26:03 "We need to have reasons for thinking that an interpretation is illegitimate beyond it proving a counter-example to a logical law." This statement might be the best illustration of the fundamental problem underlying the entire project of logical nihilism. Proving a counter-example to a logical law is the best possible reason for thinking that anything is illegitimate. This is the concept of _reductio ad absurdum._ There can be no better reason for thinking that an idea is false than proving that the idea entails a false conclusion. Perhaps the source of logical nihilism comes from a misunderstanding of the nature and purpose of an axiom. An axiom isn't something we've concluded is true due to some reasoning or evidence that leads us to believe the axiom. An axioms is true by fiat. It is simply declared to be true and any attempt to prove or disprove an axiom is pointless and misguided. It's exactly like trying to prove or disprove that bachelors are unmarried. The purpose of an axiom is to provide some basic common ground to allow us to understand each other. When people have wildly different beliefs about the world, it can be difficult for them to understand each other, but if they carefully use logic then they can potentially understand each other's reasoning. Even if they agree on nothing else, at least they have the law of non-contradiction and similar logical axioms. This universal common ground is part of what makes logic such a powerful tool. Perhaps if people aren't aware of the purpose of axioms they might be tempted to examine axioms just like any other idea and try to determine if we have good support for belief in those axioms. It makes intuitive sense, but an axiom is not that sort of idea. Axioms aren't made true in that way and we shouldn't look for that sort of support for an axiom.
If a main function of an axiom is "to understand each other" ( an axiom need no proofs and we should believe it) , what the difference between an axiom and a dogma? If i think that any proof system needs proofs and you think logic needs no proofs, how an axiom can help us to undestand each other?
@@zachdauman5464 "What the difference between an axiom and a dogma?" Axioms are understood to be arbitrary, while dogmas are presumed to be based in reality. For example, consider bachelors being unmarried. That's an axiom. Everyone takes it as true, and we must take it as true if we're to understand each other when we're talking about bachelors, but we also understand that it is arbitrary. There's no reason why bachelors are unmarried; it's just how they are. In contrast, take a dogma like the resurrection of Jesus. There's supposed to be an actual event which makes it true. People don't just believe it arbitrarily, or at least they don't think they're believing it arbitrarily. If they were to take it as an axiom, that would make it true regardless of whatever happened in history, which would make it pointless.
@@Ansatz66 Therefore any system of proofs (logic, math) based on axioms is not objective in describing reality This lead us to conventionalism. Conventionalism is the philosophical attitude that fundamental principles of a certain kind are grounded on (explicit or implicit) agreements in society, rather than on external reality. Unspoken rules play a key role in the philosophy's structure. Although this attitude is commonly held with respect to the rules of grammar, its application to the propositions of ethics, law, science, mathematics, and logic is more controversial. Science (based on logic and math) does not give an obvious truth, any scientific truth is the result of a contract between scientists. Therefore, science is not very different from religions. Science has no features that distinguish it from other methods of knowledge. So, i ask What the diffence between religion dogmas and scientific axioms on those perspective? And how can non-objective axioms help us to understand each other?
@@zachdauman5464 "Therefore any system of proofs (logic, math) based on axioms is not objective in describing reality." That must be so, since anything which can be logically proven must be true in all possible worlds. If there were some object in this world causing the truth of 1 + 1 = 2, then in any world without that thing the equation would be false. 1 + 1 = 2 cannot describe reality because it's true in any reality no matter the content of that reality. "Science (based on logic and math) does not give an obvious truth, any scientific truth is the result of a contract between scientists." Science doesn't discover axioms. It discovers theories. Theories are statements which attempt to describe reality, very much unlike axioms. The critical difference is that theories can be wrong, and therefore they are not true in every possible world. The truth of a theory is not based on a contract between scientists, but rather we expect a true theory to submit itself to experimentation and make successful predictions. "Therefore, science is not very different from religions." The biggest difference between science and religions is that science recognizes fallibility and tests ideas as opposed to making ideas sacred and forbidding people from doubting ideas.
so... everyone involved in this debate is simply confusing logic with the *language* used to communicate logical laws. yeah, you can find contradictions and instances in which certain statements don't hold true. that doesn't necessarily mean the logic the statement is attempting to express is not universally true; the language may simply be flawed. the idea behind it can still be flawless. i've watched a few of your videos on critiques of logic, or skepticism of logic's infallibility...and all the arguments seem to really be against language, not logic.
