These videos are exactly what I've been looking for. Just straight up philosophy, nothing flashy, no intellectual masturbation or clickbait. Just straight up good content. Keep it up
I took modal logic a few years ago and thought I'd never use it again since I mostly work on mind and ethics. Feels kind of nice to know exactly what's going on formally lmao.
My intuition is that the logical process breaks down in the first step, because 'p' is ill-defined. Notably, this logical chain is impossible for any *specific* example _p,_ since either we know that statement is true/false, in which case it doesn't match the definition of _p,_ or we don't know whether it is true, so we cannot assert that it meets the definition of _p._ In a way, 'p' defies the axiom of choice, because even though it allows many potential candidates, the very act of choosing a specific _p_ makes that statement no longer satisfy the definition of _p,_ and thus no longer a valid choice. It's sort of the equivalent to a statement like 'the smallest number that cannot be described in less than thirteen words'.
You make a good point. But there is a difference between assuming p is true and knowing that p is true. For example, many mathematicians have proven results assuming that the Riemann hypothesis is true. Yet obviously we don’t know whether or not it is. Unless I misunderstood you, it seems you have a problem with non omniscience?
@@BennettAustin7 The way he formally defines non-omniscience is as the statement 'there is a proposition p such that p is true and it is not known', but hidden in that definition of non-omniscience is the ability to choose a specific proposition 'p' from the set of true but unknown propositions. I would restate and accept non-omniscience more generally as 'there exist propositions that are true but are not known to be true', but reject the use of the axiom of choice to select a specific proposition p which can be used in his logical chain. Having considered if further though, I think the more fundamental problem is with his use of the 'Known' operator in his logical statements; the axiom of choice is just a good way to break it. The truth value of whether something is known or not isn't universal - whether a proposition is known to be true must be able to change over the course of a proof if it is to mean anything. So I'm not even sure Kp∧¬Kp is even a contradiction in the normal sense. After all, the very act of proving any proposition p necessitates moving from ¬Kp to Kp over the course of the proof, so this contradiction occurs in all possible proofs, not just this specific one about antirealists. Ideally we could fix K to have a consistent truth value by adding a time component, i.e. K(p,t) meaning 'p is known at time t', but that leaves our proof as: 1. p∧¬K(p,1) - p is true and is not known at step 1 to be true. 2. ∀p(p→♢K(p,2)) - p is true implies p is known at step 2 to be true for all p. 3. ♢K((p∧¬K(p,1),3) - it is possible to know at step 3 that p is true and that p was not known to be true at step 1. 4. ♢(K(p,3)∧K(¬K(p,1),3)) - it is possible that p was known at step 3 to be true, and that p was known at step 3 to be not known to be true at step 1. 5. ♢(K(p,3)∧¬K(p,1)) - it is possible that p was known to be true at step 3 and that p was not known to be true at step 1. Which means that rather than being a contradiction, this is just an explanation of how learning something works.
To progress the knowledge paradox research programme, we would first find a counter-example to falsify the proof and then revise the proof to overcome the falsification in a way that produces further understanding. Sometimes I succeed at this; sometimes not. I took symbolic logic, but was an econ major Sometimes I am not creative enough, but here goes: The crux of this proof is that there are special rules for the K predicate that allows p to be derived from (K)p. On one hand, it is strange that if I (F) a cat, that does not imply the cat exists. On the other hand, the idea that there exists a predicate that can make a statement true is also counterintuitive. Like: I did something to a statement to make that statement true. Bouncing between these ideas, we can grow the research programme.
It seems that there has been no exposition of knowers versus propositions known. If there is an instance of a thing both known and unknown, then surely there may be a different knower (or epistemic agent, perhaps), for each.
Given the central position is paradoxical then it's interesting to discover whose day job involves being a realist and whose an anti realist by trade. Social scientists tend towards being realists contrasted to anti realist theoretical physics given quantum entanglement of particle observation. Who then are the moderates? Probably comedians and artists whose day job requires contrary interpretations of reality.
It is rather troubling that antirealists seem to be motivated by an appeal to consequences. If truth were based in correspondence, then all these terrible things would be true. If your home were on fire, that would arguably be even worse, so to be consistent we also ought to be antirealist about the fire for the same reason we are antirealist about truth. In any antirealist theory that is based on such an appeal to consequences, there ought to be a principle that says something like: if p being true would entail bad things, then p is false.
What is truth? A mobile army of metaphors, metonomies, and anthropomorphism.-Fred Nietzsche Infirmation is not knowledge. Knowledge is not wisdom. Wisdom is not truth. Truth is not beauty. Beauty is not love. Love is not music. Music is the best.-Mary, stuck to seat 38 of Phydeax III
Does formal notation take a while to get a grasp on? I get it's usefulness to those who are familiar with all the symbols but as an absolute beginner, it's like translating something I already don't understand into a language I don't speak just to revert it back into English and confirm I still haven't a clue what I'm looking at😅 Idk if I'm just slow on the uptake or if it's normal to be this confused... probably the former.
Honestly tho, it can be tough to get use to at first, but so much of philosophy is vague meaningless drivel; formalising an argument in logic is soooo refreshing sometimes
What if you made the claims less vague; doesn't the paradox dissolve: • P is not known by any human on Jan 1, 1970 • P is known by myself on Jan 20, 2038
I see truth as an adjudication/evaluation and such is always contingent upon the criteria being used for adjudication and/or the process of evaluation such that any claim of truth with regard to reality is also contingent upon what the term denote with regard to the evaluator/process? (AI system will definitely blur the minor distinction that I am making to total absence, which even as I type this is dwindling ) Consider the proposition(s): Does red exist? Does morality exist? What does the term exist mean? 1) That which can have interactivity? That which can be claimed to be an aspect of what is observed? Something else? I don't denote red or morality to be existent. However, this is generally not a point of issue UNLESS various philosophical interlinkages are in play, since in general terms I can usually identify what is meant by usage and a strict consideration of ontological status is not required for the broad point being expressed. My question to you... *What would be your proposal for reconciling the various models of evaluation that are employed by different people?*
I take it this is a question for the realist, since the realist holds that truth is independent of our means of evaluation? To be clear, I'm not a realist. I'm just presenting the knowability argument in this video; I don't think it's a convincing case against antirealism.
