Thursday, August 24, 2006

Values and Validity

I've been enjoying a conversation with Alex Gregory over at atopian.org. We've been discussing moral relativism, and Alex has been asking whether I'm saying one can rationally deny demonstrated truths within axiomatic systems. Here is my answer to his question, with a little elaboration.

The truths (theorems) within each axiomatic domain exist whether we value them or not. The theorems of Euclidean geometry are true, even if we prefer non-Euclidean geometry.

In many cases, comparable theorems in different axiomatic systems contradict each other. The question is, on what basis should we value each set of axioms and theorems?

My point is that, at best, what we ought to do is subjective. What I ought to do involves a value judgment. Whether I ought to hold an axiom as true depends on how I value it (or its resultant theorems).

This happens in physics. Each scientific theory consists of a set of axioms for modeling the world, and each observation counts as an axiom. A theory is invalidated when it becomes inconsistent, and the predictions of a theory are those axioms that can be added to the system without contradiction.

If we have two scientific theories that are presently indistinguishable (say, because the distinguishing experiments are as yet out of reach), then we might still prefer one theory over another. Sometimes, this selection of axioms is based on aesthetics or taste, and one theory is valued over the other for accidental or historical reasons. For example, if one theory will benefit me, my past works and my department, I have reason to value that theory more than its competitor.

So, let's look at my personal position. I value staying alive, comfort, my ego, my loved ones, peace of mind, etc. Since I view science as vital to survival and peace of mind, I think its axioms are important, and I'm willing to live as if they are true. I accept mainstream ethical values because I see those as conducive to my comfort and my general happiness.

However, a person who has different values (or who is confused or inconsistent) will accept different axioms. For example, a person who thinks that this world is less important than some fictitious afterlife, does not fear death or discomfort. Science does little for these people, and the fact that electronics and pharma science save millions of lives each year is unimpressive to them. Their values allow them to disregard the founding axioms of all scientific systems (logical consistency and regularity) if it delivers them the particular afterlife they seek.

That some primitive screwheads reject science does not imply that science is somehow untrue under its own axioms. It's just a question of whether a man thinks the objective power of science is important.

Now, let's get back to morality. Morality is supposed to guide values, but values are used to select axioms. So how can there be an objective morality? If a person thinks that following axiomatic moral systems is unimportant, on what basis can you logically demonstrate to that person that they are wrong? Their answer to any axiomatic system will be "so what?"

I'll add here that I feel that it is generally better to "game" axiomatic systems, and to do a comparative analysis of them. I think it is morally good to ask why each system is valued the way it is, and whether the method used for assigning value is a consistent one. Is my preferred system appealing to me for biological, social or psychological reasons? Do these values cause me to be blind to defects in my preferred system? Are these values themselves worthy?

I'm still working my way through these questions.

In comparing alternative systems, one will come across systems which actively discourage comparative analysis. Christianity is one such faith-demanding system. While it would be illogical for an outsider like me to pay any heed to such demands, it is significantly harder for Christians to do so, since they presumably value the axioms of their own system to a greater degree. It can be difficult to escape these Jedi mind tricks.

It's also true that social and family bonds act to suppress comparisons. There is an inherent negative value in abandoning the shared axioms of one's family or social group. This doesn't affect me much, and my mother wonders where she went wrong.

I also can't deny that I want to feel that I'm special, and that my formulation of philosophy is right and elite, rather than merely right and mundane. This, too, could potentially sway my judgment in a manner I find distasteful.

Anyway, I think I'm getting closer to understanding the dynamics of selecting axioms, and I plan to write more on this topic.

8 comments:

Colin Caret said...

doctor(logic) said "The truths (theorems) within each axiomatic domain exist whether we value them or not. The theorems of Euclidean geometry are true, even if we prefer non-Euclidean geometry."

This seems like a crazy view to me. As we all know, an axiom system is just a set of statements. If you pair that axiom system with a logic, then you can also generate the theory of that axiom system, the set of theorems provable from those axioms with that logic.