Ordinary language philosophers seem to be the philosophers that by far most often create problems out of nowhere by using language other than ordinarily; usage of jargon (which is absolutely necessary), be medical or theological, does not fall out of ordinary language. One wonder if their project is not some great mechanism of psychological compensation. On the other side of the coin, philosophers who base philosophy on the analysis of language are also the ones who by far seem the most caught up in purposeless language games. The people involved in both of these are *almost* always English speakers. Really makes you think huh?
there isn't a problem. russel's argument depends on the assumption that P refers to a set of glyphs rather than a meaning. The sentence is "snow is white, and snow is the null set". this is a contradiction, and false. she has failed to show the existence of a true contradiction.
@Sky Gardener I agree that the heterological thing is more difficult. Natural language is inherently vague, and is not suited to writing logical statements.
Very interesting but I don't buy the counter-examples, e.g. for the prem-white one, as I understand defining the term by parts means I can substitute "prem-white" by whatever it's defined as in that context, and doing that doesn't yield a counterexample to ID.
I don't really have much to say about him... In the previous video I made with Cole, we talk about how we both like "fuck-with-ers". My impression from that book - and only from that book, since I'm not familiar with his other work - is that Stove was a fuck-with-er (though he would have denied this), and I can't help but admire that, but I'm not convinced he was a particularly good philosopher. There are a lot of uncharitable readings of his four targets, and he doesn't really engage with their arguments anyway, being more concerned with criticizing their language and exposing the historical source of their views. The first issue is simply not all that interesting to me; as for the latter, his central thesis about the importance of deductivism to their views is, I think, just obviously false (not false in the case of Popper, but obviously false for Lakatos, Kuhn, and Feyerabend). Stove definitely has some flair as a writer, and the vitriol makes it a fun read. I'll note that a good example of similar vitriol from the "irrationalist" side is provided by Feyerabend in "Conversations With Illiterates", in his "Science in a Free Society".
I'm not really interested in doing videos on individual philosophers. I prefer looking at topics or particular theories. For one reason or another Carnap just hasn't been all that relevant in any videos I've done before, despite how influential he was. I don't know whether he'll come up in the future. I don't have any near-term future plans for a video that would cover anything from Carnap.
(When I say Carnap has not been all that relevant before, I mean for the purposes of introducing the topic covered in the video, which is of course my goal in all my lecture-style videos. There are many videos I've made where Carnap's work would be relevant if you were exploring the arguments in more detail.)
My mistake; I like the emphasis on topics and theories. My reason for asking is that there are a lot of misconceptions about Carnap, particularly his mature work during his semantic period. Furthermore, I find his Inductive Logic to be a curious and somewhat neglected interpretation of probability. Since you have covered videos on Bayesian Epistemology, I am curious to know your opinions on Inductive Logic in contrast to Bayesianism.
So when i learned formal logic the first thing I was told was that statments must be true or false. Formally, p is a statement iff p is in the set U×Z_2. Where U is the set of all uterances and Z_2 is the intergens 0 and 1. An uterance in english is at minimum a sentence. Clearly now there are no contradictory statements as p ansmd ~p is false by defenition of statement.
How can Russell argue for her position without using logic? Even if she claims that certain laws of logic hold true in this specific context but not in others, then she would have to argue why that is the case, and then doing the same thing for this argument, and so on..
"then she would have to argue why that is the case, and then doing the same thing for this argument, and so on.. " . I don't see why this would be a problem if you accept a kind of coherentism in epistemology. I don't know what Russell's broader epistemological views are, but that seems like the obvious option here. What makes a logical system appropriate in a particular context is simply that this system, combined with our other beliefs, produces the "web of belief" that scores best on the theoretical virtues that matter to us: empirical adequacy, simplicity, explanatory power, non-ad-hocness, ease of applicability, etc.
