The Münchhausen trilemma

[josephpalazzo]

This is following from the thread The assumptions of science

If we ask of any knowledge: "How do I know that it's true?", we may provide proof; yet that same question can be asked of the proof, and any subsequent proof. The Münchhausen trilemma is that we have only three options when providing proof in this situation:
 The circular argument, in which theory and proof support each other (i.e. we repeat ourselves at some point)
 The regressive argument, in which each proof requires a further proof, ad infinitum (i.e. we just keep giving proofs, presumably forever)
 The axiomatic argument, which rests on accepted precepts (i.e. we reach some bedrock assumption or certainty)
 
The first two methods of reasoning are fundamentally weak, and because the Greek skeptics advocated deep questioning of all accepted values they refused to accept proofs of the third sort. The trilemma, then, is the decision among the three equally unsatisfying options.
 
In contemporary epistemology, advocates of coherentism are supposed to be accepting the "circular" horn of the trilemma; foundationalists are relying on the axiomatic argument. Views that accept the infinite regress are branded infinitism.

From: http://en.wikipedia.org/wiki/M%C3%BCnchhausen_trilemma

[LikelyToBreak]

Excellent!  =D>

I really like this kind of post.  :-D

[entropy]

I know I oversimplified things a little in the parenthetical comment I made in a post to "The assumptions of science" thread. I said that you have to start with assumptions or your argument will devolve into an infinite regress of justifications or be circular - which pretty much follows with what the Wikipedia article says except I didn't acknowledge that there is a significant number of philosophers who seem to accept the "coherentist" notion of justification. I just can't buy into coherentism. Every time I look at the reasoning, it seems that what it essentially boils down to is saying "assume a whole circular set of rationalizations as true" rather than just assume that which is directly posited axiomatically is true. For example, I have a hard time thinking what a coherentist argument against the claim that reality is solipsistic would look like. Somewhere in the circular argument against solipsism there has to be a claim that there is more to reality than "my" mind, so how is that different from just assuming that's the case axiomatically in the first place? How does circular coherence make the claim more rationally justifiable than just accepting it axiomatically?

[josephpalazzo]

The wiki link does say that both the circular and regressive arguments are weak. And one can safely say that math and science are both founded on the axiomatic argument with the proviso that theories built on a number of hypotheses(axioms) must undergo empirical oversight. The most outstanding one on a historical basis was Euclidean geometry - which was based entirely on 5 axioms that had prevailed for several centuries until the mathematicians took the fifth axiom to task. The result was non-Euclidean geometry, a must in developping General Relativity.

As to coherentism, never was I a big fan. Its major flaw is that belief and its negation could each cohere with at least one set of beliefs, and this means that contradictory beliefs could turn out to be true.

[Sal1981]

I don't think I've ever been anything other than a foundationalist by the descriptions given in the Wikipedia article.

As long as an axiom is self-evident, I fail to see the problem with them. The objection might be to nullify an axiom, but then that objection would show some short-coming or lack of scope for that axiom, and in the worst case, to be false.

I used to think that the shortest distance between two points would be a straight line, and accept that as an axiom, but that's not exactly an axiom, given non-Euclidean geometry, so the scope for that postulate is for only Euclidean geometry and hardly an axiom by its right then.

So, all axioms should be given with a provision of uncertainty, I'll grant that - but that is merely a admission of finite knowledge, i.e. since we don't know everything and have limited knowledge, we can safely conclude that even axioms are up for revision for any new knowledge that challenges an axiom, so there.

Besides, axioms should be something akin to physical laws, if a new discovery in physics shows results that disproves a long range of inductive accepted results, then we need to revise that law. Like, for example, we have inductively thought that all swans are white, until one day we find a black swan, so the theory "all swans are white" needs to be revised to include black swans, that's what I mean.

[josephpalazzo]

It's important to realize that there's a difference between axioms (postulates in science) and theorems ( theories in science). Theorems/theories are derived from the the axioms/postulates. Very few times did we need to change our  axioms/postulates. Two instances are notable. In math, Euclid's fifth axiom was shot down, and non-Euclidean geometry was born. The other was in the case of Einstein who realized that Newtonian physics was inconsistent with Maxwell's equations. His insight led him to the conclusion that one of Newton's assumptions was wrong: time was taken as absolute in Newtonian physics. Like spatial coordinates, time is relative to an observer: different observers will measure different lengths and different times.

If we look at the success of math and science, we then see that the foundational position in the Münchhausen trilemma is the one to choose, with the proviso as it was stated by Sal, that new knowledge might force us to revise our beliefs in the axioms/postulates .

