Let me start with explaining some basics of logic. To illustrate that I will use two statements:
P = clouds reach degree X of saturation
Q = clouds produce rain
P --> Q means P entails Q. In normal English it means: If clouds reach degree X of saturation, clouds produce rain. Every weatherforcast is based on that fact. And now comes the logic into play.
A. Suppose P is true and Q is true. That is the normal situation. When it rains and you check the saturation in the clouds you will find degree X.
B. Suppose P is true an Q is false. That is a very odd situation. It is not raining, though saturation is degree X. That can't be possible, for if it were possible, no reliable weatherforcast as shown in A would be possible anymore.
So we must come to the conclusion that when I know that P and P entails Q then we may say that we know Q too, or in technical terms: the epistemic status of P and Q are equivalent.
What is most important to understand here is a fundamental epistemological principle: this is a guiding principle in deductive reasoning.
C. You can say .....wait. I can think of more situations. Suppose there are no clouds and yet it is raining. That is absurd too.
No it isnt. That degree X of saturation causes clouds to convert into rain, does not imply that there cant be any other cause for rain. If P is false and yet it is raining, it only means that we need to do some more research on causes of rain.
D. Hold on! I got another one: P is false and Q is false too, heheh .... ^_^ Come on, you are joking. Of course you are right: look outside...it is a sunny day with a clear blue sky.
Now look at the reasoning I showed you in my former lecture:
If (P) I know that I sit at my computer, then (Q) I know that I am not a brain in a vat.
I do not know that I am not a brain in a vat. So,
I do not know that I sit at my computer.
What is the way of the skeptic? He attacks the Q in P --> Q. He says, that there is no way to establish the truth of Q, that is, I have no way to find out whether or not I am a brain in a vat, because whether I am in a vat or not, my sensory experiences are all the same.
The emphasis here is on KNOWING things and as we saw, one way of obtaining knowledge is by deduction.
But I have no means to be certain of Q, I can't know it. There is no escape here, by principle I have to admit that this means the I can not KNOW for certain that P. Are you still with me? ^_^
What is here the big philosophical lesson to learn?
If we want to show that the skeptic is wrong, we have to show that the way he interprets the entailment (P --> Q) is wrong.
If what I have said so far wasn't easy for you and I can understand. You also can imagine that showing that the skeptic is wrong, isn't easy either. But , yes, it has to be on this technical level of logic and epistemology, that we have to face the skeptic.
Let us summarize: The skeptic does not take things for granted. He may deny the existence of God, other minds than his own, a world of material objects behind what is immediately given to our senses,
anything other than himself and his experiences , even his own mind as anything but a set of experiences (David Hume (1711-1776), objective moral values,
the possibility of getting any knowledge other than by the senses, or by the Inductive Principle, or even by reason itself.
Alternatively, the skeptic may simply doubt these things rather than deny them outright, and skepticism may be simply a methodological theory. So you can be a skeptic in various degrees.
I hope you are not disappointed about the fact that I did not come up yet with a plethora of refutations of skepticism
Based on what I have said so far we may conclude, that philosophers arent lunatics who tell you there doesnt exist a real world and that everything is just the product of your private imagination. That is not the philosophical problem.
The problem is that we say that we KNOW this real world, which might lead to the conclusion that we can be 100% sure that there is just one material world of which we can have clear , undubitable and certain knowledge, a kind of absolute truth asit were.
So this means that we would be able to obtain knowledge that is derived from an unshakable outside (our minds) source. That is what skepticism questions. Not that we can have knowledge, but the absoluteness and certainty of that knowledge.
This has important consequences. It means for instance that we have knowledge of the universe. We look through telescopes, receive data from satelites and so on.
Is there a way to be absolutely certain that the way we see the universe is how the universe really looks like? Or looks the universe just the way we look at it?
When discussing our first question about the origin of the universe we already ran into serious trouble understanding our situation. So these are not such a simple questions at all.
Now that I have clarified the way a skeptic reasons, I hope you will agree with me, that we definitely need another lecture to discuss the possibilities of finding a way out of skepticism or to consider the option: is skepticism that bad at all? This is a real adventure.
[13:31] herman Bergson: quod dixi dixi :-)
[13:31] herman Bergson: So far on the logic (of skepticism)
[13:32] Gemma Cleanslate: ah
[13:32] ChatNoir Talon: So, the question is focused on epistemology, skepticism or both?
[13:32] herman Bergson: The focus is actually on entailment...
[13:33] Ze Novikov: can you make your proposition into a logical equation??