There isn't anything particularly problematic about realism; indeed, this is the conventional view of truth. The knowability paradox is a problem specifically for antirealist views of truth.
I feel like there is something strange going on here with the phrase "is known". Who or what exactly is counted as knowing things here? I guess it means "is known by any human" but that seems pretty arbitrary, what if my cat knows something that I don't? I was reminded of a discussion about pan-psychism that I heard recently, would that let you get around this paradox by just saying that everything knows about itself in some sense? Also if you believe in an omniscient god then I guess there's no paradox since non-omniscience just wouldn't apply? I suppose either of those scenarios would basically be indistinguishable from the realist position though... Anyway, I guess I'm just kind of confused by the anti-realest position in general. Like, what if I hop into a black hole to see what it's like in there, but then I can't escape and get squashed. Is the stuff I see inside the event horizon true since I know about it, or is it untrue since I can't get the information out? Or what about distant galaxies beyond the observable universe or in a multiverse or something. We might not be able to know anything about them, but there's no reason there couldn't be aliens living in those places that do know about them.
but doesnt this just imply that some truths i cannot know simply in virtue of my knowing them would make them false. Like i couldnt know that im dead, for example, cuz knowledge requires consciousness (assume no afterlife). seems rather obvious.
*if* god exists ????? Lol, if you start your worldview with : Let us assume god exists. Then you are open to believe and be convinced of any absurdities, because you can anytime bring an "I assume X exists" out of your hat. Homosapien born out of a virgin, water molecules turning into wine, man walking on water etc. etc. I don't think you remain within the realm of argumentation. It is a leap of faith which doesn't need justifications.
8:59 _"Truth is, as Peirce said, the opinion which is fated to be ultimately agreed to by all who investigate"_ If that is the case then we can interpret that to be some kind of asymptotical approach to truth, therefore never reached, and therefore the "principle of knowability", defined as : 9:56 _"For all propositions p if p is true then it is possible to know that p"_ would be rejected. So it seems that antirealists would NOT want to endorse the principle of knowability. Contrary to what is stated at 20:41, which would mean that non omniscience can be retained. Also. Isn't there a presupposition of epistemic transparency here ? In the proof at 19:20 you say _"if I know that p then p is true"_ justifying that assertion by saying that _"truth is a necessary condition for knowledge"_ (19:38) But you didn't demonstrate that the operator K can be applied to the operator K itself... You didn't describe how the operator behaves in that special case. What does K(Kx) means ? what does K(-Kx) means ? Is that a rule abiding use of the operator ? Can we really "know that we know x" ? Can we really "know that we don't know x" ? This would be needed in your _"epistemic principles"_ at 21:00
>> If that is the case then we can interpret that to be some kind of asymptotical approach to truth, therefore never reached Sure, we can interpret Peirce's comment in a way that is compatible with a realist theory of truth instead. But it is often taken as an antirealist theory, and all I was doing in that section is giving some examples of antirealist theories. I'm not particularly concerned about with Peirce actually believed. >> So it seems that antirealists would NOT want to endorse the principle of knowability Knowability is pretty much the definition of antirealism about truth. Of course, you can use the phrase "antirealism about truth" in a different way if you want. >> Can we really "know that we know x" ? Can we really "know that we don't know x" ? These phrases do not strike me as being any more problematic than any other use of the word "know", but sure, this seems like a plausible way to resist the argument. It may be that the epistemic principles are not as innocent as suggested.
@@KaneB Thanks for the answer ! *-"Knowability is pretty much the definition of antirealism about truth."* That is fascinating ! In the video you give an example of a realist take on truth with the correspondance theory of truth (CTOT). So maybe I am wrong, but I took every other theories of truth to be anti-realist then... Because otherwise they would be the CTOT. I thought every theory of truth that doesn't refer to reality in its definition, that doesn't pretend that it describes reality, would not be "realist" about truth. Let's take the pragmatic theory of truth for example : _P is true if p is conducive to my goal(s)._ The principle of knowability applied on this theory of truth would be : _If p is conducive to my goal(s), then it is possible for me to know that p is conducive to my goal(s)._ That seems very dubitable. But then, if the principle of knowability is rejected by the pragmatist, you would therefore classify him as a "realist about truth" ? So saying that p is true if p is conducive to my goal(s) is a realist position ? At 6:15 you say : _"In general according to realist theories of Truth propositions are true or false independently of whether anybody can in principle come to know that they are true. [...] according to realist theories the truth is something that exists completely independent of us and our activities, we discover the truth."_ How can p be "conducive to my goal(s)" _"independently of me and my activities"_ ? Are my goal(s) _"completely independent of me"_ ? Do I _"discover"_ my goal(s) ?
@@KaneB *-"These phrases do not strike me as being any more problematic than any other use of the word "know", but sure, this seems like a plausible way to resist the argument. It may be that the epistemic principles are not as innocent as suggested."* I wonder if there isn't a paradox there ? When Socrates says _"all I know is that I know nothing”_ He is saying ∀x (K(-Kx)) Isn't there a contradiction here ? Isn't it possible to reproduce a liar sentence with a self reference of the knowledge operator ?