Theists often come along to nag us that atheists also believe. Yes, we do believe. We believe in the foundational position/empirical verification, and there's no shame in admitting that. OTOH, some theists might believe also on the foundational position/evidence verification. One difference might be in their axioms/postulates. They might believe in a spiritual/immaterial world, which we don't. If we ask for burden of proof, they might believe not in the kind of evidence as we do. In their case, revelation is one kind of evidence they believe in that atheists don't accept, and we shouldn't. Time after time, we find that what people claimed through revelation turned out to be bogus. Another line of attack will be that we presuppose that the immaterial doesn't exist, hence the accusation that atheists are close minded. The counterargument is that if we agree to open the door then anything is possible: leprechauns, invisible pink unicorns, fire-breathing dragons, and every deity ever conceived.

[Solitary]

I had a Mormon ask me what the truth is? I told him that which is. He thought about it and asked me how we know that which is. I told him we know because it is actually true. He then asked me how do we know it is actually true? I told him because it is real. He stood perplexed and asked how do we know it is real? I told him because we can experience it all around us. He told me God is all around us, so God is real. I asked him how he knows this. He walked away blabbering to himself. We have to accept the world we live in as real and the world of our mind as real.

If we study the mind it can be done by studying the mind, or the material brain. They are both real, or are they? The mind is an allusion that emerges from the functioning of the brain-body, so reality is the world we live in. We can only know what is true by studying this world. Solipsism is false because it would mean only we exist and everything else is an illusion that everyone experiences if conscious. But reality exist even if it isn't experienced. Or does it?  :shock:  :-?  :-k  I assume it does, so that is real and true. Is it God, or a thought God has? It seems that we get into a self referential paradox we have to live with, or not.  8-)   :Hangman:  Solitary

[entropy]

As long as an axiom is self-evident, I fail to see the problem with them. The objection might be to nullify an axiom, but then that objection would show some short-coming or lack of scope for that axiom, and in the worst case, to be false.

One of the most common arguments you will see from advocates of coherentism is that a coherentist justification is less arbitrary than a foundationalist justification. They claim that a set of statements that are logically consistent are less arbitrary justifications than simply starting with axioms. But as josephpalazzo pointed out, the negation of each of those statements can be just as logically consistent, so is it really less arbitrary to pick either side of a contradiction than is to simply assume an axiom? To further the point - in an earlier post to this thread I used the example of how to justify assuming that solipsism is not true. A foundationalist would take that as an axiom => reality is not solipsistic. A coherentist would come up with some set of coherent statements that basically justify the same claim. The thing is that you could come up with multitudes of coherent sets of statements justifying rejection of solipsism with each set of statements being logically inconsistent relative to the other sets. There are multiple sets of coherent statements that contradict each other but they all still justify rejecting solipsism. They are all equally coherent so isn't the choice of one over another no less arbitrary than just positing the rejection of solipsism as an axiom. IOW, I'm just not buying the "coherent statements as justification are less arbitrary" line of reasoning.

Additionally, as you imply, empirical evidence has a way of trumping elaborate abstract justification whether the justification is foundationalist or coherentist. I imagine that someone could have formulated a coherentist justification for belief in the luminiferous aether (a substance posited to be the medium for light waves) and someone else a foundationalist justification - though you might have to burrow deep into the layers of justification to get to the foundationalist or coherentist difference between the two arguments. Empirically, it's been established that there is no luminiferous aether, so both the coherentist and foundationalist justifications would be equally deficient. It just strikes me as odd that the coherentist would, never-the-less, want to claim that the coherentist justification was better due just purely to it being grounded in a coherent set of statements rather than an axiom.

[entropy]

It's important to realize that there's a difference between axioms (postulates in science) and theorems ( theories in science). Theorems/theories are derived from the the axioms/postulates. Very few times did we need to change our  axioms/postulates. Two instances are notable. In math, Euclid's fifth axiom was shot down, and non-Euclidean geometry was born. The other was in the case of Einstein who realized that Newtonian physics was inconsistent with Maxwell's equations. His insight led him to the conclusion that one of Newton's assumptions was wrong: time was taken as absolute in Newtonian physics. Like spatial coordinates, time is relative to an observer: different observers will measure different lengths and different times.

If we look at the success of math and science, we then see that the foundational position in the Münchhausen trilemma is the one to choose, with the proviso as it was stated by Sal, that new knowledge might force us to revise our beliefs in the axioms/postulates .

