• Mathematical truth is not orderly but highly chaotic

    Better than stackexchange nowadays, and it is not as if Quora got better with the years.
  • US Election 2024 (All general discussion)
    She is a woman, and thus automatically at a disadvantage. She's also of color, so the DEI-hire narrative writes itself. In fact if you ask in more right wing leaning circles, she's universally reviled already for being a supposed DEI-hire who allegedly has zero qualifications, and is stupid because her laugh sounds weird. That's unfortunately the level of political discourse we can expect.Echarmion

    The political discourse "there" is right as usual. Hillary got millions of votes for being a woman, Obama for being black. Odds are that, if Hillary were Hilbert and Barack Obama were Barry O'Bryan, they wouldn't have won.

    Reveal
    Yes, Hillary won the popular vote.
  • Mathematical truth is not orderly but highly chaotic
    W*kipedia on physics also has some pretty bad articles. Horrible on history. Propagandist on politics.
  • US Election 2024 (All general discussion)
    It is Joever.

    Thoughts about Kamala Harris?Shawn

    Affirmative action.
  • Wittgenstein, Cognitive Relativism, and "Nested Forms of Life"
    Bats, Mary's room, philosophical zombies.Ludwig V

    I will quote myself quoting someone else:

    would probably be that analytics cut themselves off from most pre-analytic philosophy, did everything "in-house" which entailed a lot of reinventing of the wheel in ways that look horribly philistine and only appeal to a very specific niche of people who like goofy decontextualized thought experiments, [...]Lionino
  • Infinity
    If logic is following rules, as formalists seem to think, then to say that rules are derived from logic is circular.Metaphysician Undercover

    Logic is not "following rules". Your argument is failed as it relies on a nonsensical definition.
  • 10k Philosophy challenge
    I object to "for free".Dan

    You may object to the sky being blue. Instead of paying philosophers for their work, you want them to do work on you theory for the slim chance that they may get some mysterious 10 grand. Who unilaterally decides if they get the money? The person paying, of course.
    Even if you do actually give that money away, all the philosophers who provided meaningful, qualified input spent their time for your exclusive benefit.
    It is not even a lottery, just deception. This thread should be closed.
    :down:
  • Wittgenstein, Cognitive Relativism, and "Nested Forms of Life"
    I have not read primary Wittgenstein, so I am far from being able to lean towards either interpretation, but intrepretation aside, and taking the ideas as they are, I think that:

    Sometimes this comes out in almost essentialist terms, where a person from another culture is precluded from ever understanding another culture in its own terms.Count Timothy von Icarus

    There are elements to this that are undoutably true. You may move to China, learn the culture, eat and cook Chinese food, learn to speak Chinese better than most natives with no accent, learn Chinese history and geography, have many Chinese friends who adore you, marry a Chinese girl, raise your kids in China, be a Chinese nationalist, and yet, you will never know how it is to be Chinese, because you were not raised in China, it wasn't the culture within which you learned about the world, you didn't attend Chinese middle school and your first friends weren't Chinese. This distinction is not just important but fundamental. If our culture and language impact brain development in early childhood, there is not just an abstract difference between individuals of different cultures, but a physical one.

    This presumably applies to expressions like true and real themselves and indeed, it is precisely Wittgenstein's point that such expressions cease to be philosophically significant once we remind ourselves of their ordinary employments.

    Even within that view, one doesn't need to go the absolutist route. One may say that, even though most lexical items are relative, there are some items ('real' and 'true') whose concepts are psychological necessities stemming from our neurological configuration and thus evolutionary history — ¿does a shark have a concept of true if it can't imagine things as otherwise?, as this short movie I really like explains, we know that mental simulation is mostly a feature of mammals and avians, not of fish and reptiles.
    The quote pretty much makes the same point later:
    first, we have to share with the aliens some natural capacities and responses of a perceptual and cognitive type, giving rise to at least some similar beliefs about the world; and secondly we have to be able to share with them certain principles governing those beliefs; for one important example, that what is believed and therefore acted upon is held to be true
    Reveal
    On the topic of 'real', in the Spanish board here, @javi2541997 was talking about how Austin considers words like that to be dimensional and always have the same meaning — but don't quote me on that, not only am I ignorant of Austin but I find those classifications, as presented, to be spurious.


    How then do we recognize another form of life as another form of life? The ability to detect that something is a form of life and that it differs from our own surely demands that there be a means for us to identify its presence and to specify what distinguishes it from ours.

