Are you claiming to know this? How? According to your own account (if I understand it correctly) all knowledge is dependent on (some sort of) derivation from an initial “epistemological set”, the members of which cannot be validated. Also (if I understand you correctly) the validity of a statement (by which I mean the sort of statement which would pass for “knowledge” in this discussion, perhaps a proposition) depends both on the means by which that statement was arrived at and the validity of the statements it depends on. If that’s the case, your claim to know the above statement is somewhat shaky according to your own system, as you must have started with a non-validatable “epistemological set”, the non-validatedness of which carries through to that statement.
To return to smaller sentences, isn’t some misuse of the phrase “to know” going on around here? After all, everybody everywhere has known stuff, if not as much as they might have thought they did. If a philosophy arises that claims nobody can know stuff, isn’t it reasonable to claim that what they calling “knowing” isn’t what “knowing” really is?
Definitions are tautologies: a repetition of the same meaning in different words.
All axioms are “valid” within the field they define. It is not impossible to conceive a reality in which thought is an illusion. It is even possible to build a religion around that idea. In such a world, “thought exists” may still be taken as axiomatic, but it would represent a poor match to reality.
If you mean “valid axiom” in a way other than “accurately representing reality” then please explain how you want the phrase defined.
tominator2
No. I am claiming to be able to demonstrate it with logic. Thus, it is valid only under epistemologies which contain logic. If you wish to have our discussion under the rules of an epistemology that denies logic, please explicate one. It might be an interesting exercise.
You are correct. Well, you would be correct if I were claiming that my position represented an ultimately “valid” epistemological statement. In fact, my statement is not a member of the set of epistemological statements. It is, under Russell and Whitehead’s Ramified Theory of Types, a member of hte class of statements about epistemologies.
Really, though, that distinction is not vital in this case. Even without Russell’s constructions I could simply note that, as I did above, that I am making no claim to an absolute epistemological basis for my statement. It is entirely possible that logic is not valid. If such is the case, then my logical arguments may or may not be valid. Remember, if logic is not valid then we cannot use logic to decide that conclusions based upon an invalid epistemology are, in fact, invalid.
Words can be used in many ways. We understand this. Aynrandlover and I agreed to approach this subject as rigorously as we are able given the restrictions of time and format. Under that agreement, “know” is taken to represent a conclusion derived from a valid epistemological set.
It is not a misuse of the phrase to agree upon a particular definition.
You know, I think I’ve figured out your argument style, if it can indeed be called a style, and why I was always so quick to turn you into a strawman. You don’t actually claim anything (well, mostly you don’t), just point out inconsistencies in other’s arguments. Tricky bastard.
Anyway.
Is there some kind of term for the cless of propositions about epistemology? How is this not an epistemology in itself, even if on a different logical level? I’m blurring on this one.
We have, then, a set of epistemologies in which at least the first member of each element of the set is unable to be valid/invalid (that particular term has no meaning). But it seems to me that we also cannot ascribe validity to our propositions-about-epistemology, at least so far as the first element of that class.
So where does that leave us? Truth is conditionally true, in so far as it matches the axioms&definitions used to find it out? This is terrible! That means that not only can’t we actually “know” anything, but we can’t even be sure that we know that we don’t know, or that we don’t know that we don’t know (in fact, we really might know!) This almost turns science into a religion. ALMOST.
Um . . . haven’t we been discussing for days the basis and ramifications of my claim that there can be no valid basis for any set of epistemologies?
Besides, I prefer to think of my style as “a strong stock of reason spiced with arrogance, sarcasm, and just a hint of whimsy”.
This is why I use Russell and Whitehead’s foundation. The distinction does blur when you think of everything as nested sets which might be subsets of themselves. The RToT makes the distinction explicit. It also allows us, as I have mentioned before, to avoid those nasty Godel statements and other paradoxes of self-referentialism.
Perhaps it helps to realize that while the class of propositions about epistemology is not itself a proposition about epistemology, and a proposition about epistemologies is not an epistemology, the method we use for constructing that structure is an epistemology.
Or perhaps that doesn’t help.
Of course not. If we could ascribe validity with certainty at any point in the process we would have a natural “starting point” from which to derive all else. As I mentioned to Tomniator2, none of this applies under a system in which logic is invalid. Where logic holds, though, we can be assured that our reasoning also holds.