[13:33] Thoth Jantzen: if it weren't for skepticism, we'd never have invented the wheel, let alone be sitting here discussing this. ;o)
[13:33] herman Bergson: Our logical axiom that P --> Q where Q is false cant be a true deduction
[13:33] ChatNoir Talon: Then we'd probably have to define first what do we mean by "is" :P
[13:34] herman Bergson: No...you could see it like this....
[13:34] Ze Novikov: P does not equal Q but Q might equal P?
[13:34] herman Bergson: P is a set ....say [a,b,c,d,e]
[13:34] Ze Novikov: the variable being x
[13:34] Ze Novikov: yes
[13:35] herman Bergson: so when you know P you also KNOW [a,b,c,d,e]
[13:35] itsme Frederix: http://en.wikipedia.org/wiki/Entailment (some background reading)
[13:35] herman Bergson: well...maybe you dont know ...say a, yet you have to deduce it from P if P is true
[13:35] ChatNoir Talon: See? That's my problem right there.. I don't think we can actually KNOW anything... I believe we can think, infer, believe, suspect, deduce, etcetera, but to me knowing means having infallible truth
[13:35] Bittersweet Lime: that must not be the case - think of the set of real numbers - an ordered set, we know it - tell me the first member! :-)
[13:36] Thoth Jantzen: that depends on whether or not what you know about P is complete, no? and what it 'entails'.
[13:36] herman Bergson: Wait....
[13:36] herman Bergson: We not yet have defined what it means to say I KNOW P
[13:36] Gemma Cleanslate: ah yes
[13:36] ChatNoir Talon: right
[13:36] herman Bergson: that is question 19 ^_^
[13:37] Gemma Cleanslate: lol
[13:37] herman Bergson: What is important here is that you see here the heart of deductive reasoning
[13:37] itsme Frederix: should it be known that P , or can it exist on itself
[13:37] herman Bergson: to say that a is true because P is true means....do research..verify your deduction
[13:38] herman Bergson: Popper however would say....show that a is NOT true....than P is FALSE
[13:38] herman Bergson: again a theory down the drain..:-)
[13:39] Bittersweet Lime: that would be wrong - an effect can be true even the cause is non existing - there might be other causes
[13:39] herman Bergson: What I meant by saying that this lecture was special to me is, that today I could write down this text completely understanding what it is all about...
[13:39] Daruma Boa: thats true
[13:39] herman Bergson: this is one of the cornerstones of our thinking
[13:40] ChatNoir Talon: :)
[13:40] ChatNoir Talon: Ah
[13:40] Gemma Cleanslate: you OWN it
[13:40] herman Bergson: What do you mean BitterSweet?
[13:40] herman Bergson: I would say when you deduce a from P and a is false then P is false
[13:41] Bittersweet Lime: I referred to the sentence before - if a is not true - then b has to be false - that is not a valid conclusion
[13:41] herman Bergson: no no...that wasnt the conclusion
[13:41] Bittersweet Lime: [13:38] herman Bergson: Popper however would say....show that a is NOT true....than P is FALSE
[13:42] itsme Frederix: what if P did not exist, what about a
[13:42] herman Bergson: And what is special to me too is that is is completely clear how skepticism critizices our way of thinking if it is about absolute truth
[13:43] herman Bergson: That is a completely different question Itsme...
[13:43] Thoth Jantzen: hmm
[13:43] herman Bergson: that is an ontological question....
[13:43] itsme Frederix: but often used in discussions
[13:43] herman Bergson: then it is the wrong argument...
[13:43] itsme Frederix: agree
[13:43] Thoth Jantzen: i think 'truth' is the question - how does 'absolute' add to the word?
[13:43] herman Bergson: In logic you dont talk about what exists and what not..that is a semantic issue of reference..
[13:44] Cailleach Shan: I know that I don't know what I don't know.
[13:44] herman Bergson: You talk about TRUE and FalSE only
[13:44] itsme Frederix: isn't "truth" not ontological
[13:44] herman Bergson: no...
[13:44] herman Bergson: you can call it whatever you like....blue , green..square
[13:44] Thoth Jantzen: truth, in my view, is context dependent. some things may be true in specific contexts, or across many...
[13:45] herman Bergson: Wait...
[13:45] itsme Frederix: truth is a sence of true/false but more then just true - it got worth in it
[13:45] herman Bergson: Here we are using a number of meanings of the word truth...
[13:45] herman Bergson: In logic it is just a word...computers call it 1 and 0
[13:46] itsme Frederix: only binairy computers
[13:46] Bittersweet Lime: truth is always related to something - you cant reason without relations - so you have to have axioms - and so truth is realtive to those axioms
[13:46] herman Bergson: Yes...you could say that...