    Not sure if that is a great rebuttal. I could parody it with "How do we process the colour black as information if black is exactly the absence of information/light?". Well, absence of information is information, and absence of information about a form of life is information, all the while keeping that form of life unpenetrable to us.

    But this recreates the same Cartesian isolation Wittgenstein wanted to avoid.Count Timothy von Icarus

    Yeah.

    all of Wittgenstein's complaints about "philosophers using language wrong," can be waved away by simply claiming that Wittgenstein is not privy to the language game used by these philosophers. Perhaps being a metaphysician, a Thomist, etc. are all discrete "forms of life?"Count Timothy von Icarus

    Nice :lol: I will use that switcheroo in the future.

    It seems very possible to me to be able to "speak of something correctly," and not to really understand it.Count Timothy von Icarus

    Basically so. Saying something as learned from context allows you to say something correct, but it is not the same as understanding. When learning math, you need to understand things, you can't just memorise every equation, the infinity^infinity of them.
  • Any objections to Peter Singer's article on the “child in the pond”?
    Alright. I will take the view on the other extreme, the ars*h*le view.

    e shows that it's immoral to spend money on products we don't absolutely need, instead of giving it to charities that save livesLFranc

    I will argue instead that it is immoral to spend money on others if it is not surplus. One's economic success is, for the cases that matter here, a product of one's virtue — which includes genetic virtue. Reinvesting the fruits of work into oneself, to further one's success, is morally preferrable, as to increase society's progress. Giving it it to those that are not as virtuous is ultimately a waste of resources and holds mankind back.
    Entertainment and pleasure are also not superfluous. Without pleasure and entertainment, you won't be able to keep the same productivity. If engineers don't keep it up, many operaries will be out of a job, and the services provided, often essential, will disappear. An engineer giving up the nice things in life for the benefit of individuals with weakness of flesh (addiction) and weakness of mind (low intelligence) may result a net very-negative for mankind.
  • Wittgenstein, Cognitive Relativism, and "Nested Forms of Life"
    I think it falls short by missing grammatical facts, such as that not all words are the same. 'Village' cannot be compared to 'eg', 'ie', 'QED', 'amen', because 'village' is a content word; 'eg' and 'ie' are abbreviations that in English today have become (function) words on their own. Function words have no meaning in themselves but instead introduce a relationship between other (two) words, such is the case of basically all prepositions, and now of 'eg' — the meaning proper is therefore more abstract than of content words. But, even for function words, meaning is not use — I can't use the word 'to' properly if I don't know it brings about a directional relationship between two objects. I think what is said about the meaning of 'eg' and 'ie' here is instead its etymology. The meaning of the English word 'eg' now is 'for example', one doesn't need to know the etymology exempli gratia. Amen itself works as an interjection; you say "amen" when you end a prayer like you say "Yay" when something good happens (or when you agree with something, but it is a figurate meaning of amen).

    However, I can think of better examples for "we can also know how to use words without knowing what they mean". Those would be 'duly noted', 'force to be reckoned with', 'lead astray'. Most people don't know what 'duly' means, yet they use it all the time, especially within the phrase 'duly noted'.

    The problem is, as they don't know what the word actually means, and only learn how to use it from examples/contexts, instead of a word that brings about a mental image (an idea explored in the Tractatus), they eventually end up using it quite wrongly — such is the case of 'literally'. And then, if the word is no longer used by people who know its meaning but only by people who know its contexts, the word now has no semantic field but instead a context field — where meaning is use —, or in the worst scenario the word loses all meaning altogether — such is the case of 'literally'. From a context field, a new semantic field may arise — I could think of some examples, but I am in a hurry, and perhaps that is how 'naughty' came to mean 'mischievous'. So, in the case where a word has no more semantics but only context, meaning is indeed use, but that is not a good thing.

    In fact I completely disagree with the point on 'village'. As soon as we know the German word is a "perfect" translation of the English word, we are able to use productively. When language learning, the only times I ever asked "How would you use it in a phrase?" was either when we were dealing with a particle (function word), which for German would be 'davon' or 'ab', or with a word with no good translation to my language.

    This is not a disagreement per se of the analysis presented, I just think it is awfully simplistic and that some philosophers wrestle with language before knowing grammar.

