Glen – perhaps you can clarify things with some specific scientific examples. (Matt won’t respond to requests for practical situations>

You have stated “that scientists treat theories as provisional, but they do not treat knowledge as provisional. Knowledge is, after all, warranted true belief, so a scientist only knows something if he has become convinced that it is true.” – Now to me that doesn’t accomadate the dynamic, lively nature of scientific knowledge – or my own research experience. That, of course may be a matter of terminology – but I wonder if it is, at base, a different understanding of how knowledge is obtained.

I realise you are presenting an abstract philosophical definition. However, that is no use if it doesn’t have practical application. (It also concerns me that the practical application could well be opportunist and misleading. For exampole the claim of “biblical and theolkoiogcal truths”).

However, to take you example of the jellybean jar. Sure, before investigation people can have “beliefs” about the number of beans. Now – we have sighted 135 beans and the claim can be made that there are 135 jellybeans in the jar.

From your perspective:
Is that a “theory”? Or is it “knowledge”?

I would also like you to clarify your claim that “theories are not knowledge. Theories may or may not be true. Knowledge is true.” Again this doesn’t correspond to my experience.

Its best to clarify this with specific examples of what scientific ideas you consider knowledge and which you consider theories. (And why you think these differ). I realise you may have problems thinking of specific examples yourself. Perhaps you could reply to my specific questions.

Do any of the following aspects of scientific knowledge qualify as “knowledge” according to the abstract definition you are promoting:

Thermodynamic laws – specifically the first (conservation) and second law (entropy);

Atoms and atomic theory – especially the standard model;

The standard cosmological model;

Boyle’s gas laws

Newtons laws of motion

String theory.

Of course, words like theory and law are used here as part of the normal nomenclature rather than implying any particular status of knowledge.

If none of these qualify – could you give a few specific examples of what you would consider as scientific “knowledge” and scientific “theory?”

Look forward to your response.

[NOTE: This has been posted by Glenn, as Ken has advised me that he is experiencing a unique difficulty in posting at this site, and that his posts are being rejected. The following is Ken’s post.]

I suspect Heraclides was correct when he identified the problem as one of you not understanding what is meant be a scientific theory. From my perspective and experience you have described theory in a naive mechanical way as either true of false. In reality scientific theories are dynamic, constantly developing so as to provide better and better reflections of reality. But they are reflections of reality – not reality itself.

So they should not be described as absolutely true – although they will contain elements of absolute truth (as well as relative truth). I briefly described this in my post at Open Parachute (Epistemolo-what?!!).( Sorry I cant put a link as I think this causes rejection of my comments.)

I think this is the problem with adopting an abstract approach (no matter how many philosophers do this). Unless our knowledge is intimately connected to reality, via practice, we are bound to come to conclusions which can’t really be used.

We can take your example of the planets to illustrate scientific dynamism. At one stage orbits were assumed to be circular (good philosophical reasons for that belief, by the way). Evidence accumulating showing that this model produced the wrong predictions. Eventually it was recognised the orbits were elliptical with the sun at one of the foci.

Now, the planetary science knowledge or theories were not either “true” of “false”. They were, and still are, just imperfect reflections of reality. We didn’t throw away that theory or knowledge when further evidence came in, we modified it. As philosopher of science Alan Chalmers points out, almost inevitably (but not completely so) “new” theories contain within themselves the “old” theories as limiting cases. Usually still very useful. After all, for most purposes we still use Newtonian mechanics, don’t we?

The fact is that all knowledge, all scientific theories are provisional – it arises out of their dynamic nature. Scientists don’t normally describe their theories or knowledge as absolute truths (except to be provocative as Jerry Coyne did with the title of his recent book). We don’t normally talk about “scientific truths” in the way that theologians talk about “biblical truths.”

As for examples – I had hoped that your classification of the different areas of scientific knowledge would illustrate your understanding of theory. I guess we are stuck with the jelly beans.

Now you say that the theory there are 135 beans is a “well supported theory”, a “true belief”, “true as a matter of fact” and therefore “knowledge.”

You have presumably come to that conclusion because of the empirical evidence, the fact that we have interacted with reality, sighted the beans and counted them.

As a scientist I would say that it is scientific knowledge and a scientific theory (we actually tend to use the word theory only where ideas are well supported. Where we don’t yet have support we usually describe them as hypotheses). But I would never say it was “true as a matter of fact” or a “true belief.”

While this is a trivial example I can expand this to parallel the real world situation we have in cosmology at the moment.

