Logic Lecture: Epistemic Modal Logic and Rumsfeld Known Knowns and Zizek's Unknown Knowns

[supremeunknowledge]

The statements themselves are logically ill-posed when you consider the definition of knowledge. If you know that you do not know something, then by definition you know that you do not know it, and just that fact is contained in the set that you do know. On the other hand, you are correct that UK is a contradiction. Although, KU sounds plausible, Zizek has failed to realize that it is a subset of KK and not disjoint.

[supremeunknowledge]

If such a set of possible combinations existed, then should it not form a group under negation? Regardless, the ZRC axioms do not support the set of all sets which do not contain itself. The statements KU, and UK would be equivalent to such a set (your brain does not contain all of what you know you don't know, just the fact that you know that you don't know it). You have stumbled across Russell's paradox...

[Klorrnond]

Can't we re-frase it as in terms of conscious knowledge? In that case we don't consciously know what we actually do know. I'm not a logician. But it seems to me that Zizek and Rumsfeld are treating knowledge and the awareness of that knowledge as similar, while they are not.

I wont even start on the symbols, because the only logica that I know, is the one that you teached me in the past 18 videos :D.

[fingerpickinggood]

I know that you know that you are an tattooed logician

[theforestero]

COOL ......



[DJGBNZ]

An example that I keep thinking of is parts of my unconsciousness brain that control homeostasis. Obviously the knowledge exists for homeostasis to function or I would not be alive. However I am unaware of that knowledge and unable to consciously control homeostasis.

[DJGBNZ]

I think your dictionary is incomplete. UK should read something like 'You are unaware that you know state of affairs delta'. You possess a knowledge that you are unaware of.

Having knowledge of x and being aware of the knowledge of x should be recognized as separate propositions. But this dictionary does not allow for that.

[kleban10]

Concerning UU, can you explain how Rumsfeld would know that he does not know delta, if that is a contradiction with his being unaware that he does not know?

[CroTuschek]

@kleban10 nah he knows that he doesn't know not-delta. read closer.

[jlke45]

I think the simple answer, pace he divine Zizek, that the "unknown know" is an incoherent concept.

[LeeJohnApeDor]

This is probably a bit late, but you should be able to symbolise it as the following:

First, treat unknown as a negation of the know operator. So unknown : ¬K

In the epistemic logic that I have used, you want to represent the agent and the intended proposition. So to say that c knows that A : KcA

For second order knowledge you should be able to symbolise all Rumsfeld's and Zizek's additions as the following:

KcKcA

Kc¬KcA

¬Kc¬KcA

and Zizek's is simply:

¬KcKcA

[Xelrog]

OK. I tried to follow up with all the comments. Coming from a computer science background my question is:

Are u sure that your language (epistemic modal logic) if capable of expressing something like the KU in the first place?

Because doesn't it include the axiom 4 (positive introspection)?

Wikipedia:

"The Positive Introspection Axiom, also known as the KK Axiom, says specifically that agents know what they know."

[Xelrog]

@Xelrog as a result the system may not be able to express the UK by its definition.

[NoGreyAndGreen]

The Unkown Known is no doubtably a lie hypothetically speaking.

In leymans terms... Rumsfeld does not know that he knows something because he is being decieved.

However, it seems to me that the U-K argument is slightly self defeating because its near to impossible to say you don't know that you know something because that's like saying you do know someything, as you explained in your video.

[ACARook]

@NoGreyAndGreen You are assuming a certain definition or ontology (what it *is*) of "knowledge"...There are philosophers who would probably say that knowledge is chiefly concerned with recognizing (although how this is don't is definitely up for debate) a certain thought-content in the head of the thinker. Like if the question arose "do you know the pythagorean theorem?" and we were able to peer into someones mind and see (or we were able to have them reproduce) a^2 + b^2 = c^2 ...

[ACARook]

Other philosophers would say that just having a certain thing in your mind isn't enough...for them knowledge is more performative...if I have no idea how to correctly apply the Pythagorean theorem then I can't be said to actually "know" it... I'm not sure where I come down on that but I will say that in that light it might not be a contradiction to say I don't know that I know...think about this like: "I can act as though I have a certain thing in my mind but not actually have it in my mind."