@@MrGustavier Correspondence theory is just one example of a realist theory of truth. I chose that example because it's the most popular, and I think it's easy to understand. There are different ways of drawing the realism/anti-realism distinction. Per how I'm defining it here, yeah, it may be that some pragmatist theories land on the realist side (which isn't that surprising; the pragmatist tradition has always presented itself as a via media between realist and anti-realist approaches in different domains). Ultimately, I don't think much of importance hangs on this... We can, if you like, drop talk "realism" vs "anti-realism" entirely, and just talk about theories that reject KP and theories that accept it.
@@MrGustavier Oh yeah, Socratic statements do look paradoxical. I agree that one way of avoiding the contradiction would be to deny that the knowledge operator can be applied to itself. I assume there will be other possible solutions in this case though. For instance: we could say that the Socratic sentence is just false; that despite his protests, he knows other things.
Ok. Before getting into this, is this where you are going to talk about information and truth and that there's not really a verification process outside of our senses (which can lie to us), and a degree of pragmatic functionality (i.e. if it works as truth, it is truth), which allows for other interpretations that may be equally "true". This is the basis of the scientific method which is about process of elimination and also at the same time relies on cumulative information in which "truth" also has to fit within the framework of that cumulative knowledge which again, empiricism and is basically a game of Jenga. And nothing is definitively true, only that it's the theory that has also survived our process of elimination which is also subject to our imagination and, furthermore, there's the divorce from language and actuality so there's that too... Every theory of truth has to some de
In the physical world, a truth is that which has an effect on something else. And in that sense, even an untruth is a truth. So if knowing something means being consciously aware of it, then that means that all propositions are true. For example, Orson Welles' radio broadcast of a martian invasion was a complete concoction, yet it had an effect on conscious beings, therefore it's propositions were true. No? Furthermore, Ceci n'est pas une pipe.
Whenever I utter the sentence, "Frank Zappa was a scrambled egg", the air around my mouth moves. My utterance causes the air to move. Do you think this makes it true that Frank Zappa was a scrambled egg?
Alternatively: propositions are the meanings of sentences, utterances, beliefs, etc. Propositions are abstract and as such have no causal powers at all. The sentence "snow is white" has various effects, as does the sentence "schnee ist weiss". But the meaning that is expressed by these sentences -- both express the proposition -- doesn't do anything. So all propositions are false?
Orson Welles' radio broadcast was a fiction: its proposition (in the view of fictional world theory of Doležel and Pavel) corresponds not to this world but to a (possible) fictional world. (Doležel views fictional worlds not as real worlds but as artifacts/models/constructs similar to physical theories and math equations) They are true in that world but they don't correspond to our world. Their Mars is our Mars only to the extent that these two inter-world counterparts agree and the process of fictionalisation gives fictional Mars many properties that our does not (for example the fictional Mars hosts a declining civilisation, our does not). There is much more that can be said about the truth value of fictional statements but this might be a useful view in this discussion. Anyway, we cannot treat fictional statements in the same way we do statements about real people and things.
@@KaneB I think it's plausible that Dr. Baker knows all those truths On a more serious note: I think epistemic principle (A) is suspect One can believe that "p and q" while not believing that "p" and believing that "q", that's logically possible as far as I see So you knowing that "p and q" will not entail that you know that "p" and know that "q" since you could still lack belief in one of the conjucts What dk you think about that?
@@onion4062 Yeah, so when I forget things they stop being true. I should note that strictly speaking, in this context "K" is usually interpreted as "is known by somebody at some time", so forgetting wouldn't be a problem for the extreme antirealist. If I know that P at t1, then P is true period, at all times, even those later times when I forget P.
@@justus4684 This reminds me of the conjunction fallacy. A common error in reasoning about probability is that people will judge conjunctions to be more probable than either conjunct. For instance, people are presented with this question: "Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations. Which is more probable?: (a) Linda is a bank teller. (b) Linda is a bank teller and is active in the feminist movement." A lot of people judge that (b) is more probable than (a). So if people can judge that a conjunction is more probable than its conjuncts, then yeah, it seems that believing a conjunction will not entail believing each conjunct. Whatever degree of credence we take to be sufficient for belief, some people will have that credence in (b) but not (a). Of course, we could modify the principle to say that if you know that "p & q", then you can come to know that "p" and you can come to know that "q". Perhaps the argument could still go through with a weaker principle like this.
That's not a paradox! A fact being not known is outside of consciousness. Once the fact is known you just know it, you don't know at the same it's not known so there's your paradox going out the window. This is like saying how do you know reality is what appears to be, well isn't doubting coming from your experience of reality so if you doubt reality, you should doubt your doubting of reality... well, NO. Not knowing and doubting is the absence of certainty it's an expansion, it's not a concrete form of a fact which excludes all other facts. I feel philosophers are just making stuff up so they would have something to talk about.
>> Once the fact is known you just know it, you don't know at the same it's not known so there's your paradox going out the window I'm not seeing how this addresses the argument. The issue is with: (U) p is true and p is not known If there are unknown truths, then (U) must be part of the set of all truths. If all truths are knowable, it must possible to know (U). But it isn't possible to know (U), because knowing (U) would involve knowing that p and knowing that p is not known. >> I feel philosophers are just making stuff up so they would have something to talk about. So what if it is?