@Otávio Rapôso "Russell can claim his argument is sound and that there`re no general logical laws." Not possible because soundness presupposes logical laws. If you not only doubt, but claim, that there are no logical laws then you cannot make an argument because an argument presupposes logic. On the other hand, logical skepticism is possible, because it only doubts if there are logical laws.
the con white thing is a joke. it's two different terms depending on where it appears. that those terms happen to be made of the same glyphs is irrelevant.
Agreed! I was looking to see if anyone else had this same qualm as I did. If we even wanted to make it a same term, you'd have an adequate conditional construction to deal with it and preserve truth.
Yes. In the example "It is raining here", the meaning of "here" is different in the two senses. Very obviously, if I say "Gabriel is Italian" and some days later I say "Gabriel is not Italian", I am simply referring to different people, not violating the LNC. Gillian's counter-examples do not show that the laws of logic do not apply to ideas, only that they do not apply universally to formulas (P, Q, A). But then, what is the purpose of formulas besides referring to ideas? Logical equivalence ←→ is basically identity, and not identical of sign but identical of meanings, as what establishes identity is that both always have the same truth value, and that comes from thinking, not from manipulation of signs. In the case of con-white, the apparent source of contradiction don't need to have the same truth value, so it is not a violation of identity. Variables such as P and Q must refer to ideas, not to graphite scratches on paper. Analytic philosophy isn't sending its best. Then again, it is not particularly relevant outside of its cultural sphere, thankfully.
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@Oners82 That concern is addressed at the end of the video, I think.
26:03 "We need to have reasons for thinking that an interpretation is illegitimate beyond it proving a counter-example to a logical law."
This statement might be the best illustration of the fundamental problem underlying the entire project of logical nihilism. Proving a counter-example to a logical law is the best possible reason for thinking that anything is illegitimate. This is the concept of _reductio ad absurdum._ There can be no better reason for thinking that an idea is false than proving that the idea entails a false conclusion.
Perhaps the source of logical nihilism comes from a misunderstanding of the nature and purpose of an axiom. An axiom isn't something we've concluded is true due to some reasoning or evidence that leads us to believe the axiom. An axioms is true by fiat. It is simply declared to be true and any attempt to prove or disprove an axiom is pointless and misguided.
It's exactly like trying to prove or disprove that bachelors are unmarried.
The purpose of an axiom is to provide some basic common ground to allow us to understand each other. When people have wildly different beliefs about the world, it can be difficult for them to understand each other, but if they carefully use logic then they can potentially understand each other's reasoning. Even if they agree on nothing else, at least they have the law of non-contradiction and similar logical axioms. This universal common ground is part of what makes logic such a powerful tool.
Perhaps if people aren't aware of the purpose of axioms they might be tempted to examine axioms just like any other idea and try to determine if we have good support for belief in those axioms. It makes intuitive sense, but an axiom is not that sort of idea. Axioms aren't made true in that way and we shouldn't look for that sort of support for an axiom.
Still, it doesn't stop people from having preference for certain axioms and it's very natural to ask "why?"
If a main function of an axiom is "to understand each other" ( an axiom need no proofs and we should believe it) , what the difference between an axiom and a dogma?
If i think that any proof system needs proofs and you think logic needs no proofs, how an axiom can help us to undestand each other?
@@zachdauman5464 "What the difference between an axiom and a dogma?"
Axioms are understood to be arbitrary, while dogmas are presumed to be based in reality. For example, consider bachelors being unmarried. That's an axiom. Everyone takes it as true, and we must take it as true if we're to understand each other when we're talking about bachelors, but we also understand that it is arbitrary. There's no reason why bachelors are unmarried; it's just how they are.
In contrast, take a dogma like the resurrection of Jesus. There's supposed to be an actual event which makes it true. People don't just believe it arbitrarily, or at least they don't think they're believing it arbitrarily. If they were to take it as an axiom, that would make it true regardless of whatever happened in history, which would make it pointless.
