Your videos are really informative and well-organized. Thank you for your contributions to my knowledge. I have a suggestion/request though, could you please write down your resources in the descriptions.
I don't understand why we pretend like this is supposed to be inbuilt into the universe or something? Similarly to math, is this not just the language we use to approximately describe what we see in the world? If what we describe does not reflect reality then either our model is wrong or our language is not expressive enough. No?
What do you guys think is the best interpretation for the "if then" connective in the first example? If it's not material implication I wonder what it is and what kind of logic can model it
In arguments that DON'T equivocate (unlike these ones), you can switch premises for their logical equivalents and nothing changes. 1: if some entity e is human, then it has a 100% chance of dying 2: Socrates belongs to the catory of entities "humans" 3: Socrates will die. That is the same as: 1:if one is a human, one dies at some point 2: Socrates is human 3: Socrates dies at some point Let's see if the premises and terms can be replaced in these logical nihilist arguments... In the conclusion of the Reagan argument, what does it mean to say "if Reagan doesn't win, Anderson will"? Well, considering it's taken to be false, it probably means "in the closest possible world to w1 where Reagan doesn't win, Anderson wins". If the argument doesn't equivocate, then this phrase should have the exact same meaning in p1 as it does here in C1 and that shouldn't make p1 false. "If a republican will win in w1, then in the closest possible world to w1 where Reagan doesn't win, Anderson wins". That's simply false. The antecedent has to be true of w1, because if it isn't, then p1 and p2 equivocate between different possible worlds. So, either p1 is false or the argument equivocates. MODUS TOLLENS: the argument about the marbles also equivocates. P2 is logically equivalent to "if you grab a random marble, it probably won't be red". Again, if the argument doesn't equivocate, then this phrase should be logically equivalent to the consequent of p1. Let's see: "if the marble you grabed is big, then if you grab a random marble, it probably won't be red". It equivocates, again. YOUR MORAL ARGUMENT: what is p2 logically equivalent to? "It is inmoral to murder someone gently". Ok, and what about p1? "If you will kill someone, then you should at least do it gently". P1: it's better to kill someone gently than killing him un-gently P2: it's inmoral to kill people, even if you kill them gently. If the premises don't mean that, why would a moral realist accept them? GENERAL PROBLEMS: at one point, you ask why "probably" should be understood in one way in one sentence and in a different way in another. Well, because that's the only way of making both premises true. By using different meanings of words and phrases. If you want, claim that "it's probably not red" refers to the same thing as "if you grab a big marble, *it's probably red*", but if you do, then p2 is false. It seems like all works only because people interpret p1 to mean something because of the context in which consequent is put in. They therefore take the premise to be true. The consequent is then put out of that context, but the reader still subconsciously reads it as true. This is in the modus tollens case of course
Here are some thoughts: A modern interpretation of logic is that it's the science of entailment, not the science of correct thinking, as in the traditional psychologistic view. If it were the latter, then indeed Modus Ponens would not be a law that preserves correct thinking. It's too barren. If we can compare the laws of Logic to the laws of Physics, then there is no real problem with apparent exceptions. Laws hold in ideal conditions. In Logic the laws hold only in a very simplified "language", consisting of meaningless symbols, a handful of operators and a bit of grammar. Speaking of operators, the "probably" operator throws off the whole argument against Modus Tollens. This law works with negation and implication. By adding "probably", the truth-table of the rule is changed radically. How would you compute that? In the supposed counterexample, it seems that they want to take "probably" as a predicate, which would be a vague predicate. So, which is it? An operator or a predicate? Again, formal logic has been defined (in modern times, at least) as working in a very restricted language. If we translate MP and MT into ordinary language, we must use the simple conditional in the present indicative, i.e. "if it is..., then it is..." Most of the counterexamples used counterfactual conditionals, the future tense, extra operators, etc. If we were to translate those counterexamples using the right conditional, mood, tense, and decided on a definitive interpretation of the operators and the predicates (no vagueness allowed), I think none of them would work.
"A modern interpretation of logic is that it's the science of entailment, not the science of correct thinking, as in the traditional psychologistic view" The question is going to be which entailment relation is the "right" one. Or rather: formal logical systems can be viewed as theories of entailment, and one of the things philosophers want to know is which of these gets it right. In classical logic, A&~A entails everything; in paraconsistent logics, this is not the case. So which is right? This is the sense in which philosophers treat logic as "the science of correct thinking". I don't think this is psychologism, because the usual view is that logical laws are normative, and are not psychological generalizations in any sense. A philosopher might hold that e.g. classical logic is the "right" logic, that it correctly captures the real entailment relation, while also holding the anti-psychologist position that psychology tells us how people do reason, not how they ought to reason.
@@KaneB Ah, you got a point there about logic being normative. I'm in the middle of taking a self-taught course on mathematical logic, and you've given me something to think about. Thanks for the measured response! That's rare here on YT.
The laws of logic aren't "the science" of anything. The scientific method requires presupposing the laws of logic are true. So science depends on the laws of logic, not the other way around. If you tried scientifically verifying the laws of logic are true, you'd just be arguing in a circle (since the scientific method presupposes the laws of logic).
Aren't these just the standard paradoxes of material implication? I've been reading Priest's Introduction to Non-Classical Logic and I think your examples are addressed in Conditional Logic.
0:35 Does that hold in complete generality? If yes: there is a principle which holds in complete generality, ie it's self undermining If no: there is no reason to accept the premise, ie it's self undermining
MP and MT hold absolutely true in classical formal logic, which is an idealization we invented to model actual reasoning. These counterexamples just show that classical formal logic is not a perfect model of actual reasoning. I don't know much about other logical systems, but I would expect there cannot exist a perfect model of reasoning short of describing thought at the level of neurons.