Theists often come along to nag us that atheists also believe. Yes, we do believe. We believe in the foundational position/empirical verification, and there's no shame in admitting that. OTOH, some theists might believe also on the foundational position/evidence verification. One difference might be in their axioms/postulates. They might believe in a spiritual/immaterial world, which we don't. If we ask for burden of proof, they might believe not in the kind of evidence as we do. In their case, revelation is one kind of evidence they believe in that atheists don't accept, and we shouldn't. Time after time, we find that what people claimed through revelation turned out to be bogus. Another line of attack will be that we presuppose that the immaterial doesn't exist, hence the accusation that atheists are close minded. The counterargument is that if we agree to open the door then anything is possible: leprechauns, invisible pink unicorns, fire-breathing dragons, and every deity ever conceived.

If a theist was patient enough, I think I could walk them through how I come to have a very high degree of certainty (or very low degree of uncertainty if you prefer) that there are no supernatural events. But they'd have to be patient, because I would start the explanation at what seems to be the logical place to begin - the beingness of "my" experience. Experience itself as I experience it. That is the beginning. That's what comes before the first assumption. This isness of experience is the one thing I am completely certain of. Then there is "whatness" of experience. That is much more problematic and that is why I have a habit of bringing up solipsism. Because to make sense of the whatness of experience, it is apparent that there is a coherent mentality that is processing what we typically refer to as sensory information. This is so immediate and impactful on what I experience that it is self evident that it is so.

But if I were to try to be skeptical of every notion, I would wonder if the impression of sensory information is being stimulated at least in part by something beyond the limits of that which is providing the sensory information, or is the impression of that externality an illusion that is internally generated only by the mind (the mind being the beingness of experience)? If you go to this level of skepticism, you are at pre-empiricism; to posit something about external reality you must first assume a reality external to sensory information exists and this skepticism takes us prior to that assumption. Essentially, there is at least the logical possibility of reality being solipsistic or not and you can't appeal to empiricism to choose between them because that would be begging the question.

I choose to trust that the impressions my senses provide are generally reliable raw information via stimulation by externalities. That is an assumption. Do I know for certain that reality isn't solipsistic? No. But because I generally trust my senses to provide reliable raw information (a.k.a., I make that assumption), I feel very confident that reality isn't solipsistic. Now that is circular and invalid (though somehow still feels explanatory), so it just logically collapses down to assuming that reality isn't solipsistic. As a matter of logic, I treat that as an axiom => solipsism is false.

So with one assumption I've opened up to this seemingly vast and diverse externality that I'm generally reliably informed about by my senses - at least in the raw data sense of senses as contrasted with perception. This is a view of reality I'm not 100% certain about, but I'm very confident about it. So what do my senses appear to be informing me about that which is external to the direct beingness of my experience? There are many levels of processing of that information involved. The more closely the processing stays to the raw sensory data itself, the more confidence I have in it. The problem is that I'm not always certain just how close a particular kind of processing actually is to the raw data - perceptions go awry sometimes. The way that we deal with that limitation seems to be programmed into us. We look for patterns and appear to have a memory store of sensory data to mine when looking for those patterns. Anomalies in patterns are noted and we try to account for them but often they get pushed aside as junk data. This winnowing through sense data is an uncertain process, so the more rigorous the accounting for anomalies, the more confidence we can have in the perception formed from the raw sensory data. Now this is finally at the full empirical level.

What process do we use to take advantage of other mentalities to winnow through the sense data looking for patterns and trying to account for anomalies? The scientific method. It's based on some assumptions to get past solipsism and the relationship of sensory information aspect of mentality to the full beingness of experience itself. But, as you say, not that many assumptions. Those assumptions bring us to empiricism of science as a way of having some confidence that our assessment of reality is correct.

That's pretty much how I understand reality. If you want to convince me something exists, show me empirically. You say there is a supernatural agent you call "God", show me the empirical evidence. I've looked for it myself and heard a lot of people claim they have such evidence, but it has all come to zilch as far as I can tell. If you want to convince me of the existence of this God thingee and you don't think you should have to do so only through empirical evidence then convince me why that's the case.

That's what I'd tell the theist if they had the patience to listen.


Thanks for the refresher on the relationship of theorems to postulates.

[josephpalazzo]

Yoiu bring up a good point: trustworthiness. As a child we learn to trust our senses. As an adult, we learn to trust science, even though in the US, science is often considered to be just another source of noise in the chaos that is life. Even though it is not all perfect, science is reliable as it is self-correcting, and has delivered so much technology which has lifted our lives from cave dwellers to what we have now. Also, we should never forget that science is provisional. Contrary to what theists see this as a flaw, we should see it as a strength.

[entropy]

You bring up a good point: trustworthiness. As a child we learn to trust our senses. As an adult, we learn to trust science, even though in the US, science is often considered to be just another source of noise in the chaos that is life. Even though it is not all perfect, science is reliable as it is self-correcting, and has delivered so much technology which has lifted our lives from cave dwellers to what we have now. Also, we should never forget that science is provisional. Contrary to what theists see this as a flaw, we should see it as a strength.