[13:46] Thoth Jantzen: context
[13:46] Thoth Jantzen: :o)
[13:46] Cailleach Shan: Does a 'foundation statement' have to be 'true' to make deductive reasoning.
[13:46] herman Bergson: But that isnt an ontological issue
[13:46] itsme Frederix: truth is a statement - true just a fact
[13:46] herman Bergson: Let me explain..
[13:47] herman Bergson: this is a serious issue in philosophy....
[13:47] herman Bergson: With Wittgenstein....a statement is true when the state of affair occurs
[13:47] Bittersweet Lime: proof systems are always related to systems - there is no proof without to assume some axioms
[13:47] herman Bergson: that is an ontological interpretation of truth...
[13:48] herman Bergson: It deals with the fact that the statement refers to something that is not the statement
[13:48] herman Bergson: and that is exactly our issue here
[13:48] Thoth Jantzen: well like bitter said...
[13:48] Thoth Jantzen: such a statement and what it refers to constitute a 'system', no?
[13:48] herman Bergson: is there an external world to which statements indubitably refer to?
[13:49] herman Bergson: no BitterSweet....you are right....but here the axioms are the philosophical problem
[13:49] Thoth Jantzen: the same as an observer and the observed do as well.
[13:49] Bittersweet Lime: it is irrelevant - it would be a system and have axioms
[13:49] herman Bergson: where did you get them from
[13:49] itsme Frederix: Herman at least you propose an external observer
[13:50] Gemma Cleanslate: :-)
[13:50] herman Bergson: What do you mean Itsme?
[13:50] itsme Frederix: you talk about statements
[13:51] itsme Frederix: maybe observer is to weak, creator
[13:51] Bittersweet Lime: see, a statement is meaningless if you dont have a relation - I will show you - ajrakllkasdrklsd s arjls jaj rkla sdklrj kl - that is my statement - now what does it mean?
[13:51] herman Bergson: yes ... and the way they are declared true is the problem.....true in the sense that you can say I KNOW that P
[13:52] itsme Frederix: I KNOW is in a way passive, you might say I CREATED that
[13:52] Gemma Cleanslate: i guess we will have to research that
[13:52] Bittersweet Lime: you cannot make statements without a relation to something you already know - and this goes back until you have axioms - which you assumed to be valid
[13:52] herman Bergson: You forget the problem of the difference between meaning and reference Bittersweet
[13:53] herman Bergson: I agree Bittersweet....but how to jsutify your axioms?
[13:53] Bittersweet Lime: there is no justification - the nature of axioms is that they are assumed and create a system
[13:53] Samuel Okelly: i agree that axioms are, as bitter says, "assumed" or "believed" to be true but on what do we base this belief?
[13:53] herman Bergson: Are they undubitable knowledge, beliefs, guesses?
[13:53] itsme Frederix: axioms are truly created
[13:53] herman Bergson: Yes Itsme but how?
[13:53] herman Bergson: Based on what?
[13:54] itsme Frederix: lazyness
[13:54] Cailleach Shan: lol
[13:54] itsme Frederix: common business
[13:54] ChatNoir Talon: Based on an agreed reality between the ones observing said axioms, right?
[13:54] itsme Frederix: agreement
[13:54] herman Bergson: Falling back on axiomatic systems doesnt solve our philosophical question
[13:54] Jangle McElroy: Aren't axions ' self evident ' - as in ' water is wet'
[13:54] itsme Frederix: tautology is another thing
[13:54] ChatNoir Talon: But water may be dry if iced... oy this is giving me a head ache :p
[13:54] herman Bergson: Jangle...self evident and a tautology arent the same
[13:54] Bittersweet Lime: axioms are the building blocks to create systems - so they can be anything - if wrong or not is irrelevnt - you can create an invalid system as well with those
[13:55] Ze Novikov: can wet equal frozen?
[13:55] herman Bergson: The skeptic claims that we have no proof of an external world...that is the issue here..and axioms wont solve that
[13:55] Thoth Jantzen: depends on our definitions...and supporting axioms, i gues, no?
[13:56] Bittersweet Lime: what do you mean by external?
[13:56] Thoth Jantzen: not ALL skeptics claim that...
[13:56] herman Bergson: True Thoth..
[13:56] Thoth Jantzen: some claim we are all part OF the same world, looking at it from different perspectives within it.
[13:56] herman Bergson: By external I mean independent of our sensory experiences
[13:57] itsme Frederix: but in a way axioms mark the border of "external"
[13:57] Bittersweet Lime: ah, then australia is external to me
[13:57] Jangle McElroy: Sorry, you lost me mentioning tautology itsme / herman - 'Water is wet' isn't tautoogy in my understanding.