    And this relates to the idea that all manner of philosophical problems might be dissolved if one pays close attention to how words are used.Count Timothy von Icarus

    I am confident that you yourself disagree with that idea to some extent.
  • Wittgenstein, Cognitive Relativism, and "Nested Forms of Life"
    Ancillary point from Grayling:

    We can understand the meaning of a word, say the German word for "village" and have not the first clue how to use it in a sentence.

    Yet we can also know how to use words without knowing what they mean. For example, plenty of people use "e.g." "QED," "i.e.," or "amen," correctly without knowing what they mean.
    Count Timothy von Icarus

    I don't think this is a good point about either semantics or pragmatics.
  • How do you interpret nominalism?

    Idein or idin (ἰδεῖν)

    but this is actually from the Old French "idem et idem,"Count Timothy von Icarus

    It comes from "identité", but it is correct that it comes ultimately from idem. I don't think 'idem et idem' was a phrase in Old French, though I don't have strong means of confirmation, it raises my eyebrows at least. Εἶδος is where the -oid and -id at the end of taxonomic words come from (gibbons are not Hominids like all great apes but they are Hominoids) — but that is not Greek or Latin, it is ISV.
  • Infinity
    How does a formalist typically account for the ontology of rules? What kind of existence do rules have? Consider the rule of how to spell "judgement" for example, how does that rule exist?Metaphysician Undercover

    I explored this question somewhat in my Grundlagenkrise thread, specially in my chat with Banno, but there was no interest in the topic died after 3 days — folks prefer to go around circles about ethics instead and keep it shallow. The ontology of rules are ultimately derived from logic, be it first-order or second-order — and logical terms can be taken as primitives defined from their truth tables — and the usage of undefined terms, such as "line", "+", or, in the case of ZF, membership ∈.
  • 10k Philosophy challenge
    I doubt it. He has a pet theory that he has found (or someone pointed to him) a problem in. ChatGPT was of no help, so now he is setting up to have tens of amateur and professional philosophers work on his theory for free.
  • 10k Philosophy challenge
    I am offering a prize of $10,000Dan

    Yeah, that is bait to get people to do free work on your theory.
  • Questioning reality at a young age?
    Christian gnosticism was somewhat like that:

    Many of the so-called gnostic groups are characterized by a mythology that distinguishes between an inferior creator of the world (a demiurge) and a more transcendent god or order of being.
  • Do (A implies B) and (A implies notB) contradict each other?
    I think it should be worded as "Elvis is a man DOES imply that elvis is NOT simultaneously immortal and mortal".

    It positively implies something, rather than "does not" imply something.
    flannel jesus

    I think that is possible too, surely. Aren't perhaps "Elvis is a man does imply that Elvis is not both mortal and immortal" and "Elvis is a man does not imply that Elvis is both mortal and immortal" the same thing?

    I would say that in natural language, the former would mean that "Elvis is a man" is a piece of information that tells us there is no such contradiction; while the latter that "Elvis is a man" is a piece of information that doesn't tell us there is a contradiction. Do the two mean different things?
  • Do (A implies B) and (A implies notB) contradict each other?
    Thinking of the two as timelessly equivalentCount Timothy von Icarus

    That much I can agree with under a formalist/nominalist view of mathematics. If we take that mathematical objects are platonic objects, where, by definition, the two would be timelessly equivalent, does the Scandal of Deduction make mathematical platonism troublesome?

    Another question, what do you think of the rebuttal:

    "Sometimes universals like "All men are mortal" are not mere inductive generalisations that require that we already know that Socrates is mortal. They might have a law-like nature and so we believe them to be true because they fit with our best scientific theories. Indeed this seems to be the case with "All men are mortal". That is a scientific fact, not just an observation." — SE.phil

    I think the above comment can be exemplified in:
    α There is a strand of DNA that makes a being a man (hypothetical simplified essentialist definition of 'man').
    β By the laws of chemistry, every DNA degenerates after X years, DNA degeneration leads to death.
    γ Everyone with that strand of DNA dies after X years (follows from β).
    δ Socrates has that strand of DNA, Socrates will die after X years.

    If you think the above is an exemplification of the rebuttal, do you think it is a valid argument? The only way I see is by denying β which is denying the laws of chemistry, which is back to the problem of induction (how do you know every DNA degenerates?).

    Sum:
    • Does the Scandal of Deduction pose a problem to mathematical platonism?
    • Is the example an example of the rebuttal?
    • If not, are either valid? If yes, is it valid?