In the marble example we are simply having trouble converting natural language to formal language. The marble isprobably red and the marble is not probably red cannot both be true. By defenition of probability. Therefore p1 and p2 are both true if and only is the marble is small or the marble remains unknown. We must use the natural conditional when using binary logic, because there are a total of 16 binary operators in binary logic. If you exclude false premises then you simply have the and operator if you exclude false premises imply true conclusions you have if and only if . And so on . In each of the examples given it is simply the case that a proper understanding of the material conditional resolved the apparent paradox. As for if 1,000,000 grains of sand are a heap then 999,999 is a heap it is the case that we are making a silent argument. For all heaps of sand the cluster of sand will remain a heap after removing a grain of sand. This statement us plainly false even if we don't know for which heap or heaps it is false.
Could we assume that there exist many (infinitely many) Logics that have distinct axioms and yet are all internally consistent? Is this Logical Nihilism?
The counter examples don't work. They don't prove modus ponens isn't true they just prove they're very badly constructed and falsely reasoned and rely on misleading the reader on what the conclusion says. Eg. In the first conclusion it invites you to forget it becomes true contingent to the first premise being already shown to be true. It also relies on reasoning with the properties of the things not the things not the things themselves. If there are only three candidates, Reagan, Anderson and Carter, and Reagan and Anderson are republicans and Carter is a democrat, then if a republican wins it will be Reagan or Carter or if a democrat wins it will be carter. That's it. That's the whole flow chart for that election. The only flaw with it is if people get shot, for which case you need a contingency plan to get new candidates. Everything else in the example is just misdirection.
"That's it. That's the whole flow chart for that election." So what? That just shows that you can present the information concerning the election in a particular way. It does nothing to show either that one of these two claims is false: (1) If a Republican wins the election, then if it's not Reagan who wins, it will be Anderson (2) A Republican will win the election Or that this claim is true: (3) If it's not Reagan who wins, it will be Anderson You'd have to do one of those things in order to show that McGee's counterexample doesn't work. All McGee requires is that (1) and (2) are true, and that (3) is false. That's it. Whether or not (1), (2), or (3) are "misdirection" is irrelevant.
@@KaneB What it shows is there are correct ways and incorrect ways of constructing logics and your counter examples rely on an incorrect way of constructing them. You haven't presented a valid counter example. All the rest of your response does is reiterate the same unsound argument. As I said first: The argument relies entirely on hoping the reader doesn't notice that all the person who constructed this alleged counterexample has done is make a total mess. Your response is also a mess.
@@KaneB but 3 trivially follows from 1 and 2. If it's not reagan who wins, and it's a republican who wins, and if it's any republican other than reagan who wins, it's anderson who wins, then anderson wins. That's it. It follows from the premises that it cannot be the democrat, which leaves only reagan and anderson. So if it's not reagan, but it's either reagan or anderson, then it's anderson. This does not make any sense at all to me, am i missing something?
@@james1098778910 What McGee claims - and of course you may disagree with him on this - is that we should accept (1) and (2) but reject (3). We should accept (1) because among Republicans, Anderson is second to Reagan. We should accept (2) because the polls show that Reagan will win, and Reagan is a Republican. We should *reject* (3) because among all the candidates, Carter is second to Reagan, so if Reagan loses, it'll be Carter who wins. That's McGee's argument, at any rate. Obviously, (3) trivially follows from (1) and (2) if we take modus ponens to hold in complete generality. After all, the inference from (1) and (2) to (3) is just an application of modus ponens. But the point of McGee's argument is precisely that modus ponens does not hold in complete generality. He thinks he has a counterexample to modus ponens.
I think you're right -- this is actually a logical fallacy of hidden premises. I also thought about this while watching the video and agree with you.@@vapourmile
only to some kind of naive realist would any kind of "nihilistic" position be interesting. to everyone else (especially instrumentalists or pragmatists) it's really just trivial at best, and un-useful handwaving at worst. EDIT: actually speaking of nihilism, have you ever looked into Jacob Stegenga's book _Medical Nihilism_? apparently made a big splash and raised some skepticism towards medical studies and the current practice of medicine. has more to do with methodology, but knowing philosophy of bio is your thing, you might be interested
I don't think I count as a naive realist - at least not in this context - and I find it interesting. But I'm not sure I have much to say to anybody who doesn't find it interesting. Obviously, different people are interested in different things 🤷 I'd say I'm attracted to logical nihilism (and logical pluralism) as being aspects of a broader epistemic voluntarist position: there are no *rules* of belief formation or belief revision, period. I suppose that, if you adopt this voluntarist position, then logical nihilism (or pluralism) trivially follows, but of course, establishing this position in the first place is not a trivial matter - and part of the reason it's not a trivial matter is because of the many philosophers who reject this approach to logic! "and un-useful handwaving at worst" -- Could you expand on this point? I don't know what you mean here.
And yes, I've read part of Stegenga's book (not all of it). I'm not really sure where I stand on his conclusion, partly because philosophy of medicine is outside my area of expertise, and partly because this is a "relative significance" debate. Nobody, including Stegenga, denies that medical interventions are effective - indeed, nobody, including Stegenga, denies that there are even some "magic bullets" in medical treatment - the question is exactly how effective are they, and exactly how many "magic bullets" are there?
@@KaneB I don't think the term magic bullet does any favors. It assumes that the magic is within the bullet instead of the highly specific and sometimes incredibly rare situation that the bullet is required to be used in to have any semblance of magic. The bullet may not change but situations can change rapidly which would reduce the effectiveness of this bullet. Taking these sorts of factors into the equation and suddenly the magic seems to vanish.