OK – I have got by with the scientific theory that there are 135 beans in the jar. But after a while I notice there are things which just don’t agree. (Just like planetary orbits). Perhaps I start to realise that the volume in the jar doesn’t really correspond with that number, or some conflict exists with apparent weight. So I make some exact measurements (including re-sighting and counting the beans), like accurate measurements of the weight of the jar contents. This produces a result conflicting with the number. The improved evidence actually shows that the mass of beans in the jar is about 500% greater than it would be if there were only 135 beans. I am therefore forced to revise my theory, revise my knowledge, about the number of beans. I get a more exact picture – a better reflection of reality, and actually produce a new “problem.” There appear to be jelly beans that just don’t interact with electromagnetic radiation, but have mass and can therefore be weighed. This is the sort of problem scientists love – something new to investigate. I can assure you that in my own research a result which conflicted with my own (or others) theory was actually very welcome. At times like that I felt we had a good chance of making progress.

As a said, a trivial imaginary example but it parallels the discovery of dark matter in galaxies.

The point is that our knowledge about the jelly beans is dynamic – not “true belief”. It changes as we get more information. It may well be that for many purposes we can ignore these new types of jelly beans and the old theory would suffice. But for others we have to use the “new” theory (which contains within it the “old” theory).

Briefly, that is how scientific epistemology works. Even though you may have a number of philosopher who you think don’t agree with that. But then again they aren’t in the process of obtaining knowledge about reality. Science is and most sensible people will agree it has been extremely successful at this task.

Hi Glen,

Thanks for the definition, perhaps you could clarify something for me. It seems to me (hard to tell, but I get a whiff) that you are a bit hung up on the “true” portion of this definition. Correct me if I am wrong, but it seems that the necessarily provisional nature of scientific theories somehow places them in another category other than knowledge for you.

What I am driving at here, is that the true portion of your definition is actually not practically useful, at least as a binary TRUE/FALSE value as there appears to be no way to achieve 100% certainty about the truth of anything. Without the ability to achieve this 100% certainty, I would say that the true bit of the definition is redundant and actually practically meaningless. Unless of course, you know of any ways to achieve this 100% certainty?

For the record, I have no direct experience of science, or of philosophy (outside of the pub anyways), but I do have an opinion, and this is a blog, so:

In fact, for practical applications, it seems to me that a more useful (and honest) definition would be to replace this true stuff with a probability of certainty. Perhaps this is unorthodox, but I would then define knowledge as information about something, that has a probability of certainty. Nb. Of course, with such a definition, both the information and the probability of certainty can be incredibly complex and interrelated things.

Where does science come into this? I rather like the image of science (and scientists) as providing an evolutionary fitness function in developing/evolving knowledge. Achieving ever more detailed, useful and certain information about reality. It also seems to be hugely practical in that any technique that can be used to improve the certainty of the knowledge can, and is used to do so. This includes, but is not limited to philosophical ideas were possible.

Ken

Beliefs are provisional, not knowledge. If you have to revise a theory because part of it is mistaken then that part of the theory was false and hence was not knowledge.

Of course beliefs can be justified and mistaken, and we can latter discover things which means we change our opinion But that does not mean knowledge is provisional it means that our beliefs, even our justified ones are provisional.

Nick, “Maybe there is always room for refinement of knowledge.”

As a whole, perhaps, but there are definitely some propositions that I think it’s safe to say that we know. For example “1 + 1 = 2” or “I am now posting on my blog.”

Apologies if @16 is not so clear, my quoting of text with quotes in it was probably not a good idea.

@17 I would agree that we could probably weight the first of those statements up near the high end of certainty, but doesn’t this lead into the idea of platonic knowledge and a possible debate about whether mathematics has reality and is discovered, or is an invented construct that exists within certain constraints. To put it another way, is it possible to imagine scenarios in which we could discover that 1+12? I think I can just about do this enough to lower the certainty of that statement below 100%. To put it another way, if you deconstruct the equation, there are some pretty meaty justifications needed for the different concepts here. You will of course be aware of the contributions of Betrand Russell in this area. Having read some of his writing on this, I would suggest that the seemingly simple certainty of the equation can be seen as anything but.

The 2nd of your statements is more problematic, particularly from where I am sitting. You could be a hacker posting from Estonia for all I know. Given the context though, I am perfectly happy to accept that you are posting on your blog as a working hypothesis.

Your second statement gets even more interesting from where you are sitting, in that we could rapidly get into all sorts of thorny sense of self and consciousness issues and even good old existentialism. All of which, in my opinion is sufficient to again reduce this certainty below 100%.