@@Ansatz66
Therefore any system of proofs (logic, math) based on axioms is not objective in describing reality
This lead us to conventionalism.
Conventionalism is the philosophical attitude that fundamental principles of a certain kind are grounded on (explicit or implicit) agreements in society, rather than on external reality. Unspoken rules play a key role in the philosophy's structure. Although this attitude is commonly held with respect to the rules of grammar, its application to the propositions of ethics, law, science, mathematics, and logic is more controversial.
Science (based on logic and math) does not give an obvious truth, any scientific truth is the result of a contract between scientists. Therefore, science is not very different from religions. Science has no features that distinguish it from other methods of knowledge.
So, i ask
What the diffence between religion dogmas and scientific axioms on those perspective?
And how can non-objective axioms help us to understand each other?
@@zachdauman5464 "Therefore any system of proofs (logic, math) based on axioms is not objective in describing reality."
That must be so, since anything which can be logically proven must be true in all possible worlds. If there were some object in this world causing the truth of 1 + 1 = 2, then in any world without that thing the equation would be false. 1 + 1 = 2 cannot describe reality because it's true in any reality no matter the content of that reality.
"Science (based on logic and math) does not give an obvious truth, any scientific truth is the result of a contract between scientists."
Science doesn't discover axioms. It discovers theories. Theories are statements which attempt to describe reality, very much unlike axioms. The critical difference is that theories can be wrong, and therefore they are not true in every possible world. The truth of a theory is not based on a contract between scientists, but rather we expect a true theory to submit itself to experimentation and make successful predictions.
"Therefore, science is not very different from religions."
The biggest difference between science and religions is that science recognizes fallibility and tests ideas as opposed to making ideas sacred and forbidding people from doubting ideas.
2:58, a background voice: "Куда?!" xD
I clicked, It was indeed a "КУДА". 😂
so... everyone involved in this debate is simply confusing logic with the *language* used to communicate logical laws.
yeah, you can find contradictions and instances in which certain statements don't hold true. that doesn't necessarily mean the logic the statement is attempting to express is not universally true; the language may simply be flawed. the idea behind it can still be flawless.
i've watched a few of your videos on critiques of logic, or skepticism of logic's infallibility...and all the arguments seem to really be against language, not logic.
Ordinary language philosophers seem to be the philosophers that by far most often create problems out of nowhere by using language other than ordinarily; usage of jargon (which is absolutely necessary), be medical or theological, does not fall out of ordinary language. One wonder if their project is not some great mechanism of psychological compensation. On the other side of the coin, philosophers who base philosophy on the analysis of language are also the ones who by far seem the most caught up in purposeless language games.
The people involved in both of these are *almost* always English speakers. Really makes you think huh?
These seem more like problems with applying the laws of logic to natural language than problems with logic itself.
there isn't a problem. russel's argument depends on the assumption that P refers to a set of glyphs rather than a meaning. The sentence is "snow is white, and snow is the null set". this is a contradiction, and false. she has failed to show the existence of a true contradiction.
@Sky Gardener I agree that the heterological thing is more difficult. Natural language is inherently vague, and is not suited to writing logical statements.
Very interesting but I don't buy the counter-examples, e.g. for the prem-white one, as I understand defining the term by parts means I can substitute "prem-white" by whatever it's defined as in that context, and doing that doesn't yield a counterexample to ID.
I was watching your bookshelf video and noticed you had a copy of Popper and After. What are your thoughts on David Stoves work?
I don't really have much to say about him... In the previous video I made with Cole, we talk about how we both like "fuck-with-ers". My impression from that book - and only from that book, since I'm not familiar with his other work - is that Stove was a fuck-with-er (though he would have denied this), and I can't help but admire that, but I'm not convinced he was a particularly good philosopher. There are a lot of uncharitable readings of his four targets, and he doesn't really engage with their arguments anyway, being more concerned with criticizing their language and exposing the historical source of their views. The first issue is simply not all that interesting to me; as for the latter, his central thesis about the importance of deductivism to their views is, I think, just obviously false (not false in the case of Popper, but obviously false for Lakatos, Kuhn, and Feyerabend). Stove definitely has some flair as a writer, and the vitriol makes it a fun read. I'll note that a good example of similar vitriol from the "irrationalist" side is provided by Feyerabend in "Conversations With Illiterates", in his "Science in a Free Society".