@@KaneB sorry should probably clarify. nihilism in general is "uninteresting" in the sense that someone stumbling upon it probably won't have any eureka moment and go on to solve any real world problems. also I do agree with that stance on logic, considering different logics have different uses. there is no one supreme over arching system and they all have their own useful purposes (like fuzzy logic in AI). to say ones "correct" in describing the world is just missing the point IMO.
(A) If the statement labelled A is true then there are on laws of logic. For the sake of argument assume the statement labelled A is true then on this hypothesis we have: P1) The statement labelled A is true ---- by hypothesis P2) If the statement labelled A is true then there are no laws of logic. ---- because this is what A says Hence: C) There are no laws of logic. ---- by MP Thus we have proved that on the hypothesis that (A) is true there are no laws of logic. But this is just another way of saying that we have proved (A). So the hypothesis of our argument is true so the conclusion must be true, This we have proved: There are no laws of logic.
The first example from McGee is terribly bad. That's his grand argument against modus ponens? All he's done is provided two contradictory premises, ie. "A republican will win the election" and the premise that "If this specific republican loses, a democrat wins". He thinks he can get away with it by pretending the opinion poll is just mere "additional information" and not a premise. It's pathetic. Should have pointed it out from the start instead of wasting 20 minutes trying to provide counter arguments by equally obtuse philosophers. If one of the premises is that a republican wins the election, then it doesn't matter what the opinion poll says, **You've already accepted the premise that a republican wins** . If you wanna believe the opinion poll over the premise as true? Great! Then don't believe it's true, and modus ponens still holds. What a waste of tiiiiime.
This seems to be pretty much Mandelkern's response? Anyway, I still think McGee's counterexample is pretty compelling. It looks like (P1) is true, (P2) is true, and (C) is false. The opinion poll is what justifies those claims. If those truth-values have been assigned correctly, then we have a prima facie counterexample to MP.
@@KaneB How can you say P2 is true in the case where Carter won? It’s only because P2 is NOT true that McGee claims to have an argument. But when P2 is not true, we’re outside the example. Fame over. In fact, nobody should ever take a premise like P2 to be true in an absolute, strong as the laws of logic, sense. We know how polls work, we know they have uncertainties, and even if we knew nothing of polls, we know predicting the future entails uncertainty. P2 enters the example on weak footing whereas the prior probability that MP is solid is very high. You need strong reasons to favor upholding shaky old Premise 2 in light of the FACT not P2. Do you have any reasons that strong?
@@BrettCoryell >> How can you say P2 is true in the case where Carter won? It wouldn't be true in that case. >> It’s only because P2 is NOT true that McGee claims to have an argument Honestly have no idea what you're talking about here. McGee claims that (P2) is true. >> We know how polls work, we know they have uncertainties, and even if we knew nothing of polls, we know predicting the future entails uncertainty Sure, we could be wrong that (P2) is true; and perhaps in the actual world, opinion polling does not provide sufficient evidence to accept a claim like (P2). We can just imagine a world where opinion polling is much more reliable.
If you don't presuppose the laws of logic are universally true, then you can't make any meaningful assertions at all. Because anything you assert, it's negation could also be true at the same time & place. It loses any meaning.
none of this make sense , the example at 6:33 how claim it was a porpoise if p2 that creature is a fish. I fail to find ONE exemple not wrong in this video
I discuss counterexamples to noncontradiction briefly in the first video on logical nihilism. More generally, check out dialetheism: plato.stanford.edu/entries/dialetheism/ (I also have a few videos on dialetheism, though I never finished that series)
Since watching the first part of this video I have read Gillian Russell's essay on the subject. You don't understand it. She actually writes in that same essay, nobody really believes that first syllogism (which is a correctly constructed valid syllogism) is really an argument for logical nihilism. About it, she explicitly states: "Pluralists do not intend this as an argument for logical nihilism". She goes on to explain the point of it is to be 'a reductio on the first premise', that is, the first which has an obvious problem with it "To be a law of logic, each logic must hold generally". Pluralism means the correctness of logical laws are contingent to the field in which they operate so within the context of pluralism the first premise of this syllogism is false. One such example is the law of excluded middle, which is held true in classical logic, but is Not held true in constructive mathematics. So the law of excluded middle is not a universal law. The point being, "It is a law only under certain specific conditions" is different from "It is not a law". I also notice LEM is the first place Gillian goes to for her example too. Therefore the purpose of the syllogism as she presents it is not to argue for logical nihilism but rather to draw from its first premise a dividing line which exists between monist and pluralist logics: The first premise is true only in monist logics. For somebody who claims to be qualified to talk about the subject you appear to have some difficulty understanding simple introductory texts written about it.