@17. I am not having a good night. Of course my not equals less than and greater than symbols disappeared (html tags). The sentence should read as follows: “To put it another way, is it possible to imagine scenarios in which we could discover that 1+1!=2 ? Using the C style not equals operator.

Nick – just a brief comment (I’m not at home, I will say more later perhaps), but when I referred to the belief that I am now posting on the blog, I was referring to my own belief that I am now posting on the blog, not your belief (I could, after all, be a hacker as far as you know).

@Glen. Also, where do you stand on Reliabilism? Is a reliable process for justification sufficient for your concept of knowledge.

I would again claim context as important. If you are talking about knowledge of reality, then in my opinion, a reliable process of justification is not sufficient, as it is easy to demonstrate that you can take an input from reality, run it through a reliable process, and then have an output that does not compare to reality.

If you however, narrow the context of your knowledge, for example to a mathematical context, you could argue that given some basic axioms as the input, then all you need is a reliable process (logic) do generate/justify knowledge. There is of course some problems even here (as helpfully pointed out by Scott on Ken’s blob), as Gödels incompleteness theorems show.

Also, what definition do you use for reliable here? I have assumed repeatable, this is the normal one I use.

I will consider your other points a bit further before commenting, but in terms of your definition of reliability, doesn’t this just open up the pandoras box of certainty again. How do you know that something is working the right way or that it is supplying correct information.

Isn’t this somewhat circular if you are introducing this into a discussion on justifying beliefs.

Perhaps this is why I am used to a more process orientated concept of reliability. If you start with the same inputs, uses the same process/function, then it is a reliable process/function when you get the same results. NB. This does not pre suppose the same results each time, you could have a process that produces a random result from and input, but then you might be able to say that this reliably produces a random result.

@23 Ahhaa, I had not realized that warrant and justification were supposed to be two separate things. I cannot see the grounds for this. Isn’t this just introducing another form of unexplained certainty?

I think we can find the seed of the problem within your statement:
A “congenial epistemic environment” is one in which my belief forming processes/structures interact with stimulus in the right kind of way to form beliefs that correspond to the way the world is.

I can accept that such belief forming processes/structures could exist, but: Again, how would you know whether your belief forming structures fit this specification? Testing against reality would be my pick.

Also, it has been progressively more clearly demonstrated that the belief forming mechanisms of human beings don’t fit this specification. I have been trying to point this out to all comers over on Ken’s blog for a while, but most people ignore this point. Humans have very badly skewed senses of probability. We see patterns in randomness, agency where this is none. There are some very good explanations for this coming out of research in various aspects of human cognition where evolutionary theory is applied. You could argue that are lot of these have a touch of “just so story” to them, but they are the best explanations that we have.

I think your final statement in that post sheds further light on this “warrant” idea:
Really, I don’t see any reason for you to give up on warrant. It may be that it’s not the term that you’re accustomed to using, but it has all the features required for the ordinary process of knowledge acquisition that everyday human beings employ on a daily basis.

How is this different from gut feeling, or personal conviction (both terms that you had no time for earlier in the discussion), both things that human beings use in knowledge acquisition on a daily basis.

The fact that the human knowledge acquisition process is deeply flawed is (I think) one of the reasons why people with experience of science put effort into communicating with the public. They spend their lives struggling with their own biases and where possible removing or minimising these biases to further their research. They have experience of how there biases have led them down blind pathways. I think this is one reason that you find a high level of skepticism about “philosophical” thinking that gets a bit too far into “beautiful thought castle in the sky” territory .

Nick, what I gave as the definition of reliable is not circular. I think what you’re referring to is not circularity, but rather a problem of infinite regress. This would be a problem if I endorsed a form of internalism, but I don’t, so it isn’t.

This also applies to the “how would you know” question about a congenial epistemic environment in the post that followed. The whole point of externalism is that it rejects the need to enter into that sort of regress. I think that in order to know X, we simply need to know X. Internalism, buy contrast, says that in order to know X, we need to know that we know X. Of course, we then need to know that we know that we know that we know (etc), into infinity. This is why I reject internalism.

I think you misunderstand my reference to what people do every day. I said that the concept of warrant that I am employing is one that in fact people do use every day. You say “How is this different from gut feeling, or personal conviction (both terms that you had no time for earlier in the discussion), both things that human beings use in knowledge acquisition on a daily basis.” It’s different because warrant is not gut feeling or personal conviction. Warrant is described earlier in this thread. Sure, it has one thing in common with those other things you listed: Namely that it plays a role in the way that people form beliefs on a daily basis, but beyond that the ideas are simply not the same.