We have no way of “knowing” whether logic truly holds in our universe(s), but I find it difficult to frame a coherent position without it. Thus, I choose to act as if it holds [sub]at least with respect to this conversation. My continued support of certain sports teams obviously functions under an epistemology devoid of logic[/sub].
That might indeed be terrible, but it is not where we are left.
A statement is valid/true within an epistemological set if it is derivable from the axioms and definitions of that set. It is valid/true with respect to our universe(s) to the extent that the axioms and definitions of that epistemological set match the nature of said universe(s).
We have no epistemologically valid means of determining the extent of that match. In any epistemology in which logic holds, we can never have such a means.
Hey – if you’re going to be terrified, be terrified of the real thing.
Not at all. Science does not concern itself with questions of epistemological basis. Science asserts materialism, logic, etc. and draws conclusions accordingly. Science does not assert that it is a complete epistemology, or that it is an absolutely correct epistemology, merely that it is a useful epistemology.
Personally, I use single malt whiskey. Tonight, it’s a Glendronach sherry cask.
I’m unsure about what you mean by “demonstrate”. It sounds like “prove” but I’m sure you want to avoid that word. In any case, logic without a set of axioms is doomed to not be able to say much. Any logical argument you present will draw on those axioms, and will be valid only insofar as those axioms hold. Which leads to your next sentence:
Which is true, but not equivalent to the statement, “Thus, it is valid under all epistemologies that contain logic”. So it would appear that it is possible that an epistemology could exist that would include logic yet not lead to your conclusion.
Better than that, it sounds like fun. In any case, my previous text block should explain why I don’t feel that that’s necessary. It has not (imho) been shown that, “for all epistemologies that contain logic, the validity of the original member of its epistemological set is unverifiable” because the argument used to demonstrate this claim is both self-undercutting (because it depends on an axiom it itself asserts is unverifiable) and not powerful enough (because it makes a claim about all possible logics which I (at least) can’t see the backing for).
Hooray!
Rats!
Ultimately is a tricky word here. Do you mean to say that your position is only provisionally or temporarily valid? You claim:
Are you claiming that statements of that sort are not objects of knowledge? If they’re not, we’re in trouble. If they are, than an epistemology applies to them. In any case, even if your (2nd-level) argument about (1st-level) epistemologies looks correct, there is no reason to accept it because you haven’t laid out a basis for the valid evaluation of 2nd-level arguments. There’s a nasty infinite tower looming here.
Waitaminute…
We actually DO know what we know. Why? If we can reduce epistemologies down to god axioms and infinite regressions, we see that we cannot “validate” (know) our initial axioms and such because there is no method for their evaluation. Thus, “know” has no meaning. “Know” is an action of validation by an epistemology. Talking about knowing the beginnings of epistemology is like talking about what exists outside the universe or what happened before the big bang…it is a meaningless statement.
Now, under my previous God Axiom which I will restate (and correct an error in): “Logic is a necessary, but not sufficient, base for epistemology.”
This cannot be “known” in a strict sense because knowledge hasn’t been defined yet (as we would need an epistemology for it) and cannot be validated without using an epistemology based off it without creating a tautology. There is no “assumption” that any epistemologies even exist, merely that if one did, it would need to have logic as a part of it.
One could form the argument that logic doesn’t exist yet, but that would be (somewhat) incorrect. Logic itself is not necessarily an epistemology (Russell included ), it is merely a set of propositions, definitions, and conclusions reached within its own framework. That you will include logic in an epistemology doesn’t make it an epistemology in itself. Nothing, of course, is *stopping *you from declaring logic its own epistemology, but good luck as this thread has borne out.
So, as long as you have an epistemology, you “know” that you know. Otherwise, knowledge is an empty term.
As well, the definition of self may be completely arbitrary under my axiom and not fall into an turtle stack because until the epistemology is completed knowledge is still a meaningless term.
This leads us to a wide variety of problems (as some might see it, anyway). Off the top of my head:
The idea of “I” can be pretty arbitrary.
The entire scope of mathematics cannot be considered to be “known” without a self-referential paradox or a tautology of multiple steps.
The application of mathematics to observational reality (if/when it becomes a part of epistemology) is completely ad hoc unless there is an axiom which allows this (in which case, the axiom is just as arbitrary)
However, the best of all outcomes eminates from it:
We really know that we know what we know.