Now you're just quote mining. Unfortunately for you, I have also read Russell's articles on the subject. Here's the full quote. (You are clearly just BSing so I'm not really talking to you anymore. I write this for the benefit of any other readers who come across your comment.) Russell first presents this argument: (P1) To be a law of logic, a principle must hold in complete generality. (P2) No principles hold in complete generality. (C) There are no laws of logic. Then about this, she says: "Pluralists do not intend this as an argument for logical nihilism, of course. They think that nihilism is absurd, and since many who work on non-classical logics find the second premise plausible, they intend the argument above as a reductio on the first premise: the monist's assumption that logic must be completely general. Still, that premise has both intuitive appeal and support from historical writers on logic, and - as I will explain in the first section of this paper - nihilism is not, in the end, absurd. These two things - the plausibility of premise 1 and the non-absurdity of the conclusion - turn this sketch of a reductio on premise 1 into a sketch of a direct argument for nihilism." Obviously, pluralists who give that argument do not intend it as an argument for nihilism. They are pluralists, not nihilists! Pluralists offer the argument as a reductio on (P1); nihilists offer the argument as a sound argument for its conclusion that there are no laws of logic. Russell is *absolutely explicit* that the purpose of the argument as she presents it is as an argument for logical nihilism. This is not to say that Russell herself accepts logical nihilism. But she does take it seriously, and she sees the above argument as a compelling argument in its favour. Russell's paper is freely available online so this is all easily confirmed: gilliankrussell.files.wordpress.com/2018/05/logicalnihilism-philissues-v3.pdf
@@KaneB Nothing you wrote disagrees with what I wrote. You just haven't addressed what I actually wrote but instead extracted other details from the same document. The only bone of contention is "Russell is absolutely explicit that the purpose of the argument as she presents it is as an argument for logical nihilism" In which you have, again, just misunderstood what you read. Her essay as a whole may be an argument for logical nihilism, but that specific syllogism to which I am referring is not. You're really annoying. You don't know what you're talking about, you don't understand what you've read, and yet you still want to argue about it. Arrogance, in your case, is clearly not a virtue.
@@vapourmile LOL. The detail that I extracted was the rest of the paragraph for the quote that you took out of context. "Her essay as a whole may be an argument for logical nihilism, but that specific syllogism to which I am referring is not." She very clearly says that it is an argument for nihilism. Now please stop spamming my comments section with crap.
@@KaneB PS. I also still don't believe you have any meaningful qualification in the subject. To have have survived something like a computer science degree would have a required far better basic comprehension. What you are is an arrogant pretentious average TH-camr whose access to information on logic clearly comes primarily from Google, not formal education. FYI: The point if a formal education is to have your comprehension tested by somebody who knows if you've understood what you've read. It is the antithesis of randoms reading things, talking shit about it, and then insisting they know what they're talking about, which is what TH-cam is made of. Therefore TH-cam has many such talks on logic presented by other people who also don't understand the subject.
@@KaneB Also, to call that example "quote mining" really only reinforces the fact you don't understand how to write academic essays. You are only reinforcing the perception further than you are Not qualified to talk about this. Gillian's essay is interesting, but I definitely won't be coming back to you for anything. You are arrogant, obnoxious, pretentious and irrational and you have poor English language comprehension. That isn't the modus operandi of a qualified person. BTW. Logic is my day job.
The second example is garbage again. First of all, these aren't syllogisms. A syllogism is constructed by two premises and a conclusion which necessarily flows from them. A valid syllogism would be: All fish have lungs. All stones are fish. Therefore stones have lungs. Remember: Validity means the conclusion must follow from the premises. It Doesn't require the premises to be true. So this example is valid but unsound. Also remember: Don't stuff your premises full of conditions. This mixes up classical syllogisms with conventional Boolean logic. The most you can do to tidy it up is: Lungfish are fish with lungs. The fish in the net is a fish with lungs Therefore the fish in the net is a lungfish. That's a valid syllogism. Valid Boolean algebra is: If an item in the net is a fish and that same item in the net has lungs then that same item in the net is a lungfish. Don't build syllogisms from conditionals. Definitely don't build them from nested Boolean algebraic conditional expressions. Again in the second example the conclusion also invites us to forget it was contingent to the item being a fish, established in the first premise (which is a contingency, not a premise). So it's just badly constructed bullshit. Syllogism isn't the right tool to construct these ideas. For this kind of conditional branching you want a flow chart, not premise+premise=conclusion arrangements where the premises are replaced by conditionals. Use a flowchart for these cases where it's more easily shown they don't prove anything. So no, neither of the examples do anything to dislodge modus ponens they're just sleight of hand.
"First of all, these aren't syllogisms" It's modus ponens. If P then Q; P; therefore Q. "Remember: Validity means the conclusion must follow from the premises. It Doesn't require the premises to be true" Yeah, no shit. Everybody is aware of this. But if you want to present a *counterexample* to a purported logical law, you need a case where the premises are true and the conclusion false. "The most you can do to tidy it up is:" LOL what are you talking about. That's just a different argument, and not modus ponens.
@@KaneB I'm explaining why the examples you presented are bullshit. All we learned from this is you didn't understand what you read. You clearly aren't qualified to talk about these topics and you clearly also don't have the personal skills to discuss them either.
@@vapourmile "I'm explaining why the examples you presented are bullshit." You're not explaining it very well. Indeed, it comes across as if you don't know what you're talking about. "You clearly aren't qualified to talk about these topics and you clearly also don't have the personal skills to discuss them either. " I mean, I am literally qualified to talk about them. That is, I have actual academic qualifications in this subject. I can't comment on personal skills though!
@@KaneB Sorry, but boasting you know what you're talking and I don't is pretty much the end of the discussion. If you aren't willing to learn I'm not going to make a fight out of trying to help you.
@@vapourmile That wasn't intended as a boast - not that I have a problem with boasting. But you brought up qualifications. I was just correcting your mistaken assumption. Nothing you've written has given me a reason to think that you're in a position to teach me anything about this.
My first video on logical nihilism: th-cam.com/video/4B61OYuNEwI/w-d-xo.html
Thanks Kane! I’m finishing up my undergraduate degree in philosophy and always find your videos helpful.
Wow these counterexamples are super interesting!! Thank you for your presentation
Your videos are really informative and well-organized. Thank you for your contributions to my knowledge. I have a suggestion/request though, could you please write down your resources in the descriptions.
I don't understand why we pretend like this is supposed to be inbuilt into the universe or something? Similarly to math, is this not just the language we use to approximately describe what we see in the world? If what we describe does not reflect reality then either our model is wrong or our language is not expressive enough. No?