[1987ambrose]

I haven't got any formal idea what I'm doing at all, but it seems like the known and the unknown are different things on each side of some statements here. The things that we know that we don't know must actually be partially known in order to formulate that statement. They will 'use bombs,' 'Somewhere'. So things we 'don't know we know' are distinct from the knowledge. Like being able to store and recall data. Do you know something before you are made aware of the knowledge?

[VEGASINTN]

The U K means Kentucky will win the final four but that's a secret...uhhh ok thats a stretch great video

[bermarte]

not(K(R,D1)) ->K(R.D2)?

sorry, maybe does not make sense

[bermarte]

paraconsistent?

[drjasonjcampbell]

@bermarte hmm...I'll have to read more about this. Thanks for the heads up.

[bermarte]

@drjasonjcampbell

if u want, google for: Gent ambiguity adaptive logic (prof.Batens/prof.Vanackere)

basic idea is (P and not(P)) SOMETIMES is in reality (P1 and not(P2))..and not(P1 = P2)

:-) very nice channel!

thanks 4 your great videos!!

[bermarte]

maybe U and K could be sort of 2 different sets; with no relation..looks like a pseudo paradox-ambiguity

[izombiheartzoey]

Yo dude. Might be looking at this wrong. Isn't it a negation of a negation?

[Maarttttt]

Wow, I've never seen a black logician.

[drjasonjcampbell]

@Maarttttt LOL!! ...Funny, I was taught by a Black Logician, Kwasi Wiredu, great scholar!! But it is a new day my friend. Hope to see more young logicians of all shades doing advanced mathematical logic. Peace.

[TurloughMurphy]

wow!

I was drawn to revisit Rumfeld's speech today after reading about the Iraqi war logs that WikiLeaks published. it was there that I read Zizek's response and I ended up here! before I got here it made sense to me (they weren't really unknown knowns - we just didn't know them) but this discussion is on a different plane. one way above my head.

I'm intrigued though. I guess I'll just have to learn about philosophy (of which I know {known known} very little).

[tnvh]

It is much less complecated: the unknown know is the idiology or preconception or prejudice we don't realize. This is knowleg which we don't know that we have.

[drjasonjcampbell]

@cfpm I think you're exactly right. There's a branch of epistemic modal logic where we can discuss the collective knowledge of a group, but I think you're right we need to attribute that knowing to an outside observer The problem is, though I have gotten some really good feedback, as you've said is the "ignorant subject" I've looked through every modal book and there definitely isn't anything on the UK but symbolizing that hidden, latent knowledge is tricky because the agent doesn't know

[ACARook]

@drjasonjcampbell - Hi, couple quick things: 1) I'm not sure why you say that ~k(r)k(r) (the way you were about to symbolize the antecedent of UU) appears contradictory but you don't say that about the mere inversion k(r)~k(r) that exists as the consequent to both KU & UU. What makes U occurring in the antecedent (*logically*) a special case? In both cases you're asserting a simultaneous knowledge & lack of knowledge (or vice versa). Please correct about the logical intricacies if I'm wrong.

[ACARook]

@drjasonjcampbell -- Also, less logically and more theoretically, I tend to be a Wittgensteinian about knowledge. I would say that rather than having a certain thing in your head (and recognizing the presence of that thing or not depending on whether you're in KK or KU), knowledge can only be inferred by demonstration. I think a good example of UK is something like the implicit associations bias or the parity (across cultures) of responses to the Trolly-type cases.

[ACARook]

@drjasonjcampbell (CONT.) -- What's sufficient for saying that you "don't know that you know..." is that you repeatably & reliably act as if you have that thing in mind but it's something that you don't recognize as true (ie. the thought isn't something you would automatically assent to, say). I hope I'm not totally cold on this one & I have to say I appreciate your videos (particularly on Modal logic, which I'm trying to teach myself, I only went up through monadic predicate logic in school).

