: (1) There will be a sea battle tomorrow. (2) There will not be a sea battle tomorrow. Each of these statements is either true or false. If one is true, then the other is false. Obviously, we don't know the future, but ...


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I once wrote the Head of Philosophy at Uni of Bristol to ask about the purpose of Russell's symbolic logic because it seemed to me, as a rank amateur with no knowledge of philosophy who had just read a book about it, that it is pointless. He asked me to tea in his study and we had a good chat. He explained that I was basically correct, symbols offer no ...


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Well, it depends on what you mean by philosophy. Philosophy is practiced extensively in every field by those who seek to understand the field conceptually. Bertrand Russell is a living example that mathematics stopped being the study of arithmetic hundreds of years ago, and is largely an exercise in logic and philosophy at the graduate level. Computer ...


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We can show that the truth of "C or D" can be derived from the premises using algebra. For this, it is convenient to use a different notation for logic from the one you are using. Conjunction is denoted by juxtaposition, like algebraic multiplication. XY means "X and Y". Disjunction is denoted using +, so that X + Y means "X or Y". Negation is indicated ...


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According to Andrea Iacona Aristotle in Chapter 9 of On Interpretations believed that the disjunction of a proposition about the future or its negation was true, but the individual disjuncts were neither true nor false. Consider these two statements: (1) There will be a sea battle tomorrow. (2) There will not be a sea battle tomorrow. Neither of ...


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This is not likely using the proof checker that you are using, but it may provide a hint on how to proceed. It is however a Fitch-style proof checker. For the first one consider the following proof using disjunction elimination: I consider both cases of the disjunction in line 1 by starting two subproofs, the first on lines 3-4 and the second on lines 5-16....


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Yes-ish: it takes some work to formalize it, but it can be done. Specifically, the proof of the relevant model checking theorem gives a general method for proving, for an appropriate sentence p, a sentence of the form "If q_i implies p for each i < n, then p is true" where n is the appropriate bound and {q_i: i < n} are sentences characterizing each ...


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"Neither true nor false” means that the statement has no definite truth valued : it lives in a sort of limbo, a truth value-gap between true and false. “Either true or false” means that the statement has (exactly) one of the two truth values. To say that "Lexical definitions are either true or false" means that a Lexical definition : also known as ...


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Proof in Agda (an interactive theorem prover): data _or_ (A : Set) (B : Set) : Set where inl : A → A or B inr : B → A or B dilemma : {A B C D : Set} (f : A → C) (g : B → D) (t : A or B) → (C or D) dilemma f g (inl a) = inl (f a) dilemma f g (inr b) = inr (g b)


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Come to think of it, fairies and Pegasus may in fact exist, while Donald Trump maybe doesn't, so that "Donald Trump is the President of the United States of America" would be a more questionable statement. Most of our logical statements are about things we only believe, indeed that we only imagine, that they exist. Our semantics has better be able to deal ...


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