Thanks Kane! I finished up my undergraduate degree in philosophy and only now find your videos useful.
What do you guys think is the best interpretation for the "if then" connective in the first example? If it's not material implication I wonder what it is and what kind of logic can model it
In arguments that DON'T equivocate (unlike these ones), you can switch premises for their logical equivalents and nothing changes.
1: if some entity e is human, then it has a 100% chance of dying
2: Socrates belongs to the catory of entities "humans"
3: Socrates will die.
That is the same as:
1:if one is a human, one dies at some point
2: Socrates is human
3: Socrates dies at some point
Let's see if the premises and terms can be replaced in these logical nihilist arguments...
In the conclusion of the Reagan argument, what does it mean to say "if Reagan doesn't win, Anderson will"? Well, considering it's taken to be false, it probably means "in the closest possible world to w1 where Reagan doesn't win, Anderson wins". If the argument doesn't equivocate, then this phrase should have the exact same meaning in p1 as it does here in C1 and that shouldn't make p1 false. "If a republican will win in w1, then in the closest possible world to w1 where Reagan doesn't win, Anderson wins". That's simply false. The antecedent has to be true of w1, because if it isn't, then p1 and p2 equivocate between different possible worlds. So, either p1 is false or the argument equivocates.
MODUS TOLLENS: the argument about the marbles also equivocates. P2 is logically equivalent to "if you grab a random marble, it probably won't be red". Again, if the argument doesn't equivocate, then this phrase should be logically equivalent to the consequent of p1. Let's see: "if the marble you grabed is big, then if you grab a random marble, it probably won't be red". It equivocates, again.
YOUR MORAL ARGUMENT: what is p2 logically equivalent to? "It is inmoral to murder someone gently". Ok, and what about p1? "If you will kill someone, then you should at least do it gently".
P1: it's better to kill someone gently than killing him un-gently
P2: it's inmoral to kill people, even if you kill them gently.
If the premises don't mean that, why would a moral realist accept them?
GENERAL PROBLEMS: at one point, you ask why "probably" should be understood in one way in one sentence and in a different way in another. Well, because that's the only way of making both premises true. By using different meanings of words and phrases. If you want, claim that "it's probably not red" refers to the same thing as "if you grab a big marble, *it's probably red*", but if you do, then p2 is false. It seems like all works only because people interpret p1 to mean something because of the context in which consequent is put in. They therefore take the premise to be true. The consequent is then put out of that context, but the reader still subconsciously reads it as true. This is in the modus tollens case of course
Here are some thoughts:
A modern interpretation of logic is that it's the science of entailment, not the science of correct thinking, as in the traditional psychologistic view. If it were the latter, then indeed Modus Ponens would not be a law that preserves correct thinking. It's too barren.
If we can compare the laws of Logic to the laws of Physics, then there is no real problem with apparent exceptions. Laws hold in ideal conditions. In Logic the laws hold only in a very simplified "language", consisting of meaningless symbols, a handful of operators and a bit of grammar.
Speaking of operators, the "probably" operator throws off the whole argument against Modus Tollens. This law works with negation and implication. By adding "probably", the truth-table of the rule is changed radically. How would you compute that? In the supposed counterexample, it seems that they want to take "probably" as a predicate, which would be a vague predicate. So, which is it? An operator or a predicate?
Again, formal logic has been defined (in modern times, at least) as working in a very restricted language. If we translate MP and MT into ordinary language, we must use the simple conditional in the present indicative, i.e. "if it is..., then it is..." Most of the counterexamples used counterfactual conditionals, the future tense, extra operators, etc.
If we were to translate those counterexamples using the right conditional, mood, tense, and decided on a definitive interpretation of the operators and the predicates (no vagueness allowed), I think none of them would work.
"A modern interpretation of logic is that it's the science of entailment, not the science of correct thinking, as in the traditional psychologistic view"
The question is going to be which entailment relation is the "right" one. Or rather: formal logical systems can be viewed as theories of entailment, and one of the things philosophers want to know is which of these gets it right. In classical logic, A&~A entails everything; in paraconsistent logics, this is not the case. So which is right? This is the sense in which philosophers treat logic as "the science of correct thinking". I don't think this is psychologism, because the usual view is that logical laws are normative, and are not psychological generalizations in any sense. A philosopher might hold that e.g. classical logic is the "right" logic, that it correctly captures the real entailment relation, while also holding the anti-psychologist position that psychology tells us how people do reason, not how they ought to reason.
@@KaneB Ah, you got a point there about logic being normative. I'm in the middle of taking a self-taught course on mathematical logic, and you've given me something to think about. Thanks for the measured response! That's rare here on YT.
The laws of logic aren't "the science" of anything.
The scientific method requires presupposing the laws of logic are true. So science depends on the laws of logic, not the other way around.
If you tried scientifically verifying the laws of logic are true, you'd just be arguing in a circle (since the scientific method presupposes the laws of logic).
@@Winslow920 Never said "the science" in this context had to be empirical. "Science" here just means knowledge in the broadest sense.
Excellent Halloween themed video
Aren't these just the standard paradoxes of material implication? I've been reading Priest's Introduction to Non-Classical Logic and I think your examples are addressed in Conditional Logic.
0:35
Does that hold in complete generality?
If yes: there is a principle which holds in complete generality, ie it's self undermining
If no: there is no reason to accept the premise, ie it's self undermining
Sometimes logic laws can be truth preserving for SOME arguments. But that does not make laws of logic generally true.
MP and MT hold absolutely true in classical formal logic, which is an idealization we invented to model actual reasoning. These counterexamples just show that classical formal logic is not a perfect model of actual reasoning. I don't know much about other logical systems, but I would expect there cannot exist a perfect model of reasoning short of describing thought at the level of neurons.