As well, does epistemology necessarily include ontology? As in, must we begin with epistemology and use it to derive ontology and other metaphysical ideas?
Now, to “know” we exist it must come first. However, it seems to me that there is no way for epistemology to create/derive the idea of being or self (ontology). It would need to be defined…and very likely will lead to another tautology.
I used the word demonstrate because I have not presented a formal proof of logic. I have presented a line of reasoning and a structure which supports my conclusions. That is a demonstration.
I have no idea why you are sure I want to avoid the word proof. There is no reason to avoid it.
Yes.
Indeed. I phrased it in that manner quite specifically. I have explicitely used Russell and Whitehead’s Ramified Theory of Types in developing this argument. Perhaps you recall seeing that in some of my posts? Thus, in an epistemology in which the RToT does not hold, my argument would not be valid. Now, I used RToT because I think it lends clarity to these issues. I also use it becuase Russell and Whitehead showed that the formal structure they created was sufficient base for mathematics, which makes it a powerful tool, indeed.
It is not, however, the only logic developed to deal with sets. It is quite simple to generate a self-referential paradox in any epistemological set which allows itself to be a member of itself. Personally, I do not find such paradoxes enlightening, but if you like them then we can function under a more classical set theory.
There are also logics which allow no mention of sets at all. Under those logics, we can say nothing about the set of epistemologies.
Have we beaten this horse enough, yet?
Nice quibbble. I should have specified that denies Russell’s Theory of Types and classical set theory.
Now, if you have an alternative logic of sets which you would like to introduce, please do so. If you would like to discuss the paradoxes raised by constructing a set of epistemologies from classical set theory [sub](we have glossed them already, but we can be more specific if you wish)[/sub], please say so. If you have an argument for a non-arbitrary epistemological set, please share it.
I disagree, with the clarification made above. My result holds for any epistemological set under which RToT holds. A slightly modified argument generates an even quicker paradox under classical set theory. Your two objections are not pertinent because:
1: The argument is not self-undercutting. It is stipulated to hold only where the logic upon which it is based holds. As stated before, anyone is free to argue a counter position under an epistemology in which neither classical set theory nor RToT is valid. 2: The argument does not claim to hold for all possible logics. Indeed, I know of no way to enumerate the set of all possible logics. I find the ability to speak to any epistemology allowing the appropriate theories of sets to be quite powerful enough.
Not so tricky. Ultimate should be read as “derived from an unambiguously valid epistemological base”. Temporary has nothing to do with it. Must I again clarify the set of epistemologies under which my argument holds?
I am stating that under RToT a proposition about epistemologies is not an epistemology. This is, in fact, the hallmark of the Theory of Types. Have I not been crystal clear about that? This can indeed seem counterintuitive. All I can do, really, is refer you to Russell’s work or to a decent summary thereof. It does not mean “we are in trouble”. It means we have used a structure which allows us to discuss epistemology without running immediately into syntactic or semantic paradoxes of self-referentialism.
Quite the contrary. I have explicitely relied upon an established theory of classes.
Not really. There is no need for an infinite recursion.
The argument holds in a stipulated set of epistemologies. It can be evaluated within each such set without paradox. The same set of epistemologies, in each case, allows us to frame the statement: The argument holds in a stipulated set of epistemologies.
There is no need to climb above the second floor, so to speak, since the argument is stipulated only under epistemologies which allow us to make the statement.
Now, please do not confuse that with an argument that the epistemology which allows us to frame the statement is “ultimately valid”. I have quite explicitely been arguing that no such case can be made. Indeed, if it were possible to demonstrate such a result, we would have a rather gordian paradox.
I agree, but allow me to rephrase your position so that it is clear what I am agreeing to: knowledge is entirely dependent upon the basis for the epistemology under which it is derived. Said basis is necessarily arbitrary.
re: G.O.D
I do not think so. It does not seem impossible to create epistemologies devoid of logic. For instance: English sentences that end in vowels are true.
Not particularly useful, perhaps, but certainly possible.
I think you are incorrect, here. Logic is certainly a theory of knowledge (well, several theories of knowledge, really.) Perhaps we are having a confusion of terms, here. What do you mean by “logic” and “epistemology” in that sentence?
