On self-refuting theories: kzfaq.info/get/bejne/pphipMmVyb_PiH0.html Could there be no laws of logic? kzfaq.info/get/bejne/aqhmZLKK2rSpp30.html kzfaq.info/get/bejne/hs6Siqlyx7i9pnk.html

This is similar to rounding a number while evaluating the solution of a mathematical algorithm. Sometimes the answer is not far off, but if you're unlucky, while traveling down the path, the approximation flips something or gets exponentially amplified to the point that your solution is -1000000% off. You can see this happen in computer game physics sometimes. Unless you input definite, non-approximate truths, you can't be sure logic holds.

This was extremely interesting and refreshing. I've been away from academic philosophy for over a decade now, and I kind of expected this to be a rehash of Gödel's incompleteness or something. This was a pleasant surprise. I realise that although I took a special interest in formal logic back then, I never really pushed that interest very far, as I switched to a different field. Deffo subscribed :)

Suggestion for new video title - *“How Approximate Truth Breaks Deductive Logic”* - or something. I think the current one is a bit too general :) Anyway, great lecture! I am working with inferences and natural language atm, so these are concerns that give me sleepless nights :P

This has me thinking of Deleuze and Guattari, in the plateau on the rhizome, writing that language is precise in being vague. What they argue is that language is not "approximate" but rather that if it had static, unchanging and precise meanings, it would fall apart. When I say "apple", you cannot know whether I'm referring to a green, or red, a rotten one, or one still hanging from the tree. But that doesn't mean the truth you are getting from it is only "approximate" or "idealized", rather it means the description you have access to is not precise. If "apple" could only refer to the perfectly round red apple I found in my garden this morning, the word would be utterly useless and nobody could ever use it to describe anything except the one apple I found in my garden. For example, if you hear the story of how Newton came up with his theory of gravity when he was sitting under a tree, and an apple fell on his head, you don't know what position "sitting" means and you don't know what the apple looked like, even the tree might be a young one full of apples or a dying old tree that surprisingly still held fruit. But does that mean the truth delivered to you was only an approximation or is it rather the case that the image you get is vague and imprecise? I would certainly tend towards the latter. For the question whether that means classical logic will hold, I will vaguely (hehe) gesture towards process ontology and what it has to say about classical logic (I am also just too lazy to detail that in this comment which already feels long enough)

I don't think the concept of "approximate truth" is well defined. There are probable truths, and there are approximations of various measurements, but to say that something is approximately true is just to say that it's false. My perspective on the matter is that a given theory is nothing more than a self contained abstract systems, with no necessary relation to reality. In that sense, valid deductions in a theory are absolutely true *of the theory* , so we don't need to worry about what sorts of deductions are valid. What we actually want is not approximate truth, I think, but approximate measures. For example, I don't care if the electric potential of my capacitor is *exactly* what my theory predicts. I know that the prediction is false, and it doesn't matter. I only care that the predicted measures are accurate enough to build a working circuit. If a specific measure, as predicted by a theory, has been tested and verified to be accurate to reality within some amount of error, and that error is tolerable, the model is useful. To give an abstract example, consider the problem where we pick some positive number x>0, and we want to know if the infinite sum sin(x)+sin(x^2)+sin(x^3)+etcetera will converge. We know that, for small x, we can approximate sin(x)~x, and under this approximation, our sum is just x+x^2+x^3+etcetera. We know this sum converges when 0

Here because of the folks from Answers In Reason! Subbed!

This is the first video of yours I watched. Based on the thumbnail I was hoping you would talk about some unique case where boolean algebra doesn't work. I guess I now watched a philosophy video about approximative truth.

Great stuff man keep it up I love this kind of content

Since the year started, I started seeing more and more and more small yt chanells that are talking about philosophy, philosophers, logic etc. Sometimes I love the algorithm

to acknowledge that "truth," in some "objective" sense, is never actually accessible, but rather that only "approximate truth," in some utilitarian sense, is all we can grasp, is the first step in realizing that "truth" was never the goal to begin with. Any given "theory," in any field of inquiry, has a degree of utility. That utility is all we need to focus on, while "truth," as classically conceived, can be safely ignored.

All communication involves translation, which is Abductive. One could reason thusly: Everyone is playing the abduction game, whether they know it or not, and it is up to the cognizant to let those that call "foul" when truth can't be pinned down precisely continue to play the game with their own made up, extra rules. Just... over there a ways, at the kids table. Thanks for another great video. I enjoyed it and might possibly agree with large portions of the arguments... I think. Bayesian Regress imminent while I sort it out. ;)

Socrates is, in reality, immortal. This upends the whole argument.