In the marble example we are simply having trouble converting natural language to formal language. The marble isprobably red and the marble is not probably red cannot both be true. By defenition of probability. Therefore p1 and p2 are both true if and only is the marble is small or the marble remains unknown.
We must use the natural conditional when using binary logic, because there are a total of 16 binary operators in binary logic. If you exclude false premises then you simply have the and operator if you exclude false premises imply true conclusions you have if and only if . And so on .
In each of the examples given it is simply the case that a proper understanding of the material conditional resolved the apparent paradox.
As for if 1,000,000 grains of sand are a heap then 999,999 is a heap it is the case that we are making a silent argument. For all heaps of sand the cluster of sand will remain a heap after removing a grain of sand. This statement us plainly false even if we don't know for which heap or heaps it is false.
Could we assume that there exist many (infinitely many) Logics that have distinct axioms and yet are all internally consistent? Is this Logical Nihilism?
The counter examples don't work. They don't prove modus ponens isn't true they just prove they're very badly constructed and falsely reasoned and rely on misleading the reader on what the conclusion says. Eg. In the first conclusion it invites you to forget it becomes true contingent to the first premise being already shown to be true.
It also relies on reasoning with the properties of the things not the things not the things themselves.
If there are only three candidates, Reagan, Anderson and Carter, and Reagan and Anderson are republicans and Carter is a democrat, then if a republican wins it will be Reagan or Carter or if a democrat wins it will be carter.
That's it. That's the whole flow chart for that election. The only flaw with it is if people get shot, for which case you need a contingency plan to get new candidates. Everything else in the example is just misdirection.
"That's it. That's the whole flow chart for that election."
So what? That just shows that you can present the information concerning the election in a particular way. It does nothing to show either that one of these two claims is false:
(1) If a Republican wins the election, then if it's not Reagan who wins, it will be Anderson
(2) A Republican will win the election
Or that this claim is true:
(3) If it's not Reagan who wins, it will be Anderson
You'd have to do one of those things in order to show that McGee's counterexample doesn't work. All McGee requires is that (1) and (2) are true, and that (3) is false. That's it. Whether or not (1), (2), or (3) are "misdirection" is irrelevant.
@@KaneB
What it shows is there are correct ways and incorrect ways of constructing logics and your counter examples rely on an incorrect way of constructing them.
You haven't presented a valid counter example.
All the rest of your response does is reiterate the same unsound argument. As I said first: The argument relies entirely on hoping the reader doesn't notice that all the person who constructed this alleged counterexample has done is make a total mess.
Your response is also a mess.
@@KaneB but 3 trivially follows from 1 and 2. If it's not reagan who wins, and it's a republican who wins, and if it's any republican other than reagan who wins, it's anderson who wins, then anderson wins. That's it. It follows from the premises that it cannot be the democrat, which leaves only reagan and anderson. So if it's not reagan, but it's either reagan or anderson, then it's anderson.
This does not make any sense at all to me, am i missing something?
@@james1098778910 What McGee claims - and of course you may disagree with him on this - is that we should accept (1) and (2) but reject (3). We should accept (1) because among Republicans, Anderson is second to Reagan. We should accept (2) because the polls show that Reagan will win, and Reagan is a Republican. We should *reject* (3) because among all the candidates, Carter is second to Reagan, so if Reagan loses, it'll be Carter who wins. That's McGee's argument, at any rate.
Obviously, (3) trivially follows from (1) and (2) if we take modus ponens to hold in complete generality. After all, the inference from (1) and (2) to (3) is just an application of modus ponens. But the point of McGee's argument is precisely that modus ponens does not hold in complete generality. He thinks he has a counterexample to modus ponens.
I think you're right -- this is actually a logical fallacy of hidden premises. I also thought about this while watching the video and agree with you.@@vapourmile
only to some kind of naive realist would any kind of "nihilistic" position be interesting. to everyone else (especially instrumentalists or pragmatists) it's really just trivial at best, and un-useful handwaving at worst.
EDIT: actually speaking of nihilism, have you ever looked into Jacob Stegenga's book _Medical Nihilism_? apparently made a big splash and raised some skepticism towards medical studies and the current practice of medicine. has more to do with methodology, but knowing philosophy of bio is your thing, you might be interested
I don't think I count as a naive realist - at least not in this context - and I find it interesting. But I'm not sure I have much to say to anybody who doesn't find it interesting. Obviously, different people are interested in different things 🤷
I'd say I'm attracted to logical nihilism (and logical pluralism) as being aspects of a broader epistemic voluntarist position: there are no *rules* of belief formation or belief revision, period. I suppose that, if you adopt this voluntarist position, then logical nihilism (or pluralism) trivially follows, but of course, establishing this position in the first place is not a trivial matter - and part of the reason it's not a trivial matter is because of the many philosophers who reject this approach to logic!
"and un-useful handwaving at worst" -- Could you expand on this point? I don't know what you mean here.
And yes, I've read part of Stegenga's book (not all of it). I'm not really sure where I stand on his conclusion, partly because philosophy of medicine is outside my area of expertise, and partly because this is a "relative significance" debate. Nobody, including Stegenga, denies that medical interventions are effective - indeed, nobody, including Stegenga, denies that there are even some "magic bullets" in medical treatment - the question is exactly how effective are they, and exactly how many "magic bullets" are there?
@@KaneB I don't think the term magic bullet does any favors. It assumes that the magic is within the bullet instead of the highly specific and sometimes incredibly rare situation that the bullet is required to be used in to have any semblance of magic. The bullet may not change but situations can change rapidly which would reduce the effectiveness of this bullet. Taking these sorts of factors into the equation and suddenly the magic seems to vanish.