[ACARook]

Oh, and what about this as a (mixed) symbolization:

X is an Unknown Known to Rumsfeld (here) ⇔ K(r)X∙~K(r)K(r)X

That seems to me to describe what an unkown known is...you have to know it *and* you have to not know that you know it. But again, if I'm totally screwing up something with the symbolization, it's been a long time... :P

[drjasonjcampbell]

@ACARook You'll have to give me some time to think about that. It looks good, but its the initial K(r)X that may end up presenting a problem. But the structure looks good. Remember in the conjunct (A ∙ B) in order for the conjunct to be true both (A ∙ B) have to be true. Thus, I'm not sure on what ground K(r)X could be true though ~K(r)K(r)X looks fairly good. Can he properly be said to have ~K(r)K(r)X if the conjunct includes K(r)X which is a definitive claim of X, one requiring demonstration

[absinth1987]

For me the third case of this example, the unknown unknown, always was (and still is) the most problematical. Because how can one talk about ‘something’ when he isn’t aware of this ‘something’ at all? Because in the moment one signifies this ‘something’ it isn’t any longer ‘unknown’ in an ontological or epistemological sense. And when in this Modal Logic one signifies this ‘unknown’ with a Δ, the problem - I guess – remains the same …

[drjasonjcampbell]

@absinth1987 Thanks for participating in the discussion! The name of the video Zizek makes these statements is called "The Reality of the Virtual". I think I get his argument about the the Freudian unconscious, and I think ur interpretation is spot on. From an analytic point, how can we symbolize the UK? Within the tradition of epistemic modal logic, Rumsfeld's 3 point's can easily be sybolized, there is a syntax, but I don't know of a why to incorporate the the Freudian unconscious.

[drjasonjcampbell]

@absinth1987 I'm glad you brought up the Freudian unconscious, because they calim would be that this UK, is precisely what's sort of guiding our behavior. Since we don't know that we do know, we are in a sense guided by this suppressed knowledge. But, my question is from a logical standpoint can we claim to have this knowledge? Another viewer, soultourment27, spoke of the contrapositive, which is a great point, but it ends in the agent losing knowledge.

[absinth1987]

@drjasonjcampbell Yes we’re guided, but we’re instantaneously, in the daily situation not aware of this circumstance. Žižek maybe would answer in a reversing-rhetorical but nevertheless proper gesture that – from any standpoint, either logical or some other – the only solution for this problem would be to say that we don’t have this knowledge but rather that this knowledge have us.

[absinth1987]

@drjasonjcampbell And here things start to get really complicated, because now we have to think about what does it mean ‘to have knowledge’ and what does the ‘I’ stands for. Žižek would argue here for a decentering of the subject.

[drjasonjcampbell]

@absinth1987 You've really got me thinking. I think the decentering is spot on. And the analysis of what it means to "have knowledge" is also spot on. I'm recognizing that beneath Zizek's critique, even his political critique is a really really deep challenge to analytic philosophy. To be honest I'm more of a continental, I think the questions are more interesting. What is the "I", what does it mean? Ontologically speaking what is the "having" of knowledge?

[drjasonjcampbell]

@absinth1987 I want to know what the best minds in logic would have to say about the UK. I'm so captivated by this idea. I want to find a way to show that Zizek is right, but you're saying that the very attempt to demonstrate his rightness, itself presupposes the subject "I" AND it presuppose the "having", which is the point of his critique. The "having" is challenged by the unknown...I may have been constrained by the logic. I think you maybe right. Thank you SOOO much for that insight.

[absinth1987]

@drjasonjcampbell I’m not sure because I’m not into this Modal Logic stuff but if I would starting to think about the possibility of how to express the idea and the consequences of the concept of the unconscious in this formal language I first would guess that one has to try describing this in kind of a meta-level-perspective. One has to establish a transcendental ‘I’, the ‘I’ of the theory of the unconscious.

[absinth1987]

@drjasonjcampbell And then one has to assert that this ‘I’ is observing another ‘I’, and this observed ‘I’ is the one who is determined by its own unknown knowledge …

[absinth1987]

@drjasonjcampbell This detour via a transcendental observer (in lacanian theory the analyst or the ‘sujet supposé savoir‘ = ‚subject supposed to know) seems to be necessary due to the fact that the ‘I’ isn’t able to recognize itself as a whole, to objectify itself, it isn’t able to ‘have’ its own unknown knowledge ...