I like putting it that way - a basic axiom that pretty much everyone accepts is that our senses are generally trustworthy. It's really a fundamental notion. It's hard to make sense of much of anything in anything like the usual way we do unless you assume that is true. Yet, as you say, too many people don't reflect on science as a natural and extremely productive refinement of that very basic notion that we all accept.



Just tagging some more thoughts about coherentism on to this response:

One of the appeals that I've seen coherentists make is that what they are doing is like induction in that, like induction has different lines of evidence pointing toward a conclusion, with coherentism you have a web of various stances that provide support (justification) for another stance. While there does seem to be some similarities, the differences make the comparison dubious. In induction, the lines of evidence are empirical and the evidence may very well lead to a conclusion other than the expected or looked for conclusion or they may be no expectation of what the conclusion is at all. In coherentism, the goal of justifying a claim predetermines "the conclusion" and "evidence" that is looked for to point toward that claim is not limited to empirical evidence. Not being limited to empirical evidence, the "universe" of notions available to go into a web of justification for a coherentist claim is huge but a great many possibilities are excluded only because they do not fit into the web of justification for the particular stance looking to be justified. That's nothing like empirical induction.

[entropy]

You bring up a good point: trustworthiness. As a child we learn to trust our senses. As an adult, we learn to trust science, even though in the US, science is often considered to be just another source of noise in the chaos that is life. Even though it is not all perfect, science is reliable as it is self-correcting, and has delivered so much technology which has lifted our lives from cave dwellers to what we have now. Also, we should never forget that science is provisional. Contrary to what theists see this as a flaw, we should see it as a strength.

I like putting it that way - a basic axiom that pretty much everyone accepts is that our senses are generally trustworthy. It's really a fundamental notion. It's hard to make sense of much of anything in anything like the usual way we do unless you assume that is true. Yet, as you say, too many people don't reflect on science as a natural and extremely productive refinement of that very basic notion that we all accept.



Just tagging some more thoughts about coherentism on to this response:

One of the appeals that I've seen coherentists make is that what they are doing is like induction in that, like induction has different lines of evidence pointing toward a conclusion, with coherentism you have a web of various stances that provide support (justification) for another stance. While there does seem to be some similarities, the differences make the comparison dubious. In induction, the lines of evidence are empirical and the evidence may very well lead to a conclusion other than the expected or looked for conclusion or there may be no expectation of what the conclusion is at all. In coherentism, the goal of justifying a claim predetermines "the conclusion" and the "evidence" that is looked for to point toward that claim is not limited to empirical evidence. Not being limited to empirical evidence, the "universe" of notions available to go into a web of justification for a coherentist claim is huge but a great many possibilities are excluded only because they do not fit into the web of justification for the particular stance looking to be justified. That's nothing like empirical induction.

[Sal1981]

I don't think axioms are arbitrary, I consider them akin to physical laws, but more foundational.

They might be naive on the surface and easy to understand, but I think every axiom is carefully considered.

[josephpalazzo]

I don't think axioms are arbitrary, I consider them akin to physical laws, but more foundational.

They might be naive on the surface and easy to understand, but I think every axiom is carefully considered.

Initially they might have been chosen due to a combination of arbitrariness and insight. But as time went on, the bad ones  were filtered out. But even today, the assumptions that withstood the test of time, are they still good? I'm thinking of the concept of a point in geometry. We assume that it has no length, no width and no breadth. And that has served us well so far. But is it true as the Planck level, 10[sup:1o6gqpve]-33[/sup:1o6gqpve]cm, the smallest length we can derive from the three most basic constants - G, Newton's constant in the gravity law; h, Planck constant; and c, the speed of light. It might be that our assumption no longer holds at that scale. But then what do we do? What assumption(s) can replace it? Easier said than done.

[entropy]

I don't think axioms are arbitrary, I consider them akin to physical laws, but more foundational.

They might be naive on the surface and easy to understand, but I think every axiom is carefully considered.

I think there are almost always reasons why we choose one axiom over another, but "reasons for" are not necessarily valid justifications. For example, why do I think solipsism isn't true? It's probably because the impression of an external reality is so compelling. It being a compelling impression suffices as an explanation, but I don't think it suffices as a justification for positing the claim that solipsism is false. I don't see any grounds for why someone who might be skeptical of the claim that solipsism is false should find my "compelling impression" to be a valid argument for the position that solipsism is false. It would be like someone trying to convince me that not believing in God is wrong and if I ask them why they say, "Because I have a compelling impression that there is a God." I think that a "reason of compelling impression" just collapses down logically to "I take this as an axiom."