@@KaneB Obviously in the Ideal case of knowing all facts, it shouldn't be possible to state facts about not knowing stuff since that's a paradox but the paradox is resolved by the mere fact we know the stuff we didn't know about in the past. The proposition that "p is unknown truth" is outside of consciousness, meaning you can't say it, it exists outside of your perception. Once you know it, then you just know "p". You are just messing up contexts of consciousness and without consciousness. It's not really a paradox. There are no paradoxes in Nature, Nature is just what is. You're basically saying...I know the car works, then you crash the car and then you say, "that's a paradox because I know the car works but it's crashed now". That's why I said the paradox goes out the window, it's resolved from the very order of actions. You can't have a statement about not knowing facts in a all knowing scenario since the very statement is a product of a different scenario and then you are surprised there's a paradox. You see my point? As a fan of Philosophy myself, I find philosophers honestly wasting their time with little riddles like this one.
@@youtubehatesfreespeech2555 No, I don't see your point. If anything, it feels almost like you're explaining why it is that the paradox arises, rather than showing how the paradox is avoided. Perhaps it would be helpful to talk about one of the more formal presentations of the argument. Which step of the argument do you object to? >> I find philosophers honestly wasting their time with little riddles like this Yeah wasting time is cool 😎
@@KaneB I guess "wasting" time is subjective but I personally feel there's more fundamental questions and truth is definitely one of them but I don't think it's that type of "paradoxes" which should be the main focus. I didn't want to be condescending or anything, in case you felt that, just to make clear. As far as the argument is concerned...when you say "p is unknown truth", that statement comes from a domain which is outside of consciousness. It's really impossible to say it about any concrete "p" which you could be potentially referring to. So the "paradox" you are referring to is really a logical contradiction from the very beginning. You don't know what you don't know. Again, knowing about not knowing a fact is technically impossible because it's not possible to formulate the initial premise...you are just speculating "there's p which is true but I don't know it, PERHAPS", but you can't know what p you are talking about because if you know it, "p" is a known truth. This is like saying "5" and "-5" are contradictory. They are not because they exist in different domains, in this case mathematical domains. The moment you know you don't know something, the true statement about you not knowing, is extinguished meaning it's not true anymore. And that's why the paradox doesn't exist. You can't "know something while the thing you know is unknown" which is the basis of your argument, if there's nothing to be known. Much like 5+(-5)=0. So yeah, all truths are knowable but in that specific case that "truth" is extinguished so there's no paradox.
@@youtubehatesfreespeech2555 >> So the "paradox" you are referring to is really a logical contradiction from the very beginning You think it's contradictory to assert that there is an unknown truth -- i.e. that there are some propositions that are true, but that we don't know are true? In that case, it seems like you just reject non-omniscience. Which is fine of course, but obviously the knowability paradox isn't targeting your position anyway. >> you are just speculating "there's p which is true but I don't know it, PERHAPS" It's not speculation, it's an assumption... and the argument begins with that assumption in order to show that it is false, at least when conjoined with the knowability principle. So I'm really puzzled about what your objection to the argument is. If anything, you seem to be making the stronger claim that non-omniscience cannot be accepted regardless of whether we accept the knowability principle.
For the purposes of following this argument, the difference between them is probably not that important. However, they are distinct: "→" is the conditional, i.e. "P→Q" - "If P then Q", which in this context can be taken to be the material conditional, so "P→Q" is true when either P is false or Q is true. Note that "→Q" is nonsensical; this is not a well-formed formula. "⊢" means "logically entails". "P⊢Q" means that Q is derivable from P. Moreover, "⊢Q" is perfectly sensible; it means that Q is derivable from the empty set, i.e. derivable from the rules of the system alone. Basically, Q is a tautology.
In the order they appear in the op: 1. |- means syntactic entailment. Basically, there's a proof using rule-based string manipulation. 2. -> is the logical symbol for implication/conditional 3. => is the metalogical symbol for meta-conditional (sometimes, by some authors) While {A} |- {B} => Ø |- {A->B} in a lot of logics, which makes it seem like they all mean the same thing, there is a subtlety that's easy to overlook. Entailment works with sets, implication works with, and only with, variables in the language, and meta-implication allows us to say things about the object language without getting caught in a definitions problem. Without all that, we couldn't prove squat!
@@KaneB *-""⊢Q" is perfectly sensible; it means that Q is derivable from the empty set, i.e. derivable from the rules of the system alone. Basically, Q is a tautology."* Doesn't "⊢Q" mean that Q is an axiom of the system ?
Ok. Before getting into this, is this where you are going to talk about information and truth and that there's not really a verification process outside of our senses (which can lie to us), and a degree of pragmatic functionality (i.e. if it works as truth, it is truth), which allows for other interpretations that may be equally "true". This is the basis of the scientific method which is about process of elimination and also at the same time relies on cumulative information in which "truth" also has to fit within the framework of that cumulative knowledge which again, empiricism and is basically a game of Jenga. And nothing is definitively true, only that it's the theory that has also survived our process of elimination which is also subject to our imagination and, furthermore, there's the divorce from language and actuality so there's that too... Every theory of truth has to some de
![[TH] 2024 PMSL SEA W2D1 | Fall | ต่อเนื่อง ในสัปดาห์สอง](http://i.ytimg.com/vi/ElcO9uC_Dbk/mqdefault.jpg)
Babe wake up, new Kane B video just dropped
These videos are exactly what I've been looking for. Just straight up philosophy, nothing flashy, no intellectual masturbation or clickbait. Just straight up good content. Keep it up
Nice video!
I hope you'll do a video presenting counter-arguments to the paradox.
I'm planning on doing that, but I can't make any promises!
I took modal logic a few years ago and thought I'd never use it again since I mostly work on mind and ethics. Feels kind of nice to know exactly what's going on formally lmao.
My intuition is that the logical process breaks down in the first step, because 'p' is ill-defined.