[drjasonjcampbell]

@absinth1987 WOW!!! lol...that's hardcore. Very, very interesting point. Continental philosophers did away with the subject object distinction a long time ago, but the question becomes, have we preserved the subject object distinction in our logic? Can you have (within epistemic modal) a non subject oriented logic? Lol! Wow i really like your line "we don’t have this knowledge but rather that this knowledge has us". That's an excellent point. It's incredibly difficult to understand.

[drjasonjcampbell]

@absinth1987 At the core of this question is a challenge which is directed at the heart of psychology, can claims of knowledge really be stated if we start be saying it is unknown. Your point of signification is well stated. If it's whatever it is, is unknown it does not refer to anything with the scope. you're right about that, it is outside the scope/set, of all things known. For the UU, it's not a problem, logically, it has its symbolization within the tradition. But not for Zizek's claim.

[absinth1987]

@francopalombo Yes, I think the concept of anxiety has much in common with the Lacanian Real, or more precisely with the Real of the Imaginary, therefore it is part of the excess of subjectivity over the Symbolic, it stands near to the subject’s knowledge of the inconsistency of the Symbolic Order, it thus signifies the lack of the lack of the Other and because of this simultaneously realizes that there is nothing beyond the Symbolic – and this is really frightening …

[absinth1987]

Well, I have no idea about Epistemic Modal Logic but I’m not sure if you’re getting the whole point of what Žižek is aiming at when you are trying to solve this problem with such an analytical approach. Žižek uses the Rumsfeld-Example of course to illustrate in a very demonstrative way, with such a basic logic-problem the notion of the Freudian unconscious. The unknown knowledge is the unconscious of the subject or in this case of the culture / the politic

[soultorment27]

Axiom 4 is (KP ---> KKP) and the contrapositive would be (~KKP ---> ~KP)

If S doesn't know that S knows P, then S doesn't know P! This is because knowledge entails truth and belief...

[drjasonjcampbell]

@soultorment27 Thanks a lot for such a quick response!! Would Zizek and Plato agree with the claim ~KP? Aren't they really trying to assert / demonstrate KP? And also we have to be careful of the gettier problem and the traditional critique of JTB in assuming that knowledge entails truth and belief. Maybe I'm making it a bigger issue than it needs to be but I'm trying to stay true to both Zizek and Plato's account and I'm not sure they'd agree with ~KP...I think they want KP from ~KP.

[soultorment27]

@drjasonjcampbell "we have to be careful of the gettier problem"

The gettier problem states that justified true belief is not sufficient for knowledge, but that doesnt mean that JTB is not necessary. Indeed it's pretty much universally accepted that one cannot have propositional knowledge unless one at least has JTB...

[drjasonjcampbell]

@soultorment27 thanks for your discussion! I guess the point of the video is to take seriously Zizek and Plato's claim, even the psychoanalytic claim that we can have knowledge of something we don't know. Clearly we understand the logic, but is there a place in the logic to accommodate the unknown knowns without it resulting in the denial of one's knowledge? I guess that's the point. I want to go further than the traditional discussion, way beyond that. Try to conceptualize something new.

[drjasonjcampbell]

@soultorment27 with respect to gettier and the JTB you're spot on. This is more of a conceptual question. Clearly the fact that we are engaging in this discussion means we get it...now let's try to push the limit a bit...If Zizek really means ~KP under what conditions could he genuinely claim KP? Like you, I don't see a logical way to do it, but that might be a limitation on my part (our part). Can you seriously claim KP from ~KP? That's the challenge. Do you see the question I'm trying to ask?

[soultorment27]

@drjasonjcampbell Hmmm I'll have to think about it. I'm really no expert on epistemic logic models...

Oh by the way have you ever seen Fitch's Paradox? It's not an actual paradox per se but it's an elegant proof. It's basically an attack on anti-realist positions who are committed to the thesis that all truths are knowable. The proof reduces the claim that all truths are knowable to the claim that all truths are in fact known! You should definitly check it out if you arent familiar with it...

[drjasonjcampbell]

@soultorment27 :-) Ur the man...never heard of it heading to google now. Thanks for the heads up! I'll let you know what I find. Peace. and thanks again.

[soultorment27]

@drjasonjcampbell Yeah I'll let you know what I come up with for the "unknown knowns". & Yeah definitly check out Fitch's Paradox, it's sometimes called The Paradox of Knowability. I've been working on adequate solutions for months to save anti-realist commitments lol