I think perhaps you are using epistemology here in a sense that includes some measure of “completeness” with respect to a determinable universe. Your statement above is “logically true”, but I think you are implying something deeper which is not true.
Correct. Or else “I” can be explicitely derived from an arbitrary basis.
Correct. Well, correct if you include “an arbitrary selection of axioms” in your list. [sub]I think. It might be possible to reduce every conceivable mathematical axiom down to a tautology, but I sure don’t feel like trying it.[/sub]
Correct. [sub](Well, I reserve the right to quibble about the exact phrasing “ad hoc” should this horse start taking a beating, too, but I agree with the sentiment.)[/sub]
But only within our epistemological set, which has an arbitrary basis.
Well, one can perhaps conceive a minimal ontology which places no concern upon how one knows the nature of being. In such cases there would be no overlap with epistemology. But in general, ontology relies upon at least an implicit epistemology. (IMO – i make no claims to being complerhensively read in all branches of philosophy.)
Well, as stated above it might be derived from an arbitrary basis. But your thrust is correct: it is no more possible to find a non-arbitrary basis for knowledge of self than for any other knowledge.
First, There’s something I think you missed. I posited that logic was a necessary but not sufficient part of epistemology. That is, every epistemology needed logic, that one could have a logic-only epistemology, but logic alone isn’t in all epistemic systems.
As you might note, I must retract my comment that logic itself isn’t an epistemology. By any means it is. I don’t know what I was thinking.
Now, I do maintain that there can be no epistemology without logic. That is a strange argument indeed, but I feel it is absolutely true. I find that anyone who could challenge that would be a strange one indeed. I don’t think anyone can. This, of course, requires realizing that “logic” is a pretty blanket term for a system of propositions and reasoning-about-propositions. Any system does this, even if it doesn’t follow what would normally be considered “logical.”
However, this leads me a Russell query. We have a logic, which is an epistemology. Now, we wish to make another epistemology that includes this logic. Does it include it as a set within a set, or does it include it en todo? As it, for true rigor should it devolop the logic in tha same manner? If it can include it as a set-within-a…well, within a what is the question. Would this be a class? If rigor demands the logic be developed instead, are these to sets, then(logic alone and logic with additional props), members of the same class? You see what I mean? I’m still trying to grasp this heirarchy. I think I’m getting there, don’t give up on me yet!
Here you say “But only within our epistemological set, which has an arbitrary basis” in order to qualify my point that we really do know what we know. I find that “arbitrary”, rigorously speaking, is as useless as “knowledge” in reference to epistemological axioms. Would you agree that, strictly speaking, it is a meaningless term when used there? But then, I think we both agreed on that anyway. It still makes sense to use from where we’re standing now.
Damnit, we are going to create a SDMB Epistemology here before this thread ends! What better way to fight ignorance that to show that we really do know what we know?
Now, where do we get “self” from…or is there one? Tune in next week when our heroes fight it out in “Battle Arena Epistemology!”
Well, it would be possible to have a non-logical epistemology, in which we were passive recipients of sensory or other data whose validity we were unable to pass on rigorously. In fact, on some views, we do have that epistemology.
However, in general I think that your point that logic is essential to every epistemology is, though not quite true, still a valid point, in that any “active” epistemology that attempts to figure out the Truth, or whether there is a Truth, or even a truth, or whether a truth can exist, requires the use of logic to pursue its ends.
However, when you generalize on what a functional epistemology might be, you begin to stereotype!
But really, my point in saying that logic was a non-removable part of epistemology was to make a generalization of logic. We are so used to many of the general tenets of “logic” that I think we miss a very important point. Logic really is just a set of propositions and a structure of reasoning. It doesn’t mean that “logic” follows what we normally think of as “logic” per se. I find this distinction illuminating and important.
Ah, I feel better now. I’d thought you were using RToT to obtain a general result, where you were actually both using it and limiting yourself to just those epistemological sets under which RToT holds.
You bet. Counter-intuitive enough to be the topic of another thread “Is RToT a good way to think about epistemologies?” which would, one would hope, quickly get moved to the “Highly Specialized Debates (German bachelors only need apply)” area. Unfortunately that would mean the end of this thread, in which you have been both informative, and AFAICT, right.
