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Logic

First: I think every question has a logical answer. is it correct? Second: If the answer to my first question is yes, then what is the logical answer to the question why a cow has four legs?

I’m guessing that what you think is that every question has a satisfying answer — an answer that explains what we wanted explained or tells us what we wanted to know. And so my question is: why do you think that? For the record, I don’t think it’s true, or at least I don’t see any good reason to suppose that it must be true. Here’s an example. We can send electrons, one at a time, through a certain sort of magnetic field (one oriented “inhomogenously” in a particular direction.) The electron will respond in one of two ways: maximum upward deflection or maximum downward deflection; nothing in between. So suppose a particular electron passes through the field and is deflected upward. You ask why up rather than down. The most widely-held view among physicists is that there is no answer. The most widely-held view is not that we just don’t know, but that which way the electron went is a matter of pure chance; nothing explains it. Now this may be wrong, but there are serious reasons for...
Logic

I've come across what appears intersecting and incompatible logic systems within academia (and society). System one is what I call analytic logic: the merit of your argument or opinion is completely independent of your immutable characteristics. (Like MJ says, it doesn't matter if you're black or white). If you dismiss the merit of an argument by attacking the person who made it, you've committed a logical fallacy. The peer review process in academia avoids this potential by hiding the author's identity from reviewers. The argument or study is judged on its own merit. I call system two Identitarianism (some call it Neo-Marxism or Intersectionalism). With these rules, your ethnicity(ies), gender, and sexual orientation (etc.) are in play. Some people have more (and others less) merit because of their immutable characteristics. System two seems backwards but the rationale goes as follows: "Oppressed" groups (POC, women, trans people, gay/lesbian, poor people, etc) have access to ... (1) the norms,...

There's way too much to be said here for one short post, but a handful of points. First, As a straight, white male I'm pretty confident that there's a lot that I don't understand about what it's like to live in the country I live in (the US) as a woman, or as a Black person, or as a gay man, or transgender person, or as a lesbian or... This seems both unremarkable and important. It's unremarkable because we all are familiar with the fact that one's circumstances can sometimes make it easier to see or understand certain things. Lived experience does make a difference, and the difference it makes can be important. For example: I suspect that a great many of the people who put in place the "separate but equal" regime that finally began to crumble with Brown v. Board of Education were pretty clueless about what "separate but equal" was like for Black Americans and therefore, about whether "separate but equal" was even a serious possibility. That's hardly a shocking thing to say. ...
Logic

This is a follow up to a question answered by Dr. Maitzen on December 31 2020. The statement really was “Only if A, then B”. It came up on a test question that asked the following: “If A, then B” and “Only if A, then B” are logically equivalent. True or false? The answer is ‘false’, apparently. I reasoned that “Only if A, then B” is maybe like saying “Necessarily: if A, then B”, and this is clearly different from saying simply “If A, then B”. But I’m not sure. Any chance you might be able to help me see why “If A, then B” and “Only if A, then B” aren’t equivalent? Clearly they say different things, but I’m just not sure how to put my finger on the difference. I really appreciate the help. Thank you again.

I agree with my colleague that "Only if A, then B" is not idiomatic English, and so it's hard to know what your teacher meant. In teaching logic over the years, I've seen many examples that take this form: "Only if A, B" — leaving the word "then" out. An English example might be the somewhat stilted but acceptable "Only if you're at least 18 are you eligible to vote." That's the same as saying "You are eligible to vote only if you're at least 18." And that's different from saying "If you're at least 18, you're eligible to vote." Saying "If you're at least 18, you're eligible to vote" means that there are no other qualifications needed; being 18 or older is enough. Saying "You're eligible to vote only if you're at least 18" allows that there may be other requirements as well, such as being a citizen. So if what your teacher meant was "Only if A, B," then perhaps my example shows that this isn't the same as "If A then B."
Logic

Is there a specific label or name for the rhetorical tool of using a little bit of truth to try and disprove another claim. For example, if Person A says something like "philanthropy is less effective as a means to maximize well-being than if we just taxed everyone more" and in response Person B says "but philanthropy does some good". Even assuming Person B's response is truthful, it seems they are avoiding addressing the true question. I know this is similar to a red herring fallacy, but I was wondering if there is a more precise name (or set of work) looking at the use of a nugget of truth to try and distract from or disprove a larger issue. Thank you.