Nick, here’s why we need to avoid infinite regress in the way that I have been saying:

If it’s really true that we need to “know that we know” something in order to actually know it (this is the position I reject), then we do not know anything. This is because we can never actually get to the beginning of an infinite regress (otherwise it would be finite).

So the options are: 1) reject the model that requires the infinite regress, or 2) affirm that we know absolutely nothing about anything.

Now it strikes me that 2) seems wildly false, and actually smacks of self contradiction. If I say “I know nothing,” the obvious question is “really? Do you know that?” So I think the infinite regress has completely unacceptable consequences.

The issue is by no means, as you put it, “a bit of uncertainty.” It is not uncertainty at all that’s the problem. The problem is that if we accept internalism (the model that I think requires an infinite regress) then we must not merely be uncertain, but we must be prepared to state as fact that we have no knowledge.

Nick, to call knowledge provisional is to say that it could later be proven wrong. Obviously if knowledge is warranted true belief, then it’s not provisional.

Again, scientific claims are provisional. That has nothing to do with the infinite regress or with having to “now that we know.” It’s a different issue and a quite separate controversy to the one about the infinite regress. It’s very easy to see how the infinite regress means that we have no knowledge at all.

Let k1 = the knowledge that X is the case.

Let k2 = the knowledge that I have k1.

Let k3 = the knowledge that I have k2

And so on. As I have said, k1 is the warranted true belief that X is the case. According tot he view that I have said I hold, in order to know X, all I need is k1. This is externalism.

According to internalism, the view I reject, for any belief x, in order to actually know x, I need k2. But this means that in order to actually have k2, I need k3. But then in order to have k3, I also need k4. This continues into infinity. Since we can never actually reach infinity in this process, then it follows deductively that we can never know X.

This has nothing to do with merely being able to say that we can have “provisional” knowledge of X. This just means that whatever else we can say about X, whatever feelings of certainty of confidence we might think we can have, we cannot know it. Ever. No matter what.

This means that you can never even know whether scientific beliefs should be regarded as provisional. It means that we cannot know that it’s wrong to declare utter certainty about all of our beliefs. It means we cannot know anything at all.

In other words, the infinite regress problem is not one that says that we should be less dogmatic or more uncertain. It tells us with certainty that we don’t know anything.

You’re also attacking a straw man when you talk about “unsupported beliefs” or “unrevisable” beliefs. After all, I have repeatedly said that knowledge is not just true belief. It is warranted true belief. If a belief is warranted, then it is hardly unsupported – and I have certainly never said that we should be unwilling to revisit and revise our beliefs if necessary, even if we once thought that we knew them to be true.

Edit:

I want to tread carefully so as not to condescend, because it’s clearly a subject in which you have a genuine interest and I want to encourage, rather than annoy, so please hear this as an attempt to do that: I get the impression that until this discussion you hadn’t heard of either epistemic internalism or externalism, and these categories and the standard critiques of them, which are very well know within the subject, are a bit unfamiliar to you. For that reason, and because it looks like perhaps you’d be interested in exploring it a bit further, there are some really good resources out there (some free online ones, some books for purchase). You might find these useful:

Michael Bergmann, Justification Without Awareness: A Defense of Epistemic Externalism (for sale at fishpond here).

Alvin Goldman, “Reliabilism,” The Stanford Encyclopedia of Philosophy (online here)

George Pappas, “Internalist vs. Externalist Conceptions of Epistemic Justification,” The Stanford Encyclopedia of Philosophy (online here)

Matthias Steup, “The Analysis of Knowledge,” The Stanford Encyclopedia of Philosophy (online here)

Juan Comesaña, “We are (almost) all Externalists Now,” online at Dr Comesaña’s page at the University of Wisconsin here.

A quick additional point on the above post. I just found out that there is school of thought in the philosophy of mathematics called finitism. Perhaps this is a close cousin of externalism. Personally, I find real numbers very useful.

Again, I think you have an assumption here that is leading your reasoning astray. You say:
In this case, I argued that assuming internalism leads to the infinite regress that shows that we know nothing at all. Since this is an absurd conclusion, it counts as an argument against internalism.

You have not as yet described why an infinite regress shows we know nothing at all. You have assumed this. I have given some examples of where we can work with infinites very productively, and thus this is not the barrier that you present. I am happy to give much more explicit examples here if you would like, just ask.