After watching this, I feel like the "limits of logic" you've listed come down to variables changing and, as you mentioned at 10:08, us being unaware/disconnected from the "one true logic/oblective reality" which I think we should always strive towards. The sydney opera house example you gave was made vague enough for use in this video, in my opinion; the example could've been "What was the speed of sound in the sydney opera house on May 2nd, 2009 at 2:35 PM Sydney AEDT sharp?" instead of just "What is the speed of sound in the sydney opera house?" This reminds me of the differences between set theory and homotopy type theory (In my understanding, at least) where set theory is more "vague/loose" with what is and isn't an equal to a variable. For example, if all elements of set A are in set B, and vice versa, then A=B; however, in HoTT, two "types (X and Y)" that would be equal if they would be interpreted as "sets" in set theory now have more dimensions that could be used to distinguish between the two types, such as location and time (This also relates to your comments on "equivocation" at 10:38). All that to say that the question "What is the speed of sound in the sydney opera house?" is too approximate of a question to have anything but an approximate answer. Just my initial thoughts, and me being completely wrong is a definite possibility.

Great video as always!

Precise language will not help. In "Proofs and Refutations", Lakatos shows that even in mathematics, statements have hidden lemmas that will falsify the claims. What matters is if we deal with the hidden lemmas in a progressive way that leads to new knowledge.

just discovered this channel and i m glad

As someone with scientific training, I've never really considered anything other than "approximate truth" to be "truth" when we use that word colloquially. Or something like "an idea that provides explanation and allows us to interact with the world" - that's plenty enough for me, I don't hunger for more. The banal (to me) kind of deductive truth, where the conclusion is just the premises rearranged, is something I've never taken very seriously, it seems to have no application when it comes to understanding reality, outside maths. I've never considered this question before (and I know nothing about logic), but off the top of my head, it seems to me that logic is a post-hoc analysis of the cognitive tools we've evolved to understand and interact with the world. Should our expectations be particularly grand? I think there's some structure to reality that makes logic and maths work, and allows maths to describe nature - and that's just how nature is.

I have this concept that -- Theories can be *creative* and generative of reality. For example, in computer science, somebody will come up with a theory based on observations of the world, and it'll be directed towards some end, and the theory is like a possibility -- it is descriptive of a possibility. And then if it works out, it creates a real life situation that is well described by the theory, and proves the plausibility ("That was a true description of a possibility, and we know that because we could do it.")

The truth of a deductive conclusion is contingent upon the truth of the axioms, and the truth of the axioms cannot be determined deductively because you run into an infinite regression. Premises can only be demonstrated inductively, and induction is necessarily probabilistic.

6:14 Suppose the sentence "the only thing we can get are approximately true descpriptions of the world" is true, then that sentence is, by definition, only an approximately true description of the world. That means that there's a sense in which there exists descriptions of the world that are not only approximately true but also strictly true (given that the sentence "the only thing we can get are approximately true descpriptions of the world" would be strictly true of that wasn't the case). But if stricly true descrpitions of the world necesarily exist this constradicts our premise. It's like saying "everything is subjective" Which means that what you just said is subjective but if that is the case, there exists a subjective frame in which everything is not subjetive, but if something is objective in a subjective frame, it has to be objective in all reference frames. Therfore contradicting the premise. It's an argument similar to the barbers paradox.

From a certain perspective, the study of statistics is first and foremost a way to assign quantities to levels of confidence and perform arithmetic with them. If A and B, then C; A with 90% confidence, B with 90% confidence, therefore C with 81% confidence

Although it's true that you can't necessarily maintain approximate truths through a deductive chain of reasoning, if you treat claims as having probabilities of being true, then you can observe every possible branch individually, then sum their respective probabilities using Bayes' Rule to deduce approximate truths. There is one problem with this, which is that this process can be highly sensitive on the initial approximate truth values you assign to your premises, so if the chain of Bayesian reasoning is long enough, you could arrive at approximately true conclusions, which nonetheless seem very unlikely. All of this is to say that usually this works. Using logic and by extension probability theory (Bayes' Theorem) along with inductive reasoning (investigating the approximate truth values of the initial claims/premises) tends to work. "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" is an article, after all.

Thanks for this video.

Thanks for the video, I enjoyed this one a lot, had similar thoughts for many years now. By the way, are you familiar with John McPeck, especially his Critical Thinking and Education & Teaching Critical Thinking: Dialogue and Dialectics? He makes similar arguments about formal and informal logic, though in a more of a pedagogical context, his approach to it sounds way more reasonable to me than what I usually hear. He seems to be mostly forgotten by now despite thousands and thousands of citations (tbh, in a lot of cases I think he's cited out of habit while not being read) which is a pity.