Philosophers are usually not the right people to ask for fallacy names. Most of us don't remember many of them, and aside from a handful (begging the question, for instance) seldom mention them by name. You mention the red herring fallacy here. That's probably good enough, but it's not any better than just noting that the response misses the point. If A says that taxing would be more effective than philanthropy and B says that philanthropy does some good, all A need say is "I agree: philanthropy does some good, but my point is that it's less effective than simply taxing people." A might be right or might be wrong, but what B says is irrelevant to the claim at issue, since A 's claim is entirely consistent with B 's reply. I notice this a lot on Quora. There's a whole sub-genre of questions in which people people describe a bit of reasoning gone wrong, and then ask for the name of the fallacy. Often the person has already done a good job of saying what's wrong. Sometimes...
Logic

What fallacy is it ? hasty generalization or begging the question ? Is it really a fallacious argumnet or a valid one ? Premise1- If A is true, then B is true. Premise 2- A is true. Conclusion- B is true. We have no empirical evidence for supporting P1 and P2 therefore both are false. Since 1 or more than 1 premise is false, the conclusion will always be false. A guy argues that it is a valid argument. On the other hand, I say it is not a valid argument. I don't know which informal fallacy it is. Does this argument contain really a fallacy or the other guy is right ?

The argument is valid. That's because in logic, we say that an argument is valid if it's impossible for the premises to be true and the conclusion false at the same time. If two statements A and If A then B really are true, then so is B . If both A and If A then B are false (or better, if at least one of them is), then the conclusion might be true or might be false, but the argument is still valid; the conclusion still follows. You seem to say that if we have no evidence for something, then it's false. But that's not right. Lots of things are true whether anyone knows them. (How many worms were there in the garden plot at noon yesterday? There's only one right answer, but no one happens to know it or even have evidence.) And things can turn out to be false even if we have serious evidence that they're true. And you seem to be saying that if the premises of an argument are false, the conclusion must be false too. But that's not right, and in particular it's not right even for valid...
Logic

What fallacy is being committed here: I owned two Chevy cars – a Cruze and a Malibu – and they gave me nothing but trouble. The choke and the batteries froze up and the clutches went out on both cars. They were always in the shop. Chevy’s are poorly constructed and should be avoided. What fallacy does this person commit? fallacy of hasty generalization or fallacy of composition? It is difficult to tell if the argument assumes that parts of the Chevy car are troublesome (batteries, clutch etc.) therefore the whole Chevy car is poorly constructed making this a composition fallacy or if the person has observed a small amount of Chevy cars and made a generalization about the whole of Chevy cars which in this case it would be a hasty generalization fallacy. These fallacies are hard to tell apart and a little confusing.

The fallacy of composition is drawing conclusions about the whole from facts about the parts when the facts about the parts don't support the conclusion . Obvious case: every cell in my body weighs less than a pound. But that doesn't support the conclusion that I weigh less than a pound. The fallacy of composition is an informal fallacy: you can't tell whether it's been committed just by looking at the form of the inference while ignoring the content. In any case, the inference you're considering isn't a conclusion about a particular car—a whole—based on premises about its parts. It's a conclusion about all or most cars of a certain sort based on facts about some cars of that sort. This doesn't count as a part/whole relationship in the sense relevant for potential cases of the fallacy of composition. "Chevy cars" aren't a whole in the relevant sense. On the other hand, it would be hasty to generalize about Chevies based on a sample of two. So yes: hasty generalization. A footnote, however:...
Logic

Is it - must there be - possible to track all logical statements back to the fundamental laws of logic ( the law of identity, the law of non-contradiction, etc.) when it comes to "classical logic"? Are all logic derived from these fundamental laws?