To develop this a little further. The other infinite regress that I mentioned last time is one of precision. This is perhaps though another facet of the original infinite regress. That is, any statement of knowledge, or imagining of knowledge is by the nature of the medium in which that statement is constructed, imprecise. Language, thoughts, even something so precise as mathematics have an implicit infinite regression, as you can always ask for more precision. Even such a seemingly obvious thing such as your earlier example of 1+1=2 can open pandoras box. What are these symbols 1 and 2, and what do they mean. What does plus mean as an operation? What is equality? I would argue that I could continue to ask further questions about any answer given to the previous questions and hence we are back with an infinite regression.

I have done a little skimming of some of the articles you mentioned before, and have seen one or two things that might be a bit interesting concerning relative degrees of certainty, so will probably read a little further. One thing I was immediately struck by however, was, what seem to be some pretty large assumptions that the various arguers did not seem to be aware of, or at least did not seem to be addressing. That is: the assumption that the tools with which they are posing their arguments, are reliable and/or unlimited in applicability. That is, logic (or induction if you prefer) and human reasoning, senses, thought or even consciousness. There did not seem to be any consideration of these points, (perhaps a bit with sensory), so seemed to me rather naive (in a non condescending way).

This leads me to an important point relating to the infinite regress. Have you considered, that this might actually be an artifact of the tools you are using. In other words, infinite regresses, contradictions, paradoxes etc… all exist in the architecture of logic itself. In fact, I think that is the true interpretation of these things.

With the above point in mind, please reread your definitions of provisional, in particular:
* The fact that out current technology that enables us to engage in a certain line of inquiry has limitations that might be superceded in the future, enabling us to make more accurate claims which might differ from the claims we now make.

Does this not also apply to the technology/tools that you are using to even make your argument, in this case logic. Doesn’t this just further undermine this whole approach?

Finally, I would say the provisional nature of things is not just defined by the infinite regress, but this infinite regress is indicating that we cannot with the tool of logic prove anything to 100% certainty.

I am on my way out, but some quick responses to your last points:

1) No, I disagree, all you did was explain where the infinite regression lies, and then state that because of this we can know nothing.

How would you answer the proposal that: The levels of regression relate to layers of justification, and as such provide one mechanism whereby levels of certainty can be determined. In other words, one measure of certainty of a piece of knowledge could be how many layers of justification underpin it.

In this way, we could never be 100% certain of anything as we could never reach the bottom of the regress, but we could qualitatively compare two statements about something by comparing how many layers of justification (regression) they have. This strikes me as a very much more useful (and perhaps sophisticated) interpretation of the infinite regression than just ignoring it. This is where my questions about the utility of externalism came from.

2) You have missed by point. I have interpreted your dislike of the infinite regression to the infinite part, not the regression part. I am assuming here that you would be happy with a finite regression. And thus I am using concrete examples of other, related types of infinities to demonstrate that infinities are things that we can deal with, regressions or otherwise. Also, see my point above, what I propose there, is very much along the lines of interpreting the infinite regression as an aspect of precision. The more iterations of regression, the higher the precision.

3) Sorry, I don’t think that I understand what you are saying here. If you are saying that people should not consider these issues, then haven’t you just constructed a nice little safe box to play in. If the rules of those discussions exclude questioning the rules of the discussions, I must just repeat my question and ask: Where is the utility here? Why would you restrict things in this way? What do expect to gain from such an restricted avenue of discussion?

4) It appears to me that you are now claiming perfect techniques/knowledge for philosophical discussions. Logic as a branch of mathematics, like other mathematics, is not a static,perfect complete thing. And the substrate that it runs on is definitely not. If you think this, then my question is, when was logic v1.0 completed (isn’t there a rule of thumb about trusting version 1.0 products…)? We could also have a discussion about platonic realism here, but I think it doesn’t really matter if you think mathematics (and logic) is discovered, or created, my point still remains. You could still say, either we have more too discover, or more room to create.

All of which supports my earlier point, it seems that you guys are not considering these things, or worse choosing to ignore them without seeing or caring about the limiting consequences of that choice.

1) Yes, if you look at each layer of justification on it’s own, it would not be better (all else being equal), than any other layer of justification on it’s own. The point is, that you don’t look at it on it’s own. We are comparing stacks of justification, not individual layers. Consider the phrase “The weight of evidence”. Can you see how two concepts could be evaluated by comparing the weights of two respective stacks of justifications?

This is a probabilistic argument. As such, perhaps a probabilistic example would help.