Now, in some sense you might want to call these theorems "true" but it should be in a very highly qualified sense. To demonstrate why you should accept this, let me start with the assumption that everyone accepts the validity of inferring A from A.

Suppose, then, that I take any old claim I want like the statement "frogs are mammals". Call this the monadic axiom system FM. According to this system it is a provable theorem that "frogs are mammals". From what you said above, you would have to admit that it is true that frogs are mammals since it is a provable theorem of some axiom system. Obviously, this is incorrect, so you must not really have meant it when you said that all theorems are true.

What makes more sense is to say that all theorems are true relative to the axioms from which they are provable. That is totally different from saying that all theorems are true. I'm guessing you really meant something along these lines. Then again...

doctor(logic) said "That some primitive screwheads reject science does not imply that science is somehow untrue under its own axioms. It's just a question of whether a man thinks the objective power of science is important."

Here you seem to be saying that science is true under its own axioms, but that science is not true for the religious person because they do not accept scientific axioms. Now we have completely obliterated any notion of simple truth. This way of talking relativizes all truth whatsoever to a system of axioms. This relativization of truth gets us into some serious trouble, though. What sense can you make of this:

This sentence is absolutely true.

If truth is relative to an axiom system, then this sentence would have to be false (its content denies that all truths are relative, so it is incorrect). In that case it would be false in general, so we would still have a non-relative truth: that the absolute claim in bold above is false period, for everyone, regardless of axioms. On the other hand, if the sentence is true then it would have to be true under every axiom system. In that case we would have a non-relative truth: that the absolute claim in bold above is true period, for everyone, regardless of axioms. So either way, whether this sentence is true or false, it is so generally and not relatively. Thus, the idea that all truth (or falsity) is relative to an axiom system is refuted.

Last comment, on moral relativism. If you think morality is relative, why would you ever have a moral debate with anyone? Maybe you never have, but I will assume that like most people you have at some point in your life engaged in moral debate. The only things worth debating are facts, like whether the Earth is really flat or not. There is a truth to the matter and, by inquiry, we can presumably settle the debate.

Other things, that fall under the spectrum of personal taste, like my preference for chocolate ice cream, are not worth debating. I might say that chocolate is good, you might say that chocolate is bad, but we are not really having a debate. We all know that these are just expressions of personal taste, I agree that you dislike chocolate, you agree that I like chocolate, the apparent disagreement is entirely superficial because we are not disagreeing about anything.

The moral relativist says that morality is a matter of personal taste, but oddly enough they go on debating with people all the same. What does this tell us? That relativism is wrong? Not exactly, but it is something to seriously ponder.

If we add the premise "actions speak louder than words" the conclusion is clear. Relativists claim that morality is subjective, but in their behavior they go on debating with people over moral issues. Since actions speak louder than words, their engagement in moral debate seems to indicate that, at heart, they really believe morality is objective. I can only conclude that moral relativists are confused and don't realize that their theory is incompatible some of their most basic assumptions.

This doesn't prove that moral relativism is wrong, but it does purport to demonstrate that most avowed "relativists" don't really believe in moral relativism even when they say they do.

Doctor Logic said...

Hi Colin,

Thanks for the detailed response.

What makes more sense is to say that all theorems are true relative to the axioms from which they are provable. That is totally different from saying that all theorems are [absolutely] true. I'm guessing you really meant something along these lines.

I do agree with this, and let's stipulate it is true.

What, then, determines whether something is absolutely true? For that matter, what defines truth at all?

Truth requires some sort of test, and there appear to be lots of ways to test for truth:

1) Deductive logical proof
2) Experimental verification
3) Emotional desire, aesthetics
4) Revelation
etc.

Each set of methods and priorities for determining truth leads to different assertions of axioms, and different assertions of truth.