Regarding the opera house. Once you define your parameters you could ask the question did sound travel from point A to point B in X seconds as predicted in a hypothesis? The answers Yes or No would be logic. What was the approximate time sound traveled such distance is a tentative and physical question that requires scientific experimentation, but did the sound travel as fast as predicted Yes or No doesn't require relentless testing; It either did or didn't. You couldn't even practice science without laws of logic.

Would or can the value of speed of sound inside the opera house be something like the entire set that contains all possible measurements within all possible conateained definitions of the opera house object?

In the Sydney opera house idea, the key is to clearly state the exact premise so that some logic can be performed on it. Problems like this often crops up in programing, where some user/business functionality is unclear, and further requirements/specifications needed to be spelled out; so that a program can perform automation/logic on the premise and reach the intended conclusion. Often times, the input needs to be transformed, and edge cases for scenarios need to be tackled. Most programs are deterministic models of logic, unless you are looking at the probabilistic models used in recent AI programs. Edit: Much of these problems that you've went over are because the logic is being performed on the natural language (which is ambiguous and prone to evolving). This is why pure logic is done via programming languages, which are specific.

There is a lot of Bayesianism in what you say, it is very nice. I personally like to think of logic as a special case of a probabilistic system, one that would give a value between 0 and 1 to any logical statement such that it would satisfy several axioms, like the value of "false" is 0, the value of "true" is 1 and if "a" and "b" can be proven to be disjoint then P("a or b")=P("a")+P("b"). (I do not give any value to these probability myself, they just have to satisfy those axioms, and for instance logic, which gives values 0 and 1 only could in principle be such a probability distribution). Now you can play around with this and for instance define conditioning which is kind of fun, for instance if P["if a then b"] is high (higher than 1/2), then P["b"] is lower than P["b" | "a then b"], this means that the knowledge that "a -> b" increases the probability of "b" and by symetry decreases the probability of "a". If you apply this is maths (or science), when you have an axiom "a" and you prove theorem with it, then you increase the probability that the theorem is true, but you decrease the probability that the axiom actually is true, I like how it resonate with the fundations of maths and the way we are trying to change it completly every now and then.

Nice discussion. The concepts that you characterize as indeterminate-like swan-can be treated as open-textured concepts. Ordinary language is rife with them, and science usually starts with folk concepts from ordinary language. However, we can rationally reconstruct some of these concepts and converge upon greater rigor.

There has been since Carnap or maybe Tarski an attempt to understand the content of a theory. Popper had two notions of content: firstly he had logical content, which is all the claims that it logically implies (possibly excluding tautologies, since they have zero content) and then there is informative content, which is any state of affairs or theories or statements or propositions that the theory rules out. Popper thought that nothing (empirical) follows logically from a universal theory unless supplemented with auxiliary hypotheses. Yet the theory can exclude states of affairs without auxiliary hypotheses. My point here is that content is always best construed as the set of models that are excluded by the theory. It makes a lot of things logically neater. Approximately true theories exclude more true models - in the model theory sense - than they should (in other words they claim that certain things are false that are in fact true) It is in this sense you should understand approximate truth. The reason is, like Dummet said, what is primary about a sentence is what it rules out. So you could say that approximately true theories claim things are true when they are false. But the things that it claims are true, exclude other things from being true and that is what the (informative) content of those claims are. My other point is that in order to see what a theory rules out you have to entertain it as true. So your argument that approximate truth somehow makes deductive logic inapplicable is mistaken, since it construed logic (like most logical explanations) as a mode of justification when it is simply a way to manipulate content. To show what is included in what.

If descriptions are dependent on definitions, then an "object" is as defined. Definitions contain the subset of all possible values inherent to the object or word that is being defined, automatic. To stay consistent, we have to remove our perceptions of existence from the idea of existence. An extreme example: if, on average, we perceive an object to have similar qualia to that of a shoe, but the creator of that object has defined it as belonging to the class of tables, then it is a table, no exception.

6:00 that you can get only approximations doesn't mean that phenomenon doesn't exist, that truth perhaps its instrumental, but its in the way of truth. If the prerequisites of a category can exist, such category can exist, like the speed of sound on that place. Is there a material medium? Yes, then a speed of sound exist.