Lets say somebody is throwing a multi sided dice out of your sight. You do not know how many sides this dice has, but they tell you what number they get every time they throw it. Now consider the following series of results 1,6,3…. At position one, (as per your reasoning), you have only one event, so no way of making a reasonable statement about the number of sides. At position 2, obviously 2-5 have been ruled out,but 6 to infinity are still in play. At this point you propose a hypothesis, being that the dice has six sides. With only two events however, this is quite a weak hypothesis as it would be easy to imagine that a 10 or an 18 is thrown next. Now continue the series on for another 10 digits. 5,2,4,4,2,5,5,1,6,2. Now compare the hypothesis that you had at position two, with the hypothesis proposed at position 12 that the dice has six sides. Which one is the stronger hypothesis?

Your reasoning in point one leads only to a binary true/false capability. Given this reasoning, by what mechanism could we possibly have differing levels of certainty about something?

2) I am arguing that you could look at a regression as just a matter of precision.

3)I am not saying that people are cheating. In fact, I have said that I can see, why you could adopt such a hypothesis so to simplify the question, and thus learn something new. As I understand it, this type of technique is regularly used in maths and physics to make progress in a field when confronted with seemingly insurmountable barriers.

What I am asking you is: What is your justification for doing this? What are the new things you are learning, or trying to learn by adopting this hypothesis? In short, where is the utility of this approach?

My point here, is that from the little I have read so far, it seems that people in this area either don’t know that they are working within the constraints of an hypothesis that they have chosen, or they have forgotten this.

4) I think you might be generating another infinite regress here. I would ask how you could justify this? And you would say because you have defined this as being so, ala 100% certainty argument to avoid the infinite regress. I could then bring up an argument that Scott thoughtfully supplied for me over at Ken’s blog:

Logic is a branch of mathematics. You could perhaps interpret Gödel’s incompleteness theorems to say that there are true things that you are unable to prove using mathematical logic. In other words, logic is incomplete. Logic itself has proved that it is incomplete. Somewhat less than a perfect unchanging tool then.

Don\’t want to disturb the smooth flow of discussion between Nick and Glenn. Just want to support the concept of a logic 2.0 – especially when it comes to scientific knowledge/investigation. As Frank Wilczek has pointed out (<a href=\"http://www.edge.org/3rd_culture/wilczek09/wilczek09_index.html\">Edge interview</a>) <i>“The classic structures of logic are really far from adequate to do justice to what we find in the physical world.”</i>

I think this gets back to Plantinga\’s understanding of \"warrant\" – which I think is mechanical and would rule out much of scientific knowledge – knowledge we know to be extremely effective. This is the concept that our cognitive system it \"designed\"/\"evolved\" for specific cognitive functions and therefore may be operating in a different environment to that it was \"intended\" for.

We are now investigating phenomena well outside the environment in which our cognitive systems evolved. We have to accept that there may well be conflicts with our intuitive understanding of logic in such environments. But, I think it is well justified for use to think that we can do this quite successfully (even though some would say such investigation would have no \"warrant\").

Well that is the case for much or scientific research now. Yet we have ways of getting around that – although the comprehension of our results in the manner we are normally used to is extremely difficult (We often have to see things mathematically, rather than as particles or waves, for example). Consequently we are faced with surpassing a logic which say \"Its not the case that A and not A\". Quantum logic is postulating at least at the level of logic that it can be A and not A. Serious attempts are being made to develop computers using this logic.

Ken, Wilczek’s comment is only that logic is inadequate for a full understanding of the world. That’s true, but it doesn’t suggest that logical laws like the law of noncontradiction might be rejected one day. It only means that there is more to know that such laws do not tell us.

You say that the idea of warrant would rule out scientific knowledge, but I just don’t see how. You say: “We are now investigating phenomena well outside the environment in which our cognitive systems evolved.”

That’s not important. What’s important is that when we use our belief forming faculties, we’re using them in an environment that is conducive to their reliably gathering information. Whether this is the environment in which they developed in history is not the issue.

As far as the subject of quantum logic scenarios in which “A and not A” can be the case, you’d need some examples there.

Nick, it’s important (inasmuch as any of these discussions are important, that is) that you realise why the dice / layers of justification is definitely unlike the infinite regress. Let me offer another attempt, and if this one fails too, I’ll leave it there.

Here’s how the dice example works: At the time you make the hypothesis about there being 6 sides, based on current observation it has justification of a certain strength. Then you roll again, and the number of observations increases, strengthening the level of justification. And so on, through more and more “layers” of justification. It’s very clear to both of us how this example works. At each point, if someone says “Do you currently have justification for believing your hypothesis about 6 sides?” The correct answer is “Yes, to some degree, based on knowledge we have already gained from observation.” (Take note of the word “yes,” because this will become important.)