Have you considered doing a video on Rudolf Carnap? If so, the recent Stanford Encyclopaedia entry is worth a look
I'm not really interested in doing videos on individual philosophers. I prefer looking at topics or particular theories. For one reason or another Carnap just hasn't been all that relevant in any videos I've done before, despite how influential he was. I don't know whether he'll come up in the future. I don't have any near-term future plans for a video that would cover anything from Carnap.
(When I say Carnap has not been all that relevant before, I mean for the purposes of introducing the topic covered in the video, which is of course my goal in all my lecture-style videos. There are many videos I've made where Carnap's work would be relevant if you were exploring the arguments in more detail.)
My mistake; I like the emphasis on topics and theories. My reason for asking is that there are a lot of misconceptions about Carnap, particularly his mature work during his semantic period. Furthermore, I find his Inductive Logic to be a curious and somewhat neglected interpretation of probability. Since you have covered videos on Bayesian Epistemology, I am curious to know your opinions on Inductive Logic in contrast to Bayesianism.
The only truth which holds in philosophy is that counter examples is a given ...or does it?
So when i learned formal logic the first thing I was told was that statments must be true or false. Formally, p is a statement iff p is in the set U×Z_2. Where U is the set of all uterances and Z_2 is the intergens 0 and 1. An uterance in english is at minimum a sentence. Clearly now there are no contradictory statements as p ansmd ~p is false by defenition of statement.
How can Russell argue for her position without using logic? Even if she claims that certain laws of logic hold true in this specific context but not in others, then she would have to argue why that is the case, and then doing the same thing for this argument, and so on..
"then she would have to argue why that is the case, and then doing the same thing for this argument, and so on..
"
.
I don't see why this would be a problem if you accept a kind of coherentism in epistemology. I don't know what Russell's broader epistemological views are, but that seems like the obvious option here. What makes a logical system appropriate in a particular context is simply that this system, combined with our other beliefs, produces the "web of belief" that scores best on the theoretical virtues that matter to us: empirical adequacy, simplicity, explanatory power, non-ad-hocness, ease of applicability, etc.
@Otávio Rapôso "Russell can claim his argument is sound and that there`re no general logical laws." Not possible because soundness presupposes logical laws. If you not only doubt, but claim, that there are no logical laws then you cannot make an argument because an argument presupposes logic. On the other hand, logical skepticism is possible, because it only doubts if there are logical laws.
Someone didn't listen to the whole video :P
the con white thing is a joke. it's two different terms depending on where it appears. that those terms happen to be made of the same glyphs is irrelevant.
Agreed! I was looking to see if anyone else had this same qualm as I did. If we even wanted to make it a same term, you'd have an adequate conditional construction to deal with it and preserve truth.
Yes. In the example "It is raining here", the meaning of "here" is different in the two senses. Very obviously, if I say "Gabriel is Italian" and some days later I say "Gabriel is not Italian", I am simply referring to different people, not violating the LNC. Gillian's counter-examples do not show that the laws of logic do not apply to ideas, only that they do not apply universally to formulas (P, Q, A). But then, what is the purpose of formulas besides referring to ideas? Logical equivalence ←→ is basically identity, and not identical of sign but identical of meanings, as what establishes identity is that both always have the same truth value, and that comes from thinking, not from manipulation of signs. In the case of con-white, the apparent source of contradiction don't need to have the same truth value, so it is not a violation of identity. Variables such as P and Q must refer to ideas, not to graphite scratches on paper.
Analytic philosophy isn't sending its best. Then again, it is not particularly relevant outside of its cultural sphere, thankfully.
Keep the good work..I have learnt so much things form you...
This is sick!
These deliberations are pointless.