I didn’t miss it; I simply disagree. I also disagree with your definition of logic: Logic really is just a set of propositions and a structure of reasoning. From that, I gather that you are implying that any structure or reasoning from propositions is a logic. To me, using the word in such a broad sense renders it all but meaningless. In fact, logic is generally taken to mean a method or set of principles for reasoning that allow for structured deduction and avoid direct contradiction. The last stricture, or course, is why the concept of paradox exists.
Regardless, even if we take your broad definition it does not apply to: English sentences that end in vowels are true.
The above is an epistemology. It allows us to differentiate valid knowledge from invalid knowledge. But it contains no structure for reasoning. Unless, of course, you view a direct test for validity as a “structure for reasoning”. If you do, then “logic is necessary for epistemology” becomes “epistemological tests are necessary for epistemology”, which would seem to be true, though not particularly interesting.
Polycarp has already mentioned the counterexample of a passive epistemology.
Consider, for simplicity’s sake, an epistemological statement to be a simple object (type 0). Any particular logic, then, is a class of epistemological statements (type 1). An epistemology containing logic is also a class of epistemological statements (type 1). All of the members of logic are also members of the epistemology which includes logic. Logic, however, is not a member of the epistemology which includes logic. A class may contain only objects of a lower order than iteself.
A class of epistemologies (type 2) can also exist which conatains logic, an epistemology inclucing logic, and other simple epistemelogicla statements. This class, however, is not an epistemology.
I may have fostered some confusion, here, because I sometimes use the word “set” when I should use “class”. Old habits are hard to break. A class is, basically, what we call a set under the theory of types.
If I did, I wouldn’t have used it.
I use arbitrary, in this context, to mean “not validated through any epistemological process”. The distinction I was trying to emphasize it that “We really know that we know what we know” is true within our epistemology but ultimately stands upon a hollow base.
Yes. But makes sense . . . is different from is true.
I do not know. But I assume one exists for the purpose of living.
tominator2
Yep. Though, as I say, using classical set theory gets you to the same place, but first you get all dizzied up in paradox, and you’ll regret it in the morning.
Well, it’s the best one I have been able to come up with. Classical set theory is useless. Group Theory really doesn’t seem to gain us anything over classical set theory, and I don’t feel up to formulating methods of epistemological operation anyway.
I wouldn’t mind burning a few brain cells on a new approach, though, if you have one in mind.
Hmmm.
“English sentences that end in vowels are true.”
How does this, even in a Russell way, avoid self-reference? It seems that if we accept this as our epistemology, then, we really would even know that our epistemology was right.
Seriously.
I was wondering whether you would see that. You are getting better at seeing the layered implications of my examples. I would seriously start to worry, if I could prove you existed.
First, the vowel epistemology is obviously a sentence in English.
But, it is also a proposition about English sentences. As such, it cannot be a member of the class “English sentences” in a semantic evaluation. This is not a case of paradox, but the same rules apply. Thus, RToT deals with circularity in the same manner as paradox (All English sentences that end with a vowel are false).
One way to think of this is that the vowel epistemology is not an English sentence under RToT.
Another (perhaps better) way to think of it is that the vowel epistemology as written is semantically empty under RToT. It seems well-formed, but in fact it has no meaning.
A way to rephrase the vowel epistemology to conform to RToT might be: English sentences not about English sentences are true if they end in a vowel.
Accept it based upon what?
Any self-consistent epistemology will “validate” its initial proposition. It would have to, since the tests for validity all derive from (or at least may not contradict) that initial element. This is the reasoning behind: The Bible is the inerrant word of God. I know this because the Bible tells me so.
Epistemologically, of course, this is no more invalid a position than one which declares circular reasoning to be invalid. We can never have assurance that either is based upon a solid foundation. But it is no more valid, either.
The “All english sentences that end in vowels are false” was riding me all day, haha. Wondered if you were going to say something about that.
But this brings me, invariably, to tominator’s point.
Is This theory of types a good way to think about epistemology? Why?
It seems to me that our classical set theory and “classical” ways of thinking about logical propositions will lead us down the path of paradox. Theory of types, when properly constructed, leads us away from paradox, but have we actually accomplished anything? As you noted, we simply “rephrase” things to stray away from self-reference.
But like the turtles…they are still there even if we choose not to look at them.
Or are there other advantages not yet discussed here?