Suppose Bob asserts that there are absolute truths, and that it is vital to know what they are. If Bob perceives that the detection of absolute truth is impossible given our human faculties, he may assert that revelation is the only way to know absolute truth. In that case, the contingent truths of science are subordinate to scripture because Bob has explicitly devalued verification to the point that it is trumped by revelation. In that case, the experimental result that the Earth is more than 6,000 years old, true though it may be within a scientific system, is regarded as false because revealed truths obtain a higher priority.

Is it rational for Bob to be a creationist? It might be, in some circumstances. If Bob regards life without absolute truth (and, typically, without an afterlife) as not worth living, then his choice might be rational. Bob may feel that a chance at access to absolute truth is more important than guaranteed access to available but non-absolute truth.

Absolute truth seems to rely on an absolute prioritization of truth tests. Is there a uniquely correct way of establishing this ranking? I don't see it.

What sense can you make of this:

This sentence is absolutely true.


Though I don't think this particular proposition works, I'll try to address what appears to be the spirit of the attack. Maybe, your argument would work just as well if you said that "P is absolutely true," or rather "I absolutely assert P."

My response is that I'm not making an absolute assertion that there is no absolute truth. I'm just stating that we have found no indisputable basis for a claim of absolute truth.

In other words, what does it mean for one to "absolutely assert" a proposition versus simply "asserting" it? Or, put another way, what is the test for absolute truth versus relative truth? I'm saying that, so far, we haven't found any remotely objective ways of doing this.

At best, we can try to find common ground either upon shared truths, or upon priorities for testing the truth of claims. For instance, on what basis are we to judge that, say, experimental verification should trump aesthetics? The most intuitive answer would appear to be that scientific theories are more useful than aesthetics. But then truth becomes slave to utility in a way that many people would reject.

Last comment, on moral relativism. If you think morality is relative, why would you ever have a moral debate with anyone?

Persuasion.

In the case of gastronomic taste, I don't really need to debate you about the deliciousness of chocolate unless we can only have one item of food between us. However, ethical debates frequently involve competing interests, and in that case, it is often of immense value to me that I try to convince you to act in a particular way. To that end, I can only use argumentation to appeal to values (and related axioms) that you already hold. You might hold that preserving life is more important than your desire to maintain freedom to own guns, and you might therefore be willing to compromise on gun ownership if I can show that certain gun restrictions will save lives. In this case, my argument doesn't require that we share precisely the same axioms, nor that any moral axioms be absolutely true.

I also might be able to show that another person's moral position is logically inconsistent, and this might weaken that person's commitment to an objectionable moral position (assuming they value logical consistency, i.e., they will not deply the Da Do Do Do, Da Da Da Da defense!).

Beyond persuasion there is aesthetics. I just hate to let a bad argument lie. :)

Colin Caret said...

doc, excuse me for saying so, but I think you are still off topic. Also, just on a side note, I for one would love to see a discussion on here that doesn't at some stage end up in ad hominem attacks against creationists. I mean, there are a lot of us out here who are not creationists and don't really much care what creationists believe.

Anyway, you say that the creationist might regard the scientific theory of the age of the Earth as false, and this is clearly correct. In fact, anyone could regard just about anything as false if they wanted to for some reason. But what does "regarding" as true or false tell us about truth??

The way you talk about these issues you make it sound like, whatever I believe makes certain things true for me because those things would follow from my beliefs. That is insane!

Someone may believe the Earth is flat, and they may then in virtue of their belief regard it as true that the Earth is flat... but that doesn't make it true!! I'm afraid this person is simply horribly mistaken, the Earth is not flat, regardless of what priority they place on various beliefs or tests of truth.

Now, rationality is a totally different animal. It could be quite rational for someone to beleive the Earth is flat. In fact, we have every reason to think that lots of people, in fact, rationally did believe such things thousands of years ago. This just goes to show that rational belief and true belief are different things.

But here is where it really comes out...