But that is absolutely not how the infinite regress works. It’s a difference not merely in degree, but in kind. Here’s how the infinite regress – I will use the labels k1, k2, k3 and so on as used earlier.

I hold a belief k1. If someone says “do you have justification for k1?” Here I cannot say yes. All I can say is “Only if I have some justification for k2. Otherwise I have none at all” If they then ask “Do you have justification for k2?” I must say “Only if I have some justification for k3. Otherwise I have none at all.”

And so on. So the dice example and the idea of levels of justification are not cases like the infinite regress. They are entirely separate issues.

I sense that you are getting a little tired of this discussion Glen, so perhaps I could make a bit of a summary of my position for the sake of clarity.

The essential point of contention is related to the infinite regression you find when justifying knowledge, in your words:

Let k1 = the knowledge that X is the case.
Let k2 = the knowledge that I have k1.
Let k3 = the knowledge that I have k2

You are unhappy with the infinite regression, so have by definition removed it. In your words:
The whole point of externalism is that it rejects the need to enter into that sort of regress. I think that in order to know X, we simply need to know X. Internalism, buy contrast, says that in order to know X, we need to know that we know X. Of course, we then need to know that we know that we know that we know (etc), into infinity. This is why I reject internalism.

This amounts to a claim of 100% certainty that we know things (in this case X). I think this is an extraordinary claim, and as such requires extraordinary justification. In this case, I would argue that you need to have a 100% certain justification to support it. To undermine this claim therefore, only requires the injection of some level of doubt.
I consider that I presented some very real grounds for doubt. I will try and summarise the main areas for doubt below.

1)What is wrong with infinity anyway. Infinities do not mean that we know nothing, they just mean that we cannot be 100% certain. We can, and do work productively with infinites in many different ways. In the case of this particular infinite regression, we can consider the number of layers of regression as a weight of evidence, and use this (all else being equal) to compare hypotheses in a qualitative way.

2) Are you sure that this is actually an infinite regression. Perhaps at some point in the layers of justification we run into a prime justification, that for whatever reason doesn’t require further justification, and then this is actually finite. Or, we could run into the original hypothesis again, in which case we have a circular justification. You cannot be sure that this is not the case without traversing all the layers of justification.

3) The argument from utility. Cutting off the infinite regression by definition, is just a less useful approach to take. Treating everything as having a level of uncertainty, avoids the trap of incorrect 100% certain beliefs, at no cost above having 100% certain beliefs. Thus, 100% certainty is less useful.

4) The argument from precision. The infinite regression found with the justification of knowledge is not the only infinity here. There is also a question of precision. How can something be 100% certain without it being 100% precise. I would argue that it might not even be possible to be 100% precise using language, human thoughts or even mathematics. This could however in some ways be considered as another aspect of the justification infinite regress.

5) Are the tools with which you make your argument 100% reliable? This is an argument made with logic, using the human consciousness and communicated using human languages. All of these are arguably incomplete. In the case of the human consciousness, modern research is unearthing large amounts of evidence about the biases and blind spots that we as a species have. One of the most relavent blind spots here is that our instinctive senses of probability are very skewed.

6) Perhaps the infinite regression is just an artifact of the limitations of the logic used. When we see infinities within maths, and logic as a part of maths, you could argue that these are not aspects of reality, and are just limitations inherent in the actual architecture of maths. Thus: The infinite regression is not actual, but just a limitation of our toolset that could be possibly be resolved using another method. This is perhaps really part of 5, but I have split it out for clarity.

Please note, that I am not necessarily saying that I believe all of these arguments are true, I am just saying that they can be made logically, and as such open up doubt on your position.

All of this aside though, I would again finally suggest to you, that if you could provide an example of the utility of your position, then I would have some interest. As it stands, I don’t see any grounds for it, and no use for it either. In short, it has nothing to offer.

I am happy also to leave the discussion there. Just some final words about my motivations in engaging in this discussion.

The discussion that occurred previously on Ken’s blog had a very high emotional content that I thought was obscuring some of the issues. Fortunately there’s none of that here. With one of your final comments in that discussion you mentioned epistemic externalism as a way of being sure (which I read as 100% sure, i.e certain) that we have knowledge, or can know something.

Having no direct experience of science or philosophy I was interested in how this idea worked, particularly in terms of it’s utility to us in gaining knowledge.