    PS:
    But the "Scandal of Deduction," is about why we find the results of deduction and computation surprising and informative. We are physical beings. We do not compute in "no time at all."Count Timothy von Icarus
    Is this about all computation then and what I wrote above irrelevant?
  • Infinity
    Funny, I never realised 'judgment' was even a possible spelling, even though I have obviously seen it tens of times; my brain simply filled the 'e' in. 'Judgment' looks awful to me, like it would have to be pronounced /jud-gh-ment/.
  • Do (A implies B) and (A implies notB) contradict each other?
    Is that the right English translation of that?flannel jesus

    That was my proposal at least, as I proved, even before that post, that it cannot be ¬(A → (B and ¬B)).

    would you say A → (B or ¬B) can be worded as "Elvis is a man does not imply that Elvis is both mortal and immortal"flannel jesus

    I am obliged to say yes here. So yes.
  • Do (A implies B) and (A implies notB) contradict each other?
    Yes, I have the same feeling, especially when we lack a third truth value, which is something that we do use — implicitly so at very least — in natural language.
    For example:
    'Beautiful', everybody knows what that mean; 'not beautiful', does that necessarily mean ugly? No. If "beautiful" is P, converting "not beautiful" as ¬P will give rise to things that violate common sense.
    All in all, as you said, classical logic is useful for constrained cases, we are abusing its good-will here.
    Take Javi's thread https://thephilosophyforum.com/discussion/15333/ambiguous-teller-riddle/p1 , where a third value is needed.
  • Do (A implies B) and (A implies notB) contradict each other?
    Fair suggestion. But I see an issue. Take for example this:

    Elvis is not a man – ¬A
    Elvis is a man does not imply that Elvis is both mortal and immortal – (A → ¬(B and ¬B))
    These two do not entail that Elvis is a man.
    Lionino

    For clarity, "both mortal and immortal" here is just meant to stand for any contradiction, in an "educational" manner.
    The advantage of (A → ¬(B and ¬B)) is that when you say ¬A (that A is False), it does not entail A.
    But if your "translation" is just "A", we have a contradiction and therefore everything follows. Thus, I think that just A is not a good way to put "A does not imply a contradiction".

    Furthermore, (A→¬(B∧¬B))↔A is invalid, so my suggestion and your suggestion are not agreeable between each other.
  • Do (A implies B) and (A implies notB) contradict each other?
    Some further thought:
    The phrase «A does not imply a contradiction» really means specifically «A being true, it does not imply a contradiction». I think this meaning is indeed encapsulated in A→¬(B∧¬B), especially when it can be translated as «A implies True».
    The more global meaning of «A does not imply a contradiction» is «A being true or false, it does not imply a contradiction», which is not something we would say in everyday language, after all, one of the conditions of «A being true or false, it does not imply a contradiction» is that «A being false, it does not imply a contradiction».
    Does the phrase «A being false, it does not imply a contradiction» make any sense whatsoever?
  • Do (A implies B) and (A implies notB) contradict each other?
    Here is the thing I found about your example.
    ¬A,J entail (A→(B∧¬B))
    If ¬A is a premise, it will always entail A→(B∧¬B), no matter what the second premise is. Why? Because, if the second premise is the denial of ¬A (¬¬A which is A), it will be explosive therefore everything goes; if the second premise is not the denial of ¬A, A is given as False (because ¬A is given as True) and so A→(B∧¬B) is True because B∧¬B just means False in all cases.

    "a implies this particular non-contradiction"flannel jesus

    The issue is that if you say "non-contradiction" it can mean pretty much mean anything, while ¬(B∧¬B) is not just any non-contradiction but something that is always True no matter what. That is a detail, the goal anyway is to translate "A does not imply a contradiction", not any other phrase.
  • Do (A implies B) and (A implies notB) contradict each other?
    In a certain sense, we might be inclined to say that P(I) = O in the same way we would like to say 2+2 just is 4. However, if I includes enough nodes then all of the world's super computers running P(I) until the heat death of the universe still won't have been able to actually compute O yet.