We study logic in school and I understand nothing of it despite actually liking logical schemes in cpu as a child. I still think that the knowledge is very limited if it can be actually acquired and it is really hard to deal with the irrationality of the world we live in. I hope the philosophy guys are doing well cause they think a lot

I was actually just thinking about this the other day. To most people Dialetheism seems like an issue, because of explosion, namely, that if we accept some true contradictions, then we need to accept all contradictions. But it seems like as long as you don't think truth is binary 1 - 0, true, false dichotomy, there's no reason why you couldn't accept true contradictions. As long as your view is on a spectrum of "closer to truth" or farther from it, then there's nothing contradictory about allowing true contradictions. For example, one I tend to believe in, I tend to think of both property dualism, and neutral monism (as well as a kind of epistemic idealism, but that's not important for this case) are both true. In the above case, to be a dualist is in direct contradiction to be a monist, you cannot both believe there's only one state of existence and multiple. However, if I merely say that property dualism is true in one sense, and that in a greater sense "neutral monism" strikes me as "truer" but not so much so that property dualism is false, then I'm not engaging in a contradiction. All I mean to say is that, nothing is wrong with violating "the laws of logic" so-called as long as you're not forcing yourself into a rigid binary of accepting them as either a or not a. It's a lot like the Buddhist talk of conventional truth and ultimate truth. Not that one is not true, but some are more true in certain contexts or with certain parameters than the other. Incidentally, I was thinking about this in terms of objectivism and objective morality. For me, objectivity is incoherent, since an "objective position" in ordinary language means "perspective-free perspective" position just means perspective, and objective means stance or mind independent, so therefore perspective-free. I also take morality to be in the area of value, and not fact. So to talk about a moral fact is like talking about an ant-giraffe. To me, they're just incoherent notions. However, I am willing to grant them to the objectivist/moral realist as long as they're dialethic in regards to the above property of truth as I described before. It's not particularly problematic that anything is a contradiction, as long as it's not in absolute terms that the parameters are specified in.

I think we just need to be clear about the scope of deductive logic. It's fine as a step in dialectic if the intended logical relationships are unclear to who you're talking to. It's a tool for communication. What follows dialectically is of course whether the ideal premises are adequate, which really is just the soundness phase of analysis. 'True enough' is a matter of consensus appraisal in the context of each communicative process. The aim is to argue to agreement as to the more comprehensive and coherent system of ideals. Rationality is purposive and idealistic, but most importantly a dialectic process.

When talking about the different ways the same word can be used in such a way that deductive logic doesn't hold, you could prove or assume that an implication is true for all different understandings of the word allowing for deduction despite the uncertainty of the exact meaning

If one form of 'approximate truth' is uncertainty, then we do have a logic for that. The Bayesian interpretation of probability as a rational degree of credence can be used to create probability logic. Ernest Adams defines an argument as p-valid if the improbability of the conclusion does not exceed the sum of the improbabilities of the premises. In simple cases this means a valid argument cannot have highly probable premises and an improbable conclusion. The logic differs from ordinary classical logic though.

In the event that deductive reasoning needs to be used on approximate ideas, more well defined definitions along with an approximate truth value, i.e. 80%, 33% etc, can be used. The result would be something like approximate likelihood of an outcome rather than a binary truth.

Imagine a gradient of white and black on a finite line. Is there a clear point of difference between where white begins and where it ends in relation to the black colour? no? does this mean that there is no such thing as the colour black or the colour white? no? see where this is going? just because I can not define what a chair is (because the varieties are endless) doesn't mean that there is no such concept as a chair and doesn't mean I can't say facts about the chair.. food for thought.

Technically, you can “do anything” in infinite-order metalogic.

A good example of a conclusion offering less information is the basic equality. That two things are being equal doesn't tell you what they are. And this can be extended to a concept of similarity, which is an approximate equality, sort of. Obviously things become mighty confusing from there, because you have to qualify the error in similarity to be able to wield such a technical monstrosity. What is similar enough? What are the domains of comparison? And who is judging whether it actually means something? Ergo, similarity is a potentially mighty dangerous concept, if only one boils it down through logic.

I think there might be a way to get exactly true descriptions of the world (think of something like "deductive" reference rather than inference), but just like with the typical problems that are raised about deductive inference, it probably wouldn't be super "informative" and we may not get the rich theories that we see in science.

This is basically the same idea of the vSauce video "Do Chairs Exist." Another great illustrative example is that when asked "which ship is the real ship of theseus", the problem is not one of identity, but one again of natural language. If the real ship of theseus is meant to mean the one that is, say, registered under port authority as the ship of Theseus, being used actively as the ship of theseus, then it's clearly the new one. If the real ship is meant to refer to the collection of original boards, then it's clearly the old one. It is a matter of the lack of precision inherent in natural language

Truth is always "tensed."