Along the way I have read a few interesting things that could speak to evaluating the place of intuition in the formation/gathering of knowledge. This is one of my personal interests.

However, also along the way, I discovered a key point of disagreement with you about the way to interpret this infinite regress in the justification of knowledge.

With your latest phrasing of this infinite regression, you have included the word only, and used it in such a way as to effectively disallow evidence. I.e you will accept k1 only if you have some justification for K2. If we accepted this, then I think that we have no way of comparing levels of certainty between hypotheses etc…, and as such, I have no choice but to agree with Ken, that this is an anti scientific stance. I am sorry if this offends you, but that is my reading of your position.

PS.. That new security code system you have, does not work at all well, it takes many attempts to get the posts through.

Ken, this could merely be my own lack of creativity, but I just don’t know what it even means to talk about “extending,” say, the law of non-contradiction. Could you elaborate, perhaps with an example?

They are misrepresentations Glenn. I explain why I wrote what I did but you have presented them as having been written for other reasons.

Any one who is a decent person can verify this for themselves.

Please apologise and remove your inaccurate and misleading statements about me.

Well, Glenn, I have.

Do you not understand what I mean by the 2 slit experiment or Schroedinger\’s cat?

Is the problem that you have trouble with QM (Don\’t we all)?

However, I think you will appreciate that I can\’t give an introductory course in the comments sections of a blog.

Just accept that it shows that an electron (say) can be in position A and position B, or in position A and not in position A, at the same time.

And that you use technology every day based on that logic.

(By the way – can’t you change the background colour of your code – it’s almost impossible to read).

Ken, I’m familiar in very basic terms with the double slit experiment, but it definitely has nothing to say about the law of non-contradiction being extended. I’m assuming then that you think that the Schroedinger’s cat example carries the full weight of the explanation.

However, Schroedinger presented his example precisely because he recognised that there was an interpretation of quantum mechanics out there (namely the Copenhagen interpretation) which resulted in a contradiction and he wanted to show that this was so so that he could get people to reject that model. Granted, the following quote is from a Wikipedia article, but it’s a fair summary: “Schrödinger did not wish to promote the idea of dead-and-alive cats as a serious possibility; quite the reverse. The thought experiment serves to illustrate the bizarreness of quantum mechanics and the mathematics necessary to describe quantum states.”

None of this implies that the law of contradiction might be incomplete or that it could be altered or extended.

Now I don’t think that either outcome of this very specific issues has implications for the subject of the blog post, but I really can’t see a case for saying that laws of logic might be “extended,” just because there’s no coherent explanation of what that actually means.

By the way, if the contrast between the code and the background was too great it could be read by some spam bots. It\’s supposed to require human effort 🙂

[I’ve edited this comment of mine, as the original was needlessly impatient and therefore unkind. My apologies for this.]

Ken, I don’t imagine you’ll like me saying so, but I think you just misunderstand the double slit experiment if you think that it literally shows that a photon can be there and yet in the same sense not be there at the same time. It doesn’t do this, yet you’ve become convinced that it does.

Also (and doubtless you will like this no more than the previous comment), you are still wrong in your description of Plantinga’s idea of warrant as “mechanical,” and I consider that you’re using the term only for rhetorical effect. You also mistake me if you think that I don’t think the law of non-contradiction can be extended on account of my notion of warrant. In fact the two issues are barely related at all.

In all honesty, I don’t see much constructive purpose in continuing to re-visit the same issues with you, so I am just going to leave it there.

Regarding the code – I made the change because the normal spam filter seemed to target you and only you for some reason (apart from the typical spam/porn bots), preventing you from commenting. You were the only person claiming that they were being prevented from commenting (although I’m inclined to think you were pressing “preview” instead of “post/comment”). Be flattered at the change!

Glenn, maybe you can help me out here.

I know that Plantinga doesn’t hold that only true beliefs can have warrant. Some false beliefs can be warranted. But only true beliefs can have warrant sufficient for knowledge (lets say k-warrant).

With this in mind, why say that knowledge is Warranted *True* Belief? If a belief has k-warrant, wouldn’t it have the property of being true simply by default? It seems that if the belief in question couldn’t have k-warrant if false, then a better candidate for knowledge would be something like K-Warranted Belief, or Fully Warrant Belief, since it’s not enough for the belief to be *merely* warranted, but then if we say K-Warranted True Belief, it’s almost a waste of words, since to have k-warrant is a property that only true beliefs can have in the first place.

This may be a minor quibble, but it does seem to make the “True” aspect of Warranted True Belief a bit superfluous. I don’t know.

Thoughts?