    So then, in a very important functional sense P(I) is not "the same thing as O."
    Count Timothy von Icarus

    How not? There are several algorithms to solve mathematical problems — in this context being symbol manipulation from one form to another. For example, solving square matrices of dimension NxN through reduction of order requires n^3 operations. If we have a 300x300 matrix, aren't the matrix and the determinant related to each other intrinsically anymore?
    Twenty years ago, many things that are computable now would not be computable, does it make X≠Y then but X=Y now?
  • Do (A implies B) and (A implies notB) contradict each other?
    (a→¬(b∧¬b))flannel jesus

    «A does not imply a contradiction»

    (a→¬(b∧¬b)),¬a entails (a→(b∧¬b)). That is a problem. Now I don't know what «A does not imply a contradiction» is in logical language, as a↔¬(b∧¬b) and¬(b∧¬b)→a also don't work . Perhaps the question is spurious.
  • Do (A implies B) and (A implies notB) contradict each other?
    This will all be explained in my forthcoming magisterial book introducing Hegelian-Semiotic-Process-ThomismCount Timothy von Icarus

    You might want to ship it with lubricants, it sounds unpenetrable.

    You are importing "the axioms of the theory." They are nowhere to be found.Leontiskos

    They are found in "S". Or you can just replace "S" with axioms of the theory. Axioms are naturally assumed.

    You know equally well that ¬P follows.Leontiskos

    I don't. I know that S and ¬P can't coexist. I know that S, so ¬P can't be the case. ¬¬P is P.

    Tidbit: my notifications:

  • Do (A implies B) and (A implies notB) contradict each other?
    So if we say "A implies a contradiction" is false, it is the same as saying "A does not imply a contradiction"Lionino

    Some posts ago, I shrugged the issue aside by saying the two don't mean the same thing. Well, when is "A implies a contradiction" False? When A is True. And before, we decided that "A does not imply a contradiction" is a "translation" of A→¬(B∧¬B).
    Here is the problem: A entails (A→¬(B∧¬B)), which means that A entails {«A implies a contradiction» is false}; but (A→¬(B∧¬B)) does not entail A, which means that {«A implies a contradiction» is false} does not entail A. That agrees with common sense.
    Since one entails the other but other does not entail one, we may say that everytime «A implies a contradiction» is false, «A does not imply a contradiction» is true; but it is not everytime «A does not imply a contradiction» is true that «A implies a contradiction» will be false. Therefore there is an assymetrical relationship between the two statements quoted.
    The prover confirms my intuition:
    (a→¬(b∧¬b)) does not entail ¬(a→(b∧¬b))
    ¬(a→(b∧¬b)) entails (a→¬(b∧¬b))
  • Devil Species Rejoinder to Aristotelian Ethics
    Interesting, but I agree with Fooloso4's post. On the other hand, perhaps BobRoss' problem points that Aristotle's ethics can't be universalised, meaning: what is good for the devil species and for us are contraries, so good becomes an empty term that can refer to anything at all and even to contraries. That would be the case if 'good' here was about the end itself, instead of the act of fulfilment itself — then the term is not empty in light of a devil species.
  • Climate Change (General Discussion)
    It doesn't matter what I think, I don't make policy. If people worried about things under their control rather than things they will never be qualified to deal with, this planet wouldn't be so full of people who can't find the end of a queue.
  • Mathematical truth is not orderly but highly chaotic
    It just so happens, nowadays, most scientists are not natural philosophers — which is a shame, but a consequence of the expansion of scholarship and accessibilisation of knowledge.
  • Climate Change (General Discussion)
    Is "hottest since X" the same phrase as "extremely hot"? You are constantly asking these dumb questions.
  • Mathematical truth is not orderly but highly chaotic
    I'm always intrigued why a conversation about math morphs to conversation about physics.ssu

    When you were never taught how to go around the territory you are exploring, you tend to wander outside of that territory as the walk goes on. Same thing. It doesn't help that one of the chatters here is using wiki links to completely make stuff up as he goes.
  • US Election 2024 (All general discussion)
    That is simply perfectly accurate — ten years ago. Nowadays both sides are the left side.

    Vance will change the presidential term limits and rule for the rest of his life.frank

    Finally. Total Vance dictatorship. Yay!
  • Do (A implies B) and (A implies notB) contradict each other?
    The same logic applies to MT...
    Assuming contraposition and MP is the same as assuming MT.
  • Do (A implies B) and (A implies notB) contradict each other?
    Where did I say that? MP+contraposition is equivalent to MT. MP itself can be proven from more fundamental operations. If you are using those operations to prove something you are using MP, but with extra work.
  • Do (A implies B) and (A implies notB) contradict each other?
    MP+contraposition is just MT. So you are not proving φ→(ψ^~ψ)⊢~φ without MT.
  • Do (A implies B) and (A implies notB) contradict each other?
    Why would you need a proof of X in order to find a proof of Y that doesn't use X? That makes zero sense.