What about the claim that “all the claims we make about the world are approximately true”? Whether that’s an a priori or empirical claim leads to different problems. But insofar as it is self referential, then I think the crisis is a bit overstated, at least with regard to formal logic and it’s useful application to natural language. I wonder whether Saul Kripke’s Naming and Necessity might shed light on the problems of mapping what is rigid onto what is approximate. Thanks for this thoughtful video!

The more and more formal mathematics and logic I studied, the clearer it was that we were just winging it regarding its application to the real world. The more you see proofs, you realise there's no way the real world could be so strict. Then you see model theory and you realise that we've privileged some mathematical axioms, deductive systems, and results with our attention, but out of practical concerns. We have tunnel vision about mathematics: we've historically only focused on results in those parts of mathematics that can be approximately applied to the real world , and now most people think that that's all the math there is and that the logical system that supports it is the one true logic

Is this just a matter of definitions rather than logic? We experience complex patterns and name subsets of this when we spot sufficient similarities.If this is useful to live and to communicate then we don't need to make stricter definitions...until we need to do so. Everything is approximate. Is there more being said here?

The traditional deductive logic is designed as two valued logic, which can be quantified as 0 and 1. There is nothing in between. If you are looking for an approximate logic, the probability theory is what it is, which leads to a "partial truth" by percentage. In the probability theory, 0 and 1 are merely two possible cases among many others.

It is true that approximate truth isn’t preserved in logical manipulations of content, that is why it is imperative that a working theory of verisimilitude is created. Verisimilitude is the ratio between truth and content. Many people have just abandoned the verisimilitude project (started by the way by Popper). There has been some advance in the last couple of years, Mormonn for instance has created a topological theory of verisimilitude, that seems to get a lot of what Popper wanted out of such a theory.

If there is One True Logic, why should we expect it to be inapplicable to say, arguments in ordinary language? Or arguments about empirical theories? This may be question-begging, but if there is One True Logic, I'd expect it to at least accommodate those cases! The upshot is, I'd expect the One True Logic, if there is such a thing (though I don't think there is), to not be classical logic. But that still leaves a lot of possibilities on the table. And to my eye, there are ways of taking approximation, imprecision, vagueness, etc. into account when we perform our reasoning, and that reasoning is still perfectly "deductive." We can just report our errors and uncertainties along the way. That's what we do in say, statistical inference. And there we find a perfectly deductive theory of non-deductive reasoning. Sometimes imprecision is actually very useful. Another example: What's the referent of 'n' in "let n be an even number?" Well, it's not exactly specified. All we know is that it's some even number. So in our reasoning about 'n' we're not allowed to use properties which aren't true generically of all even numbers. So we can't conclude that 'n' is divisible by four, say. And that's good! (There are different models of what's going on here, and they track pretty closely with different models of vagueness/sorites problems) And finally, what I'd say about classical deductive logic being an idealization is what I'd say about any other kind of idealization we use. It's merely instrumental. It's useful to reason "in the limit" because it has practical implications for deciding what to do and believe.

Applicability of any logic to an appropriate domain of objects is fundamental to the natural language application of logic, but perhaps only approximately. However, great precision has been devised out of approximate beginnings. So it is the vector of demonstrable returns, understood partly in terms of empirical testimony and partly in terms of logic's internal apparatus, that gives the ultimate sense of logic's truth beyond merely formal consistency. But a demonstrably growing trend of a theory about the world becoming more precise, even within the bounds of merely approximately so, that is the theoretical and practical unit of assaying what truth there is in a system of thought, even of logic systems though they are so many and of such different types. So a formal theory of all logic would have to account for this in a paradigm that would be a form of metalogic not yet fully articulated in the field.

in my opinion all truth in approximate: even things like math and logic where we should know that the consequences of axioms are what they must be. but those axioms can only be defined in terms of natural language, and natural language is itself only approximate. the trick is just that logic and math are among the few fields where the only possible errors would have to be in communication of a small set of simple rules, which turns out to allow it to be so nearly correct we may ignore the approximation and still yield results which are extremely often useful for anything which may be approximately described in their terms. but i'll admit it's hard to really say much about anything, purely in this framework

The Sidney opera house sound does have a specific speed at a specific speed between 2 specific points at a specific moment. Only our perception has no specific idea of it

Could you maybe do a video on the positives and negatives of analytical philosophy?