At best, we can try to find common ground either upon shared truths

So, as far you are concerned, truth is something personal? There is MY truth and YOUR truth, there is the truth held by President Bush and each other person? I just can't get my mind around this. It seems patently incorrect to the data of how we use the truth predicate. I just don't find relativization of truth to be a very convincing way of reading any ordinary discourse. What reason could there possibly be for thinking that truth is personal?

Doctor Logic said...

Colin,

I understand your frustration here, but if your position is on such solid ground, why not address the issue? What is the test for an absolute truth?

To me, it seems unreasonable for you to demand I accept a new category of truths when you fail to identify the distinguishing characteristics of such truths. It's like asserting that there are special electrons, without identifying what makes them special, or what tests we might use to identify them.

Your response is an example of persuasion. A plea for me to adopt the same criteria for truths (e.g., science, logic, some attempt at rejecting human and personal predilections) lest I be labeled a sympathizer of flat-Earthers or Republicans. However, your plea is misdirected, for I already hold to truth tests similar to your own.

For example, you rhetorically suggest that I would pat the flat-Earther on the back rather than scold him for rejecting my standards of truth. But, as the ad hominem in my original post illustrates, I am perfectly willing to persuade others to adopt my (our?) preferred truth tests.

What your response lacks is any answer to the subjectivity of truth test selection. Yes, you and I agree that the Earth is not 6,000 years old, and that holding such a view rejects truth tests we feel are important. However, how are we to logically convince someone that they should adopt our testing procedures?

We cannot. We can only persuade the dissenter that she would be happier, more satisfied, or in some way feel better if she agreed with our approved methods of truth testing. However, this process of persuasion seems hopelessly subjective. Clearly, there are some people who would prefer to reject key axioms and live in what we consider to be blissful ignorance rather than accept our worldview. They are willing to risk self-delusion rather than accept more reliable truth testing procedures.

I'll note that there are some people who profess belief in a rational world, but who are simply inconsistent in their views, and they can be led to a more consistent view by logical argument. For example, some people accept the idea that there should be a logical coherence of experience and meaning (as we do), but they simply get confused about their own definitions by taking words out of context (i.e., they run afoul of ordinary language philosophy). For these people, there is a lot that can be done using experiment and logical argumentation.

However, not everyone believes that all meaning and things of value are to be found in the logical structure of experience. There are people who believe that the most important things in life (e.g., free will) are sublime, and cannot be reasoned about, and are not even subject to logical constraints. In many a debate, non-materialists have all but said that life in a purely material world is not worth living. I'm not convinced they would continue to maintain such an opinion if they came to accept my belief in such a world, but that is their present value judgement. They beg the question for non-materialism in the same way we beg the question for logic and predictability. Material minds cannot be sublimely free, they say. Non-material things are unknowable to the point of being devoid of sense, say we. Where we subjectively value human-objective tests for truth, they subjectively value human-subjective ones.

So, let me focus this debate with some questions for you.

Why is the non-materialist absolutely wrong to reject scientific statements when they conflict with, say, revealed truth?

What is the test of absolute truth, i.e., what is the correct prioritization of truth tests and why?

If absolute truth is defined by some convention (e.g., ours), why is it important to live by it?

Finally, as for your tangent about creationists... Maybe you think I suspect you of being a creationist. I don't, and never have. I admit that I made an ad hominem attack on anti-science types in my original post, but this seems a rather late stage to be complaining about it. The comment about creationists in my last comment was, if anything, flattering to creationists, not insulting to them. I also hadn't noticed a pattern of ad hominems against creationists. I think I rarely mention them because their views are poorly regarded, even among theists.

Colin Caret said...

Okay, let me try to start this over. It seems to me that the confusion coming up is between justification and truth. I am happy to say that there are all sorts of routes to rational belief, all sorts of different methods of justification, but it seems like a terrible mistake to say that there are many different kinds of truth.

Now, you want an argument why truth should be taken to have this privileged, categorical status? Well, basically the argument is a linguistic one. Here goes a version of it.