[13:57] ChatNoir Talon: Australia is extrernal to most
[13:57] itsme Frederix: axioms do not belong to the system but found it in a external (nothingness)
[13:58] herman Bergson: That is a philosophical view Itsme :-)
[13:58] Gemma Cleanslate: i see this continuing on thursday
[13:58] Gemma Cleanslate: :-)
[13:58] herman Bergson: At least Australia is far away for me ^_^
[13:58] Qwark Allen: indeed
[13:58] Qwark Allen: cya then
[13:58] itsme Frederix: well at least its a view and at least some avatars see it
[13:58] Bittersweet Lime: but the conclusion is wrong that they would have to be founded "in" something at all - they can be abstract
[13:58] ChatNoir Talon: You can fortune-tell, Gemma :-)
[13:58] Cailleach Shan: lol Oz is my cousin..
[13:59] Daruma Boa: bye q
[13:59] Daruma Boa: and gemma
[13:59] itsme Frederix: abstract foundings why not, no problem
[13:59] Bittersweet Lime: like math - it is constructed inwhere?- inside nothing - it is simply there - we discover its rules
[13:59] Thoth Jantzen: umm
[13:59] Thoth Jantzen sits on his hands
[13:59] ChatNoir Talon: lol
[13:59] herman Bergson: Ok....I think you all have enough questions to do research on now till Thursday :-)
[13:59] Gemma Cleanslate: oh ok lol
[13:59] Gemma Cleanslate: yes
[14:00] ChatNoir Talon: Yay! Homework!.. oh, wait... that's not fun...
[14:00] herman Bergson smiles
[14:00] ChatNoir Talon: :P
[14:00] herman Bergson: You are free to do as yo like
[14:00] Cailleach Shan: I need a little lie down.....my brain hurts.
[14:00] ChatNoir Talon: Right with ya Cailleach
[14:00] itsme Frederix: well we can add Bayes to entailment and explore other worlds of reasoning
[14:00] herman Bergson: Ok...
[14:01] herman Bergson: Re -read this lecture and discussion in the blog
[14:01] herman Bergson: Watch out NEW URL
[14:01] Samuel Okelly: attempting to find "proof" for "belief" will take more than just one more lesson i think herman :)
[14:01] Daruma Boa: think i must^^
[14:01] Ze Novikov: Tyvm herman and see you all next time, same place, same dimension...
[14:01] herman Bergson: http://thephilosphyclass.blogspot.com
[14:01] Daruma Boa: hope to have time on thursday^
[14:01] Thoth Jantzen: for me, 'knowing' is 'believing' to a very high degree of probability....
[14:01] herman Bergson: Sure Ze..with pleasure ^_^
[14:02] ChatNoir Talon: Thanks for the class Herman! ^^
[14:02] itsme Frederix: Good structured Herman, nice lecture
[14:02] Daruma Boa: blogger is not foud says it
[14:02] Thoth Jantzen: ...high enough so the knowledge likely won't get refuted in this lifetime, anyway.
[14:02] Cailleach Shan: Thanks Herman.... I will continue breathing in and out! That's all I really know for sure.
[14:02] Thoth Jantzen: ;o)
[14:02] herman Bergson: MAYDAY...TYPO!!
[14:02] ChatNoir Talon: daruma, Herman made a typo :P
[14:02] Gemma Cleanslate: ♥ Thank Youuuuuuuuuu!! ♥
[14:02] Gemma Cleanslate: Herman
[14:02] Daruma Boa: oh ha, herman^^
[14:02] Gemma Cleanslate: see you thursday all
[14:02] ChatNoir Talon: http://thephilosphyclass.blogspot.com
[14:02] herman Bergson: http://thephilosophyclass.blogspot.com
[14:03] ChatNoir Talon: Bye y'all!
[14:03] Daruma Boa: yeah, better
[14:03] Daruma Boa: thanks
[14:03] Daruma Boa: bye gemma^
[14:03] Alarice Beaumont: thanks Herman.. i will have to reread all that....too much conclusions and false and true lol
[14:03] herman Bergson: ok Alarice...
[14:03] herman Bergson: Getting it in the blog first thing in the morning
[14:07] herman Bergson: Thank you all
Stephen Law will be lecturing at Open Habitat on Saturday 6 June at 11:30am to 12:30pm
(which is 7:30pm to 8:30pm Linden time) and you are all invited. There will be an update between now and then on the details (the group it is running through is The Open Habitat Project) which can be found in search.