You articulate good

Seems to be saying that we're just playing a language game a la Wittgenstein and that we narrow or widen the scope of this language game depending on context

In summary: 1. Words are vague, so no statement is ever precise 2. If something is roughly/generally true, its part might not be (some organisms live for centuries, so human life is really short; but “human life is short” is not necessarily true by itself) 3 If some things are roughly true, then their combination might not be (temperature on the North Pole is not that much different from any other place; North Pole is lethally cold)

I call it controlled scepticism it's like when you think as a mini you in your head but you stop yourself from having this linear regression of a mini u inside a mini u and just keep it at one level or we could just doubt every object that exists but out of practical necessity we shouldn't

On the first point of approximate truth abstract deductive reasoning or reansoing based on abstract concepts can be absolut like math but once applied to the real world like math applied in physics then it becomes uncertain

Good vídeo.

The logical operations themselves aren't approximations, but the variable representations are approximations of reality or just concepts in general, doesn't have to have any ground in reality. "This statement is false" fails to look at the biological history of linguistic evolution as a byproduct of brain function. Its limited context is what makes the logical operations on the statement possible, thus allowing us to categorize it as an example of what we call a paradox. Without the reduction into simpler workable chunks, we can't make any statements like "that's an example of a paradox" This is a concrete statement on the original paradoxical statement. Math in general uses this form of reduction to make things workable for math people, doesn't say anything about the accuracy of its representations, thus they are mostly discussed in the context of pure math without any attachment to actual reality. When you bridge the gap between the thought process and its relationship to reality like in physics, that's when things become a bit wishy washy, handwavy, etc.

A quick note, I think logic is an artwork expressed by us humans to approach truth to make the world around “usable”. Precise things are maybe a thing for the future.

The speed of sound in the Sydney Opera House is a probabilistic quantity.

The idea that approximate truth can break formal logic is an interesting one but I would argue the imprecise use of language doesn't make a strong case for idealizations to be wrong or even for them to be of limited use (and by limited I mean to a degree that would significantly alter the reasons why we use them). I would say that at best, it makes a case of the strengthening of the precision of natural languages that we use. To go back to the argument about the speed of sound in a particular room, just because there is no speed of sound for the entire room (unless its temperature gradient field is null), it doesn't mean that there is no such thing as the speed of sound for particular pockets of the room where the temperature is exactly the same. It also doesn't mean we can't say the average speed of sound in the room is X. My point here is that just because there exist a continuous field of ''speed of sound'' in the room, that doesn't mean the whole concept should be thrown out. It's a bit of an equivocation fallacy in my opinion to equate the value of the imprecise language used to the value of the concepts that are underlying the context of a conversation. To give an example : just because I use the word blue to describe turquoise doesn't mean turquoise or blue are invalid or don't exist as colors or even that the idea of precise color descriptions is invalid. At best, it means I used imprecise language and should be more precise next time I speak if my intention is to be more consistent.

A thought that I have been stuck on for a while now is that all language is simply "Point-Grunt" communication. One points at a "thing" object/concept/noun, and then grunts a sound. Another looks at the pointed thing, also points and grunts the sound that he heard. This is what all definitions are. Approximation is obviously a factor in that the two are looking at the same thing with different angles, and they cannot hear themselves the same as they hear each other. With modus podens and deduction, I don't see it as anything other than nested definitions, which you seemed close to be getting at. This logic is not measuring anything. It is all about meaning. Are you familiar with WordNet? It basically defines all words into nested syllogisms.

The validity of an argument allows us to check whether someone’s criticism of our conclusions affects our premises. Validity should be renamed the principle of the retransmission of falsity. If our argument is invalid then the criticism of the conclusion doesn’t affect our premises, which means that we have not opened ourselves up to learning whether our theory is false.

We could see logical arguments in the same way we see goods in a market. We could say logical arguments are goods exchanged in a free market of logical arguments. We contribute arguments to the market and receive arguments from the market. We get to use our logical arguments for as long as they can hold up against the forces of nature and discard them when they wear out. This is how we treat clothes, houses, and other goods on the market. With this view, we don't care about whether or not the logical arguments are true, only whether or not they are useful. This is a pragmatic view of logic. Rather than caring about the truth of the argument, we care about what it can help us achieve.

Thought cannot truly cannot be quantified unless we create multiple system to allow us to measure them In a way we can comprehend. As a result we get language and arithmetic. Despite precise numerical values which can be universally replicated through the course of space time, language is limited by universal acceptance of certain words within the given lexicon of a language. Despite it not being specifically finite, language is merely a way of transmission of information of specific emotions. As result, logic is created by the limitations of the English language because we are forced to think in this manner by using specific words to entail one’s view. Until we can transmit our brainwaves and create a translation system, only when will human communication will evolve. However, I’d argue that our vocal systems are perfect by design and we must create a new standard of communication to break free of the limits of logic

This video alone is why probabilistic models of physics will eventually replace our current paradigm. The inseparability of bias, lingual encoding, and mathematical representation of systems.