Truth is a semantic concept. It is something we use for semantic commentary, in cases where we lack the ability to directly express the content we are interested in. When I say "its true that the sky is bue" I am just expressing that the sky is blue. This much seems to follow simply from the linguistic data: truth is a device that gives us a way of reiterating, emphasizing, or generalizing over meaningful expressions of our language.

Because the expressive parts of our language -- sentences, and so on -- have objective, public meanings they also have categorical truth values. We all know that, as a matter of fact, the Earth is not actually flat. Thus, it is false that the Earth is flat. Period. Without qualification. Doesn't it just seem to make sense that truth and falsity are non-relative concepts? After all, it is one of the most salient features of our concept of truth that it is something objective and independent of our beliefs.

However, relative justification is perfectly reasonable. There is nothing odd about it at all. What is rational for you or me to believe depends on lots of factors specific to our respective epistemic positions. These include all sorts of cultural and technological factors as well as the quality of education offered by our parents or community and our natural abilities. It might be rational for someone living in Ancient Greece to believe the Earth is flat, while it is irrational for you or me to believe as much. No big deal.

Still, it is a mistake to take truth and justification to be the same thing. What you are calling "tests for truth" are just methods of inquiry. There are, of course, a variety of methods of inquiry known to mankind. Clearly, the most fruitful such method is the scientific method, but it is not exhaustive.

What these tests have in common is that they deliver justification in some degree. A scientific test does a very powerful job of delivering justification with respect to our empirical theories of the world. Some philosophers think that introspection or intuition might deliver justification with respect to our ethical, logical, and modal (non-empirical) theories of the world.

But we should not confuse these tests with truth itself. Presumably, truth is something independent of our best theory. Yes, our tests for truth, our epistemic methods, give us reason to regard some things as true over others. Still, we can always be mistaken, so despite how good a test may be or how passionately we may endorse it, its results are never guaranteed to be the truth.

doc: What your response lacks is any answer to the subjectivity of truth test selection.

I hope you see now that I am comfortable with "truth test selection" being subjective. I just hope to have made it clear that this is not the same as saying that truth is subjective.

Let me take a stab at some of your questions. I don't know if I can say anything about the first one, but I'll try with the second and third.

doc: What is the test of absolute truth, i.e., what is the correct prioritization of truth tests and why?

As you probably see, I don't really distinguish between truth and absolute truth. What I do distinguish is truth from some other relativized notions (like justification or belief). There are lots of tests for truth, in fact just about any epistemic method can be considered a test for truth. What makes one test better than another depends on its track record with respect to the virtues of the theories it produces. Are they adequate to the data? Are they ontologically parsimonious? Do they have some degree of explanatory power? These are the criteria that count when it comes to theories and the best theories point to the best tests for truth -- whatever methods led to those theories.

doc: If absolute truth is defined by some convention (e.g., ours), why is it important to live by it?

It is not defined by convention. That is what I have been trying to say, perhaps unclearly. I don't know if it is important to live according to the truth. That is no part of what I have been arguing. For all I know about happiness and the good life, it might be better for us to believe some falsehoods.

Closing comments...

doc: Maybe you think I suspect you of being a creationist. I don't, and never have.

No, no, sorry if it sounded that way.

doc: I admit that I made an ad hominem attack on anti-science types in my original post, but this seems a rather late stage to be complaining about it.

Maybe so, it was somewhat tangential. Sorry.

Doctor Logic said...

Colin,

I think you have nicely rephrased our debate in terms of methods of inquiry, or rather, justification versus truth. The key statement in your response was this one:

But we should not confuse these tests with truth itself. Presumably, truth is something independent of our best theory. Yes, our tests for truth, our epistemic methods, give us reason to regard some things as true over others. Still, we can always be mistaken, so despite how good a test may be or how passionately we may endorse it, its results are never guaranteed to be the truth.