Notably, this logical chain is impossible for any *specific* example _p,_ since either we know that statement is true/false, in which case it doesn't match the definition of _p,_ or we don't know whether it is true, so we cannot assert that it meets the definition of _p._ In a way, 'p' defies the axiom of choice, because even though it allows many potential candidates, the very act of choosing a specific _p_ makes that statement no longer satisfy the definition of _p,_ and thus no longer a valid choice. It's sort of the equivalent to a statement like 'the smallest number that cannot be described in less than thirteen words'.
You make a good point. But there is a difference between assuming p is true and knowing that p is true. For example, many mathematicians have proven results assuming that the Riemann hypothesis is true. Yet obviously we don’t know whether or not it is.
Unless I misunderstood you, it seems you have a problem with non omniscience?
@@BennettAustin7 The way he formally defines non-omniscience is as the statement 'there is a proposition p such that p is true and it is not known', but hidden in that definition of non-omniscience is the ability to choose a specific proposition 'p' from the set of true but unknown propositions. I would restate and accept non-omniscience more generally as 'there exist propositions that are true but are not known to be true', but reject the use of the axiom of choice to select a specific proposition p which can be used in his logical chain.
Having considered if further though, I think the more fundamental problem is with his use of the 'Known' operator in his logical statements; the axiom of choice is just a good way to break it. The truth value of whether something is known or not isn't universal - whether a proposition is known to be true must be able to change over the course of a proof if it is to mean anything. So I'm not even sure Kp∧¬Kp is even a contradiction in the normal sense. After all, the very act of proving any proposition p necessitates moving from ¬Kp to Kp over the course of the proof, so this contradiction occurs in all possible proofs, not just this specific one about antirealists.
Ideally we could fix K to have a consistent truth value by adding a time component, i.e. K(p,t) meaning 'p is known at time t', but that leaves our proof as:
1. p∧¬K(p,1) - p is true and is not known at step 1 to be true.
2. ∀p(p→♢K(p,2)) - p is true implies p is known at step 2 to be true for all p.
3. ♢K((p∧¬K(p,1),3) - it is possible to know at step 3 that p is true and that p was not known to be true at step 1.
4. ♢(K(p,3)∧K(¬K(p,1),3)) - it is possible that p was known at step 3 to be true, and that p was known at step 3 to be not known to be true at step 1.
5. ♢(K(p,3)∧¬K(p,1)) - it is possible that p was known to be true at step 3 and that p was not known to be true at step 1.
Which means that rather than being a contradiction, this is just an explanation of how learning something works.
hello Kane, just wanted to say these videos are really informative and i love to learn philosophy from you. thank you so much!
To progress the knowledge paradox research programme, we would first find a counter-example to falsify the proof and then revise the proof to overcome the falsification in a way that produces further understanding.
Sometimes I succeed at this; sometimes not. I took symbolic logic, but was an econ major Sometimes I am not creative enough, but here goes:
The crux of this proof is that there are special rules for the K predicate that allows p to be derived from (K)p. On one hand, it is strange that if I (F) a cat, that does not imply the cat exists. On the other hand, the idea that there exists a predicate that can make a statement true is also counterintuitive. Like: I did something to a statement to make that statement true. Bouncing between these ideas, we can grow the research programme.
It seems that there has been no exposition of knowers versus propositions known. If there is an instance of a thing both known and unknown, then surely there may be a different knower (or epistemic agent, perhaps), for each.
I do love me some sentential logic and logical connectives!
Given the central position is paradoxical then it's interesting to discover whose day job involves being a realist and whose an anti realist by trade. Social scientists tend towards being realists contrasted to anti realist theoretical physics given quantum entanglement of particle observation. Who then are the moderates? Probably comedians and artists whose day job requires contrary interpretations of reality.
Would love to see a follow up video!!
It is rather troubling that antirealists seem to be motivated by an appeal to consequences. If truth were based in correspondence, then all these terrible things would be true. If your home were on fire, that would arguably be even worse, so to be consistent we also ought to be antirealist about the fire for the same reason we are antirealist about truth. In any antirealist theory that is based on such an appeal to consequences, there ought to be a principle that says something like: if p being true would entail bad things, then p is false.
Second half of the video is a very good example illustrating why doing non-typed multimodal logic is bad.
What is truth? A mobile army of metaphors, metonomies, and anthropomorphism.-Fred Nietzsche
Infirmation is not knowledge. Knowledge is not wisdom. Wisdom is not truth. Truth is not beauty. Beauty is not love. Love is not music. Music is the best.-Mary, stuck to seat 38 of Phydeax III
KO only works with onmicience if given with these logical terms.
Does formal notation take a while to get a grasp on? I get it's usefulness to those who are familiar with all the symbols but as an absolute beginner, it's like translating something I already don't understand into a language I don't speak just to revert it back into English and confirm I still haven't a clue what I'm looking at😅
Idk if I'm just slow on the uptake or if it's normal to be this confused...
probably the former.
Honestly tho, it can be tough to get use to at first, but so much of philosophy is vague meaningless drivel; formalising an argument in logic is soooo refreshing sometimes
nah ull get used to it
Its just some good old "modal logic". Read a bit bout it on wikipedia, get to know what the glyphs mean and you should be fine.
What if you made the claims less vague; doesn't the paradox dissolve:
• P is not known by any human on Jan 1, 1970
• P is known by myself on Jan 20, 2038
I see truth as an adjudication/evaluation and such is always contingent upon the criteria being used for adjudication and/or the process of evaluation such that any claim of truth with regard to reality is also contingent upon what the term denote with regard to the evaluator/process? (AI system will definitely blur the minor distinction that I am making to total absence, which even as I type this is dwindling )
Consider the proposition(s): Does red exist? Does morality exist?
What does the term exist mean? 1) That which can have interactivity? That which can be claimed to be an aspect of what is observed? Something else?