The problem here, I think, is that there's no one answer to the question "What are the fundamental laws of logic?" We can do things in different ways, and things which are fundamental on some accountings will be derived on others. Let's assume that there is a definite answer to the question "What are the logical truths of classical logic?" (I'm using this as a proxy for "logical statements." If we want to expand it to include principles of inference, like modus ponens, that's okay too.) Note that the set of all such truths will be infinite, but that's okay. And to make "classical logic" well-defined, let's assume we mean truth-functional and first-order predicate logic, in which our first assumption is indeed correct. Then there are sets of rules and/or axiom schemes that provably allow the derivation of every logical truth thus understood. As just noted, there is no one way to so this, and the different ways won't contain the same axioms and/or rules. Even "the law of non-contradiction" will show...
Logic

how would i use natural deduction to prove this argument to be correct? Its always either night or day.There'd only be a full moon if it were night-time. So,since it's daytime,there's no full moon right now. i have also formalized the argument using truth functional logic i'm not sure if it is completely correct though and would much appreciate the help. symbolization key: N: night D: day Fm: full moon Nt: night time Dt: day time ((N V D) , (Fm → Nt) , (Dt → ¬Fm))

There's a problem with your symbolization. The word "since" isn't a conditional. It's more like a conjunction, but better yet, we can treat it as simply giving us another premise. So in a slightly modified version of your notation, the argument would be N v D F → N D ∴ ¬F But from the premises as given, the conclusion won't be derivable. The reason is simple. You are assuming that if it's day it's not night and vice-versa. That may be part of the meaning of the words, but the symbols 'N' and 'D' aren't enough to capture it. The easiest fix is to treat "day" as "not night." That gives us N v ¬N F → N ¬N ∴ ¬F In this case, the first premise is a tautology and not needed. The argument is just a case of Modus Tollens. If you want something less trivial, you can drop the first premise and add a premise like this: D ↔ ¬N F → N D ∴ ¬F The first premise amounts to making the "v" exclusive. From there it's easy to complete a proof. A couple of extra comments. First, in the English version, you add a...
Physics
Logic

In an answer to a question about logic, Prof Maitzen says he is unaware of any evidence that shows classical logic fails in a real-life situation. Perhaps he has never heard of an example from physics that shows how classic logic does not work in certain restricted situations? A polarizing filter causes light waves that pass through it to align only in one direction (e.g., up-down or left-right). If you have an up-down filter, and then a left-right filter behind it, no light gets through. However, if you place a filter with a 45 degree orientation between the up-down and left-right filter, some light does get through. It seems to me that classic logic cannot explain this real-world result. Thanks!

I'm sure that Stephen Maitzen will have useful things to say, but I wanted to chime on in this one. You have just given a perfectly consistent description of what actually happens in a simple polarization experiment that I use most every semester as a teaching tool. Classical logic handles this case without breaking a sweat. But there's another point. You've described the phenomenon in terms of light waves. That's fine for many purposes, but note that the wave version of the story of this experiment comes from classical physics, where (for the most part at least) there's no hint of logical paradox. The classical explanation for the result is that a polarizing filter doesn't just respond to a property that the light possesses. It also changes the characteristics of the wave. Up-down polarized light won't pass a left-right filter, but if we put a diagonal filter between the two, the classical story is that the intermediate filter lets the diagonal component of the wave pass, and when it does, the light...
Truth
Knowledge
Logic

Given a particular conclusion, we can, normally, trace it back to the very basic premises that constitute it. The entire process of reaching such a conclusion(or stripping it to its basic constituents) is based on logic(reason). So, however primitive a premise may be, we don't seem to reach the "root" of a conclusion. Do you believe that goes on to show that we are not to ever acquire "pure knowledge"? That is, do you think there is a way around perceiving truths through a, so to say, prism of reasoning, in which case, nothing is to be trusted?

There's a lot going on here. You begin this way: Given a particular conclusion, we can, normally, trace it back to the very basic premises that constitute it. If by "conclusion" you mean a statement that we accept on the basis of explicit reasoning, then we can trace it back to the premises we reasoned from simply because we've supposed that there are such premises. On the other hand, most of what we believe doesn't come from explicit reasoning. (I don't reason to the conclusion that I had a burrito for lunch. I just remember what I ate.) And even when it does, the premises don't usually constitute the conclusion. The easiest way to see this is to consider non-deductive reasoning. A detective may conclude that Lefty was the culprit because a number of clues point in that direction. Maybe a witness saw someone who looks like him; maybe he had a particular motive for the crime. But the clues don't constitute Lefty being the criminal; they merely make it likely. After all, even given all the...

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