I'm not convinced that truth and justification are independent. That is, it seems that truth is that which is justified, and a method of inquiry is that process we utilize to get to the truth.

Intuitively, you are correct that the truth feels like something one might reach by any number of methods, and that it should therefore be regarded as independent of method. However, you also say this:

When I say "its true that the sky is bue" I am just expressing that the sky is blue. This much seems to follow simply from the linguistic data: truth is a device that gives us a way of reiterating, emphasizing, or generalizing over meaningful expressions of our language.

This suggests that truth is a form of confidence in a proposition justified by a method. That when I "learn the truth about a crime," I reach not just a possible theory of what happened, but a theory in which I have high confidence. And I reach this confidence by using a method of inquiry.

What makes one test better than another depends on its track record with respect to the virtues of the theories it produces. Are they adequate to the data? Are they ontologically parsimonious? Do they have some degree of explanatory power? These are the criteria that count when it comes to theories and the best theories point to the best tests for truth -- whatever methods led to those theories.

In spirit, I'm right with you here. :) The best theories point to the best methods. That is, prediction is the arbiter not only of truth, but of methods of inquiry because the test of a theory is in the comparison of the theory's results with experiment (physical or computational). Historically, revelation and intuition have been miserable at delivering reliable theories, so they should get booted as tests of truth.

Also, it could be said that objectivity relies on shared prediction. An objective statement is a recipe for getting a particular answer. Add 2 and 2 and get 4, or burn hydrogen in oxygen and get water. Then the question is whether all absolute truths need to be objective in this way. I think this might be the determining factor in our debate. If objectivity is a requirement of truth, then this would certainly support your claim, even if it falls a little short of proving it.

However, the idea that prediction should serve this role seems to be controversial. (Maybe it's only controversial in the blogosphere.) For example, if prediction has this role, then morality is certainly relative. Moral theories predict nothing except how we will feel about a sequence of events, not whether such a sequence is intrinsically good or bad.

I'll give you another example. Theists hold that there are unverifiable truths, and that reliance on prediction begs the question for materialism. Theists would complain that there could be no emotional truths (e.g., concerning love). Indeed, certain attributes of God might be viewed as subjective truths.

Do you think objectivity is necessary for truth?

Colin Caret said...

I certainly do think objectivity is necessary for truth. They are, in my book, interdefinable concepts. Now I am coming around to understanding your point and I probably should have gotten it earlier. You are echoing a type of argument that is often advanced by anti-realists such as Dummett and the logical positivists. According to this theory, truth just is determined by epistemic practice. They might say that X is true if and only if...

1) X would be part of our best overall theory, or

2) X would be justified at the limit of inquiry, or

3) X would be assented to by anyone under ideal conditions C (where these conditions may be partially constitutive of the truth of X)

In that case, your view is far from peculiar or obviously wrong, it is part of a long tradition of powerful anti-realist theory. I have a lot of respect for these types of theories, but in the end I don't think they convince me. And as to this comment:

revelation and intuition have been miserable at delivering reliable theories, so they should get booted as tests of truth.

But what have we been using in this discussion? It seems to me that the difference between your view and mine is a difference of intuition about truth. So I think you might want to be cautious about throwing out intuition. After all, it is really the only tool we have for exploring such non-empirical topics as semantics (truth, etc.) and modality. If you throw out intuition entirely, then you end up having no data to settle debates about these subjects.

Doctor Logic said...

Hi Colin,

Sorry for the delay in getting back to you.

You are echoing a type of argument that is often advanced by anti-realists such as Dummett and the logical positivists.

And sorry if I hindered your understanding by playing my verificationism a little close to my vest. The mere mention of verificationism can sometimes induce convulsions when I bring it up in debates. :)

It seems to me that the difference between your view and mine is a difference of intuition about truth. So I think you might want to be cautious about throwing out intuition.

This comment got me thinking, and I've just written a new post about intuition. I agree that intuition is important, but I think that intuition comes in different varieties, some good, some not so good.