I don't denote red or morality to be existent. However, this is generally not a point of issue UNLESS various philosophical interlinkages are in play, since in general terms I can usually identify what is meant by usage and a strict consideration of ontological status is not required for the broad point being expressed.
My question to you...
*What would be your proposal for reconciling the various models of evaluation that are employed by different people?*
I take it this is a question for the realist, since the realist holds that truth is independent of our means of evaluation? To be clear, I'm not a realist. I'm just presenting the knowability argument in this video; I don't think it's a convincing case against antirealism.
Maybe I'm missing something. What would be the consequence of simply admitting that not all true prepositions are knowable in principle?
There isn't anything particularly problematic about realism; indeed, this is the conventional view of truth. The knowability paradox is a problem specifically for antirealist views of truth.
I feel like there is something strange going on here with the phrase "is known". Who or what exactly is counted as knowing things here? I guess it means "is known by any human" but that seems pretty arbitrary, what if my cat knows something that I don't? I was reminded of a discussion about pan-psychism that I heard recently, would that let you get around this paradox by just saying that everything knows about itself in some sense? Also if you believe in an omniscient god then I guess there's no paradox since non-omniscience just wouldn't apply? I suppose either of those scenarios would basically be indistinguishable from the realist position though...
Anyway, I guess I'm just kind of confused by the anti-realest position in general. Like, what if I hop into a black hole to see what it's like in there, but then I can't escape and get squashed. Is the stuff I see inside the event horizon true since I know about it, or is it untrue since I can't get the information out? Or what about distant galaxies beyond the observable universe or in a multiverse or something. We might not be able to know anything about them, but there's no reason there couldn't be aliens living in those places that do know about them.
but doesnt this just imply that some truths i cannot know simply in virtue of my knowing them would make them false. Like i couldnt know that im dead, for example, cuz knowledge requires consciousness (assume no afterlife). seems rather obvious.
This seems vaguely familiar.
As a theist, I have to believe all truths are known. If God exists, and if he's omniscient, he would have to know every true proposition
*if* god exists ????? Lol, if you start your worldview with : Let us assume god exists. Then you are open to believe and be convinced of any absurdities, because you can anytime bring an "I assume X exists" out of your hat.
Homosapien born out of a virgin, water molecules turning into wine, man walking on water etc. etc. I don't think you remain within the realm of argumentation.
It is a leap of faith which doesn't need justifications.
Based on
@@whatsinaname691 Based on the definition of omniscience
What is the saying p & unknowable p to us ı didnt understand that is that saying what is the p or when we sayes the p are we sayin the Knowable p
İf we taked the all p are knowable p thats cannot be thats impossible
8:59 _"Truth is, as Peirce said, the opinion which is fated to be ultimately agreed to by all who investigate"_
If that is the case then we can interpret that to be some kind of asymptotical approach to truth, therefore never reached, and therefore the "principle of knowability", defined as :
9:56 _"For all propositions p if p is true then it is possible to know that p"_
would be rejected.
So it seems that antirealists would NOT want to endorse the principle of knowability. Contrary to what is stated at 20:41, which would mean that non omniscience can be retained.
Also.
Isn't there a presupposition of epistemic transparency here ?
In the proof at 19:20 you say _"if I know that p then p is true"_ justifying that assertion by saying that _"truth is a necessary condition for knowledge"_ (19:38)
But you didn't demonstrate that the operator K can be applied to the operator K itself... You didn't describe how the operator behaves in that special case. What does K(Kx) means ? what does K(-Kx) means ? Is that a rule abiding use of the operator ? Can we really "know that we know x" ? Can we really "know that we don't know x" ? This would be needed in your _"epistemic principles"_ at 21:00
>> If that is the case then we can interpret that to be some kind of asymptotical approach to truth, therefore never reached
Sure, we can interpret Peirce's comment in a way that is compatible with a realist theory of truth instead. But it is often taken as an antirealist theory, and all I was doing in that section is giving some examples of antirealist theories. I'm not particularly concerned about with Peirce actually believed.
>> So it seems that antirealists would NOT want to endorse the principle of knowability
Knowability is pretty much the definition of antirealism about truth. Of course, you can use the phrase "antirealism about truth" in a different way if you want.
>> Can we really "know that we know x" ? Can we really "know that we don't know x" ?
These phrases do not strike me as being any more problematic than any other use of the word "know", but sure, this seems like a plausible way to resist the argument. It may be that the epistemic principles are not as innocent as suggested.
@@KaneB Thanks for the answer !
*-"Knowability is pretty much the definition of antirealism about truth."*
That is fascinating !
In the video you give an example of a realist take on truth with the correspondance theory of truth (CTOT).
So maybe I am wrong, but I took every other theories of truth to be anti-realist then... Because otherwise they would be the CTOT.
I thought every theory of truth that doesn't refer to reality in its definition, that doesn't pretend that it describes reality, would not be "realist" about truth.
Let's take the pragmatic theory of truth for example :
_P is true if p is conducive to my goal(s)._
The principle of knowability applied on this theory of truth would be :
_If p is conducive to my goal(s), then it is possible for me to know that p is conducive to my goal(s)._
That seems very dubitable. But then, if the principle of knowability is rejected by the pragmatist, you would therefore classify him as a "realist about truth" ?
So saying that p is true if p is conducive to my goal(s) is a realist position ?
At 6:15 you say :
_"In general according to realist theories of Truth propositions are true or false independently of whether anybody can in principle come to know that they are true. [...] according to realist theories the truth is something that exists completely independent of us and our activities, we discover the truth."_
How can p be "conducive to my goal(s)" _"independently of me and my activities"_ ? Are my goal(s) _"completely independent of me"_ ? Do I _"discover"_ my goal(s) ?