@@Liliquan "Magic bullet" is just Stegenga's term for particular types of medical interventions. He's not using the term "magic" literally.
@@KaneB sorry should probably clarify. nihilism in general is "uninteresting" in the sense that someone stumbling upon it probably won't have any eureka moment and go on to solve any real world problems. also I do agree with that stance on logic, considering different logics have different uses. there is no one supreme over arching system and they all have their own useful purposes (like fuzzy logic in AI). to say ones "correct" in describing the world is just missing the point IMO.
(A) If the statement labelled A is true then there are on laws of logic.
For the sake of argument assume the statement labelled A is true then on this hypothesis we have:
P1) The statement labelled A is true ---- by hypothesis
P2) If the statement labelled A is true then there are no laws of logic. ---- because this is what A says
Hence:
C) There are no laws of logic. ---- by MP
Thus we have proved that on the hypothesis that (A) is true there are no laws of logic. But this is just another way of saying that we have proved (A). So the hypothesis of our argument is true so the conclusion must be true, This we have proved:
There are no laws of logic.
It makes sense tho
The first example from McGee is terribly bad. That's his grand argument against modus ponens? All he's done is provided two contradictory premises, ie. "A republican will win the election" and the premise that "If this specific republican loses, a democrat wins". He thinks he can get away with it by pretending the opinion poll is just mere "additional information" and not a premise. It's pathetic. Should have pointed it out from the start instead of wasting 20 minutes trying to provide counter arguments by equally obtuse philosophers.
If one of the premises is that a republican wins the election, then it doesn't matter what the opinion poll says, **You've already accepted the premise that a republican wins** .
If you wanna believe the opinion poll over the premise as true? Great! Then don't believe it's true, and modus ponens still holds. What a waste of tiiiiime.
This seems to be pretty much Mandelkern's response?
Anyway, I still think McGee's counterexample is pretty compelling. It looks like (P1) is true, (P2) is true, and (C) is false. The opinion poll is what justifies those claims. If those truth-values have been assigned correctly, then we have a prima facie counterexample to MP.
@@KaneB How can you say P2 is true in the case where Carter won? It’s only because P2 is NOT true that McGee claims to have an argument. But when P2 is not true, we’re outside the example. Fame over. In fact, nobody should ever take a premise like P2 to be true in an absolute, strong as the laws of logic, sense. We know how polls work, we know they have uncertainties, and even if we knew nothing of polls, we know predicting the future entails uncertainty. P2 enters the example on weak footing whereas the prior probability that MP is solid is very high. You need strong reasons to favor upholding shaky old Premise 2 in light of the FACT not P2. Do you have any reasons that strong?
@@BrettCoryell >> How can you say P2 is true in the case where Carter won?
It wouldn't be true in that case.
>> It’s only because P2 is NOT true that McGee claims to have an argument
Honestly have no idea what you're talking about here. McGee claims that (P2) is true.
>> We know how polls work, we know they have uncertainties, and even if we knew nothing of polls, we know predicting the future entails uncertainty
Sure, we could be wrong that (P2) is true; and perhaps in the actual world, opinion polling does not provide sufficient evidence to accept a claim like (P2). We can just imagine a world where opinion polling is much more reliable.
If you don't presuppose the laws of logic are universally true, then you can't make any meaningful assertions at all.
Because anything you assert, it's negation could also be true at the same time & place. It loses any meaning.
none of this make sense , the example at 6:33 how claim it was a porpoise if p2 that creature is a fish. I fail to find ONE exemple not wrong in this video
Well . There are no counter examples to the Law of Non-Contradiction. That holds universally . So ..
I discuss counterexamples to noncontradiction briefly in the first video on logical nihilism. More generally, check out dialetheism: plato.stanford.edu/entries/dialetheism/ (I also have a few videos on dialetheism, though I never finished that series)
when one speaks of "laws of logic", does that include laws of thought
also?
Since watching the first part of this video I have read Gillian Russell's essay on the subject.
You don't understand it.
She actually writes in that same essay, nobody really believes that first syllogism (which is a correctly constructed valid syllogism) is really an argument for logical nihilism.
About it, she explicitly states:
"Pluralists do not intend this as an argument for logical nihilism".
She goes on to explain the point of it is to be 'a reductio on the first premise', that is, the first which has an obvious problem with it "To be a law of logic, each logic must hold generally". Pluralism means the correctness of logical laws are contingent to the field in which they operate so within the context of pluralism the first premise of this syllogism is false.
One such example is the law of excluded middle, which is held true in classical logic, but is Not held true in constructive mathematics. So the law of excluded middle is not a universal law. The point being, "It is a law only under certain specific conditions" is different from "It is not a law". I also notice LEM is the first place Gillian goes to for her example too.
Therefore the purpose of the syllogism as she presents it is not to argue for logical nihilism but rather to draw from its first premise a dividing line which exists between monist and pluralist logics: The first premise is true only in monist logics.
For somebody who claims to be qualified to talk about the subject you appear to have some difficulty understanding simple introductory texts written about it.
Now you're just quote mining. Unfortunately for you, I have also read Russell's articles on the subject. Here's the full quote. (You are clearly just BSing so I'm not really talking to you anymore. I write this for the benefit of any other readers who come across your comment.)
Russell first presents this argument:
(P1) To be a law of logic, a principle must hold in complete generality.
(P2) No principles hold in complete generality.
(C) There are no laws of logic.