Just saw your channel.. I really like thus content .. can you name 12 books that can lead me to get an understanding of what your channel is about

While the variability of precision does of course effect the truth outcome it is not important if it falls within the range of acceptable significant digits, hence the acceptance of the +/-. Real life is quite forgiving of being a little fuzzy around the edges.

Speed of sound depends on air pressure/density. Or not?

Forgive my naivety as it's been decades since I studied quantitative theory in logic; but I offer that the main (dare I say zen-like-moment) tenet that I gleaned was that *everything* inevitably leads to if/then statements as the only real conclusion to be drawn from any discourse. Perhaps I over-simplified or got it totally wrong. The only thing I feel certain about all that is that I've lived more than 30 years from that vantage point, as I could never conclude otherwise, myself. It seems to be quite relevant to this discussion. What's the scope of deduction at any given moment, as dust specks in a dust storm.

Now i want to see data charted from a speed of sound sampler in the Sydney Opera House, which takes a sample every hour for 12 months.

Does anyone know if indwterminate values can be used as a valuation for hypothesis, to differentiate this from assumptions? I like this idea more than assuming the truth of a hypothesis, instead you take an assumption as indeterminate.

Resumiendolo. Los límites de la lógica es que son idealistas. Entonces, no esta bien adaptado a la realidad misma la cual se encuentra llena de probabilidades y estadísticas. Por ende, se requiere un progreso científico de la lógica.

Aproximate truths aren’t a problem if the part that isn’t strictly true is irrelevant for the argument because if you say: a ^ b therefore a, this holds true even if b is false, this means that even without strictly defining Socrates or any other concept you can make a valid deduction as long as the relevant part is preserved

So i guess the limit of logic pretty much in a boundary of human ability to validate the true nature of the premise and since we could only describe approximate truth of the premise itself, we could only make do with approximate truth of conclusion from the premises.

I wonder how much of the logical issues and solutions aren't simply linguistics tricks. Terence McKenna argued that language preceded meaning, and, after delving into Wittgenstein's ideas, it seems to me that Terence made an important point that even the deductive/inductive models are simply a particular linguistic trunk trying to convey information.

Does conceptual indeterminacy apply to conceptual indeterminacy I wonder, to speech strictness, to approximation, to difference, and so on. I wonder if conceptual indeterminacy, in effect, cancels itself out in some capacity at least.

I can't get past a sneaking suspicion that philosophy, although not just philosophy, persists not for its logical utility or any other downstream value but because it provides a particular (perhaps peculiar) transmission medium for the generatively self-propagating invocation of more language. Philosophy being a language game without closure because this is precisely how any complex adaptive communications system assures sustainable continuity in any context. Truth as a concept is eminently more valuable as a function of its uncertainty in anything other than the most trivial of circumstances and the competitive narrative communications systems that develop around it are implicitly, perhaps, unconsciously oriented towards an asymptotic approach towards closure. This is in many ways a corollary of the notion that psychological selves are inversely (or is that reflexively) defined by a goal-seeking that, if ever arriving at closure and resolution would then be to entirely invalidate the difference and distance by which that self persists - so, complexity in physics, biology, intelligence, language and logic persist as though they were possessed an intentional agency of not finding resolution, truth, certainty, whatever. The point perhaps being that none of these systems actually possess impermeable or inviolable agency and certain identity - this is their hidden raison d'être. Logic is incomplete because it has to be to persist and your linguistic, competitive and differential reflex to my ad hoc assertions confirms that the only winner in this game is language. TL;DR: Laws persist because they are faulty.

All physics and mathematics are not absolute and are continuously evolving. Theories are being refined over time when new observations contradict established scientific notions. Theories are sort of mental paradigms that help in understanding in a broader context culture and civilization.

Is there any good literature on this?

Attempts to prove logic has limits... ...using logic

"Some old guy, going around annoying the people of athens" lmao i wish i could have been there just to see/hear some of those conversations.

Thinking illogically gets the answers you need when conventional methods are no longer available

Perfectly representing a system by subjectively selecting variables for their relevance to a system is a fallacy. Asking for the speed of sound is a semantically broad request. When we model systems the quest would look more like “what’s the best way to construct the opera house in order to maximize sound quality”. In this case the speed of sound in the opera house is a consequence. Of our modeling of systems will likely always be approximations, but language will always be insufficient in representing reality simply due to semantics & interpretation.

you are cold, put on some kind of heater

go for it!!!!!!!!!!