@@KaneB *-"These phrases do not strike me as being any more problematic than any other use of the word "know", but sure, this seems like a plausible way to resist the argument. It may be that the epistemic principles are not as innocent as suggested."*
I wonder if there isn't a paradox there ?
When Socrates says _"all I know is that I know nothing”_ He is saying ∀x (K(-Kx))
Isn't there a contradiction here ?
Isn't it possible to reproduce a liar sentence with a self reference of the knowledge operator ?
@@MrGustavier Correspondence theory is just one example of a realist theory of truth. I chose that example because it's the most popular, and I think it's easy to understand.
There are different ways of drawing the realism/anti-realism distinction. Per how I'm defining it here, yeah, it may be that some pragmatist theories land on the realist side (which isn't that surprising; the pragmatist tradition has always presented itself as a via media between realist and anti-realist approaches in different domains). Ultimately, I don't think much of importance hangs on this... We can, if you like, drop talk "realism" vs "anti-realism" entirely, and just talk about theories that reject KP and theories that accept it.
@@MrGustavier Oh yeah, Socratic statements do look paradoxical. I agree that one way of avoiding the contradiction would be to deny that the knowledge operator can be applied to itself. I assume there will be other possible solutions in this case though. For instance: we could say that the Socratic sentence is just false; that despite his protests, he knows other things.
Ok. Before getting into this, is this where you are going to talk about information and truth and that there's not really a verification process outside of our senses (which can lie to us), and a degree of pragmatic functionality (i.e. if it works as truth, it is truth), which allows for other interpretations that may be equally "true". This is the basis of the scientific method which is about process of elimination and also at the same time relies on cumulative information in which "truth" also has to fit within the framework of that cumulative knowledge which again, empiricism and is basically a game of Jenga. And nothing is definitively true, only that it's the theory that has also survived our process of elimination which is also subject to our imagination and, furthermore, there's the divorce from language and actuality so there's that too...
Every theory of truth has to some de
In the physical world, a truth is that which has an effect on something else. And in that sense, even an untruth is a truth. So if knowing something means being consciously aware of it, then that means that all propositions are true.
For example, Orson Welles' radio broadcast of a martian invasion was a complete concoction, yet it had an effect on conscious beings, therefore it's propositions were true.
No?
Furthermore, Ceci n'est pas une pipe.
Whenever I utter the sentence, "Frank Zappa was a scrambled egg", the air around my mouth moves. My utterance causes the air to move. Do you think this makes it true that Frank Zappa was a scrambled egg?
The king of France is bald!
Alternatively: propositions are the meanings of sentences, utterances, beliefs, etc. Propositions are abstract and as such have no causal powers at all. The sentence "snow is white" has various effects, as does the sentence "schnee ist weiss". But the meaning that is expressed by these sentences -- both express the proposition -- doesn't do anything. So all propositions are false?
@@KaneB No, but it causes me to have to process that information. And someone else might actually think it true and cause them to go into a frenzy.
Orson Welles' radio broadcast was a fiction: its proposition (in the view of fictional world theory of Doležel and Pavel) corresponds not to this world but to a (possible) fictional world. (Doležel views fictional worlds not as real worlds but as artifacts/models/constructs similar to physical theories and math equations) They are true in that world but they don't correspond to our world. Their Mars is our Mars only to the extent that these two inter-world counterparts agree and the process of fictionalisation gives fictional Mars many properties that our does not (for example the fictional Mars hosts a declining civilisation, our does not).
There is much more that can be said about the truth value of fictional statements but this might be a useful view in this discussion. Anyway, we cannot treat fictional statements in the same way we do statements about real people and things.
What's the solution? 😳
If you're asking me personally: I don't really see this as a problem because I'm fine with accepting that all truths are known ¯\_(ツ)_/¯
@@KaneB Do you never forget things?
@@KaneB
I think it's plausible that Dr. Baker knows all those truths
On a more serious note:
I think epistemic principle (A) is suspect
One can believe that "p and q" while not believing that "p" and believing that "q", that's logically possible as far as I see
So you knowing that "p and q" will not entail that you know that "p" and know that "q" since you could still lack belief in one of the conjucts
What dk you think about that?
@@onion4062 Yeah, so when I forget things they stop being true.
I should note that strictly speaking, in this context "K" is usually interpreted as "is known by somebody at some time", so forgetting wouldn't be a problem for the extreme antirealist. If I know that P at t1, then P is true period, at all times, even those later times when I forget P.
@@justus4684 This reminds me of the conjunction fallacy. A common error in reasoning about probability is that people will judge conjunctions to be more probable than either conjunct. For instance, people are presented with this question:
"Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations. Which is more probable?:
(a) Linda is a bank teller.
(b) Linda is a bank teller and is active in the feminist movement."
A lot of people judge that (b) is more probable than (a). So if people can judge that a conjunction is more probable than its conjuncts, then yeah, it seems that believing a conjunction will not entail believing each conjunct. Whatever degree of credence we take to be sufficient for belief, some people will have that credence in (b) but not (a).
Of course, we could modify the principle to say that if you know that "p & q", then you can come to know that "p" and you can come to know that "q". Perhaps the argument could still go through with a weaker principle like this.
That's not a paradox! A fact being not known is outside of consciousness. Once the fact is known you just know it, you don't know at the same it's not known so there's your paradox going out the window. This is like saying how do you know reality is what appears to be, well isn't doubting coming from your experience of reality so if you doubt reality, you should doubt your doubting of reality... well, NO. Not knowing and doubting is the absence of certainty it's an expansion, it's not a concrete form of a fact which excludes all other facts.
I feel philosophers are just making stuff up so they would have something to talk about.