Then about this, she says:
"Pluralists do not intend this as an argument for logical nihilism, of course. They think that nihilism is absurd, and since many who work on non-classical logics find the second premise plausible, they intend the argument above as a reductio on the first premise: the monist's assumption that logic must be completely general. Still, that premise has both intuitive appeal and support from historical writers on logic, and - as I will explain in the first section of this paper - nihilism is not, in the end, absurd. These two things - the plausibility of premise 1 and the non-absurdity of the conclusion - turn this sketch of a reductio on premise 1 into a sketch of a direct argument for nihilism."
Obviously, pluralists who give that argument do not intend it as an argument for nihilism. They are pluralists, not nihilists! Pluralists offer the argument as a reductio on (P1); nihilists offer the argument as a sound argument for its conclusion that there are no laws of logic.
Russell is *absolutely explicit* that the purpose of the argument as she presents it is as an argument for logical nihilism. This is not to say that Russell herself accepts logical nihilism. But she does take it seriously, and she sees the above argument as a compelling argument in its favour.
Russell's paper is freely available online so this is all easily confirmed:
gilliankrussell.files.wordpress.com/2018/05/logicalnihilism-philissues-v3.pdf
@@KaneB
Nothing you wrote disagrees with what I wrote. You just haven't addressed what I actually wrote but instead extracted other details from the same document.
The only bone of contention is
"Russell is absolutely explicit that the purpose of the argument as she presents it is as an argument for logical nihilism"
In which you have, again, just misunderstood what you read.
Her essay as a whole may be an argument for logical nihilism, but that specific syllogism to which I am referring is not.
You're really annoying. You don't know what you're talking about, you don't understand what you've read, and yet you still want to argue about it.
Arrogance, in your case, is clearly not a virtue.
@@vapourmile LOL. The detail that I extracted was the rest of the paragraph for the quote that you took out of context.
"Her essay as a whole may be an argument for logical nihilism, but that specific syllogism to which I am referring is not."
She very clearly says that it is an argument for nihilism.
Now please stop spamming my comments section with crap.
@@KaneB
PS. I also still don't believe you have any meaningful qualification in the subject.
To have have survived something like a computer science degree would have a required far better basic comprehension.
What you are is an arrogant pretentious average TH-camr whose access to information on logic clearly comes primarily from Google, not formal education.
FYI: The point if a formal education is to have your comprehension tested by somebody who knows if you've understood what you've read. It is the antithesis of randoms reading things, talking shit about it, and then insisting they know what they're talking about, which is what TH-cam is made of.
Therefore TH-cam has many such talks on logic presented by other people who also don't understand the subject.
@@KaneB
Also, to call that example "quote mining" really only reinforces the fact you don't understand how to write academic essays.
You are only reinforcing the perception further than you are Not qualified to talk about this.
Gillian's essay is interesting, but I definitely won't be coming back to you for anything. You are arrogant, obnoxious, pretentious and irrational and you have poor English language comprehension.
That isn't the modus operandi of a qualified person.
BTW. Logic is my day job.
The second example is garbage again.
First of all, these aren't syllogisms. A syllogism is constructed by two premises and a conclusion which necessarily flows from them.
A valid syllogism would be:
All fish have lungs.
All stones are fish.
Therefore stones have lungs.
Remember: Validity means the conclusion must follow from the premises. It Doesn't require the premises to be true. So this example is valid but unsound.
Also remember: Don't stuff your premises full of conditions. This mixes up classical syllogisms with conventional Boolean logic.
The most you can do to tidy it up is:
Lungfish are fish with lungs.
The fish in the net is a fish with lungs
Therefore the fish in the net is a lungfish.
That's a valid syllogism.
Valid Boolean algebra is:
If an item in the net is a fish and that same item in the net has lungs then that same item in the net is a lungfish.
Don't build syllogisms from conditionals. Definitely don't build them from nested Boolean algebraic conditional expressions.
Again in the second example the conclusion also invites us to forget it was contingent to the item being a fish, established in the first premise (which is a contingency, not a premise). So it's just badly constructed bullshit. Syllogism isn't the right tool to construct these ideas. For this kind of conditional branching you want a flow chart, not premise+premise=conclusion arrangements where the premises are replaced by conditionals. Use a flowchart for these cases where it's more easily shown they don't prove anything.
So no, neither of the examples do anything to dislodge modus ponens they're just sleight of hand.
"First of all, these aren't syllogisms"
It's modus ponens. If P then Q; P; therefore Q.
"Remember: Validity means the conclusion must follow from the premises. It Doesn't require the premises to be true"
Yeah, no shit. Everybody is aware of this. But if you want to present a *counterexample* to a purported logical law, you need a case where the premises are true and the conclusion false.
"The most you can do to tidy it up is:"
LOL what are you talking about. That's just a different argument, and not modus ponens.
@@KaneB
I'm explaining why the examples you presented are bullshit.
All we learned from this is you didn't understand what you read.
You clearly aren't qualified to talk about these topics and you clearly also don't have the personal skills to discuss them either.
@@vapourmile "I'm explaining why the examples you presented are bullshit."
You're not explaining it very well. Indeed, it comes across as if you don't know what you're talking about.
"You clearly aren't qualified to talk about these topics and you clearly also don't have the personal skills to discuss them either.
"
I mean, I am literally qualified to talk about them. That is, I have actual academic qualifications in this subject. I can't comment on personal skills though!
@@KaneB
Sorry, but boasting you know what you're talking and I don't is pretty much the end of the discussion. If you aren't willing to learn I'm not going to make a fight out of trying to help you.
@@vapourmile That wasn't intended as a boast - not that I have a problem with boasting. But you brought up qualifications. I was just correcting your mistaken assumption.
Nothing you've written has given me a reason to think that you're in a position to teach me anything about this.