# from not and and, we can define the rest def Not(a): return (1.0 - a) def And(a,b): return (a*b) # Or can be made or Not and And def Or(a,b): return Not(And(Not(a),Not(b))) I wondered about this. It looks like probabilities might be ok there. And this is also made of statements that don't change over time.

A basic, ordinary conception of truth is presupposed in our having a language and in our way of being. It’s not truth as “approximation “. That suggestion contradicts itself because then the claim “truth is approximation “ would not itself be true nor would a definition of what “approximation” is. You’d also likely bump into circularity between definitions of truth and approximation. The historical source of this problem is in scientism - the metaphysical faith that all of reality must confirm to a certain fashionable way of understanding science (which itself misunderstands science, but that’s another matter). Ultimately, truth cannot be approximation, it cannot coherently be defined as such without self defeating the claim. We can discuss, in certain contexts, truths about probabilities and truths about approximation, but those truths aren’t themselves approximately true or probably true. Truth is not knowledge or certainty. Neither Epistemology nor logic is ontology. And the vagueness of language is more a feature than a bug. You need a better theory of meaning rather than assuming we are “approximating” or “idealizing” all the time. Lots of defects in the video which lead to the incoherent conclusion that truth is approximation. Lots of confusions in the video and in the comments.

Well, from what I understand, it seems to me that this approach to the concept of approximate truth is a new way of relativizing the concept of truth, which, as we know, was received and accepted by the Second Vatican Council and, certainly, constitutes the biggest mistake that currently affects and degenerates our culture. As I have been away from the study of Logic for many years, I think that the concept of tautology is what is applied to consider a formula or proposition reliable of the truth, such as it is in itself, as the Greeks also adopted it and later, much of human history.

At its foundation, do you think logic is prescriptive or descriptive? I personally think its prescriptive which gives us issues such as the white-black swan dilemma that you mentioned. I'm not convinced that capital "L" Logic exists independent of the human mind (such as perhaps how Bertrand Russell argued for with his Logicism). What do you think? I enjoy your work and thx for coming on our show a while back👍

"Even behind all logic and its autocratic posturings stand valuations or, stated more clearly, physiological requirements for the preservation of a particular type of life. For example, that the determinate is worth more than the indeterminate, appearance worth less than the “truth”: despite all their regulative importance for us, these sorts of appraisals could still be just foreground appraisals, a particular type of niaiserie [silliness], precisely what is needed for the preservation of beings like us. But this assumes that it is not man who is the “measure of things” . . . We do not consider the falsity of a judgment as itself an objection to a judgment; this is perhaps where our new language will sound most foreign. The question is how far the judgment promotes and preserves life, how well it preserves, and perhaps even cultivates, the type. And we are fundamentally inclined to claim that the falsest judgments (which include synthetic judgments a priori) are the most indispensable to us, and that without accepting the fictions of logic, without measuring reality against the wholly invented world of the unconditioned and self-identical, without a constant falsification of the world through numbers, people could not live - that a renunciation of false judgments would be a renunciation of life, a negation of life. To acknowledge untruth as a condition of life: this clearly means resisting the usual value feelings in a dangerous manner; and a philosophy that risks such a thing would by that gesture alone place itself beyond good and evil." (Nietzsche, Beyond Good and Evil, 3 & 4)

6:54 - that's when I realized the answer you are skirting. .... it's all deductive. Your starting approximation is itself a deduction. And I would say, yes, any deductive reasoning must follow the approximation. If you do a thought experiment you have to adhere to the rules you set up for the experiment. But the bigger point is that you are letting the imperfect nature of language weigh on your progress. Things don't have to be described in language in order to understand them. In fact, it's the reverse; with understanding come the words to describe. And, THAT is why nobody else will know what you are talking about, lol Peace

I'd say as soon as you start thinking about the real world you've technically stopped doing logic and started doing science. Approximate theories that approximately conserve approximate truth are what science is all about, the key is in keeping track of your uncertainties.

Hi Kane, you should have realized, of course, that you're reached an approximately truth conclusion ;-) - using your conclusion, and apply it to your discourse as in this video. Could you make a new video on the same subject with another approximately truth conclusion ?

We’ll in that case we should try and establish truth that are closest to reality as possible. For example we might say nothing does not exist: there are no two ways about this it seems absolut not like the Sydney opera house where there are an intimate number of things to consider. Nothing is like 0 and zero interacting with anything will remain 0.

The vagaries of vocabulary. The incompatibility of multiplication and addition.