>> Once the fact is known you just know it, you don't know at the same it's not known so there's your paradox going out the window
I'm not seeing how this addresses the argument. The issue is with:
(U) p is true and p is not known
If there are unknown truths, then (U) must be part of the set of all truths. If all truths are knowable, it must possible to know (U). But it isn't possible to know (U), because knowing (U) would involve knowing that p and knowing that p is not known.
>> I feel philosophers are just making stuff up so they would have something to talk about.
So what if it is?
@@KaneB Obviously in the Ideal case of knowing all facts, it shouldn't be possible to state facts about not knowing stuff since that's a paradox but the paradox is resolved by the mere fact we know the stuff we didn't know about in the past. The proposition that "p is unknown truth" is outside of consciousness, meaning you can't say it, it exists outside of your perception. Once you know it, then you just know "p". You are just messing up contexts of consciousness and without consciousness. It's not really a paradox. There are no paradoxes in Nature, Nature is just what is.
You're basically saying...I know the car works, then you crash the car and then you say, "that's a paradox because I know the car works but it's crashed now".
That's why I said the paradox goes out the window, it's resolved from the very order of actions. You can't have a statement about not knowing facts in a all knowing scenario since the very statement is a product of a different scenario and then you are surprised there's a paradox. You see my point?
As a fan of Philosophy myself, I find philosophers honestly wasting their time with little riddles like this one.
@@youtubehatesfreespeech2555 No, I don't see your point. If anything, it feels almost like you're explaining why it is that the paradox arises, rather than showing how the paradox is avoided. Perhaps it would be helpful to talk about one of the more formal presentations of the argument. Which step of the argument do you object to?
>> I find philosophers honestly wasting their time with little riddles like this
Yeah wasting time is cool 😎
@@KaneB I guess "wasting" time is subjective but I personally feel there's more fundamental questions and truth is definitely one of them but I don't think it's that type of "paradoxes" which should be the main focus. I didn't want to be condescending or anything, in case you felt that, just to make clear.
As far as the argument is concerned...when you say "p is unknown truth", that statement comes from a domain which is outside of consciousness. It's really impossible to say it about any concrete "p" which you could be potentially referring to. So the "paradox" you are referring to is really a logical contradiction from the very beginning. You don't know what you don't know.
Again, knowing about not knowing a fact is technically impossible because it's not possible to formulate the initial premise...you are just speculating "there's p which is true but I don't know it, PERHAPS", but you can't know what p you are talking about because if you know it, "p" is a known truth. This is like saying "5" and "-5" are contradictory. They are not because they exist in different domains, in this case mathematical domains.
The moment you know you don't know something, the true statement about you not knowing, is extinguished meaning it's not true anymore. And that's why the paradox doesn't exist. You can't "know something while the thing you know is unknown" which is the basis of your argument, if there's nothing to be known. Much like 5+(-5)=0. So yeah, all truths are knowable but in that specific case that "truth" is extinguished so there's no paradox.
@@youtubehatesfreespeech2555 >> So the "paradox" you are referring to is really a logical contradiction from the very beginning
You think it's contradictory to assert that there is an unknown truth -- i.e. that there are some propositions that are true, but that we don't know are true? In that case, it seems like you just reject non-omniscience. Which is fine of course, but obviously the knowability paradox isn't targeting your position anyway.
>> you are just speculating "there's p which is true but I don't know it, PERHAPS"
It's not speculation, it's an assumption... and the argument begins with that assumption in order to show that it is false, at least when conjoined with the knowability principle. So I'm really puzzled about what your objection to the argument is. If anything, you seem to be making the stronger claim that non-omniscience cannot be accepted regardless of whether we accept the knowability principle.
what is the difference between the "⊢" and "→" and "⇒"; don't they all just mean entails?
For the purposes of following this argument, the difference between them is probably not that important. However, they are distinct:
"→" is the conditional, i.e. "P→Q" - "If P then Q", which in this context can be taken to be the material conditional, so "P→Q" is true when either P is false or Q is true. Note that "→Q" is nonsensical; this is not a well-formed formula.
"⊢" means "logically entails". "P⊢Q" means that Q is derivable from P. Moreover, "⊢Q" is perfectly sensible; it means that Q is derivable from the empty set, i.e. derivable from the rules of the system alone. Basically, Q is a tautology.
In the order they appear in the op:
1. |- means syntactic entailment. Basically, there's a proof using rule-based string manipulation.
2. -> is the logical symbol for implication/conditional
3. => is the metalogical symbol for meta-conditional (sometimes, by some authors)
While {A} |- {B} => Ø |- {A->B} in a lot of logics, which makes it seem like they all mean the same thing, there is a subtlety that's easy to overlook. Entailment works with sets, implication works with, and only with, variables in the language, and meta-implication allows us to say things about the object language without getting caught in a definitions problem. Without all that, we couldn't prove squat!
@@KaneB *-""⊢Q" is perfectly sensible; it means that Q is derivable from the empty set, i.e. derivable from the rules of the system alone. Basically, Q is a tautology."*
Doesn't "⊢Q" mean that Q is an axiom of the system ?
Ok. Before getting into this, is this where you are going to talk about information and truth and that there's not really a verification process outside of our senses (which can lie to us), and a degree of pragmatic functionality (i.e. if it works as truth, it is truth), which allows for other interpretations that may be equally "true". This is the basis of the scientific method which is about process of elimination and also at the same time relies on cumulative information in which "truth" also has to fit within the framework of that cumulative knowledge which again, empiricism and is basically a game of Jenga. And nothing is definitively true, only that it's the theory that has also survived our process of elimination which is also subject to our imagination and, furthermore, there's the divorce from language and actuality so there's that too...
Every theory of truth has to some de