Wednesday, December 27, 2006

Defining Subjective and Objective

How does one define the objective and the subjective? It's not as easy as it sounds.

If we aren't careful, we might find that everything is one or the other, and the distinction will mean nothing. If everything is subjective or everything is objective, what good is the distinction? What are we going to use the distinction for? It would be a pointless exercise.

What we are looking for is a distinction under which some things are objective and everything else is subjective.

First, let's admit that everything we know is known through our own faculties of reason and sensation, both of which are known to be imperfect. If susceptibility to such imperfection defines the subjective, then everything would be subjective (so we rule out that definition).

Second, let's also admit that the subjective nature of our individual faculties might be a matter of objective fact. So, if the distinction is to be made, I think we ought to be able to make it whether or not every fact in the universe could be objectively known.

I think that these two admissions lead me to propose the following definition:
An attribute of a thing is subjective when it cannot be determined that the attribute is a feature of the thing itself rather than a consequence of our mental faculties.
Note that, under this definition, if we don't have evidence of the faculty-independence of an attribute, we regard that attribute as subjective.

So, what constitutes evidence of faculty-independence?

I think that evidence of faculty-independence comes in the form of high-precision, alternative comparators. To explain, let's look at why physical mass is regarded as objective.

Technically, humans aren't sensitive to mass, but to force. So we're asking, is "how heavy a thing feels" just a subjective perception? In absolute terms, weight is subjective - a small child will find a 100 pound weight immovable, but an average adult won't. However, what we're really asking is whether relative weight is a measure of something about the weighed objects, or whether it is just about how we are perceiving them.

The way to test this is to find something other than personal sensation of force to use as a comparator. A balance scale, for example. Based on how comparatively heavy two objects feel, you can pretty accurately predict which way the scale will tip when the scale is used as a comparator. You can also do the reverse, and, based on the scale, predict which will feel heavier. You can do this independently of the visual size, shape or composition of the objects.

I think a lack of an acceptable external comparator is what makes a field subjective. If I have two rooms, one containing an ugly person, and another containing a beautiful person, there's no 'beauty-meter' I can poke through the keyholes to tell me which room is which. If I could build such a device, it could work only by emulating me (e.g., through training against my tastes).

Likewise, there's no justice machine that tells us whether one act is more just than another. Any such machine would have to be trained or conditioned against our tastes (e.g., through the use of juries and legal precedent).

Can another person act as an external comparator? I think the answer is "no," and that precision is the vital clue here.

In objective fields, human-trained machines can outperform their trainers. For example, based on my experience with some 1-pound weights, I can devise a machine (such as a balance scale) that can compare two masses weighing hundreds of pounds. More importantly, this machine can be far more sensitive than me when it comes to weighing very small masses. So, I can use the machine to extrapolate beyond my senses and get higher precision, and verify that this sensitivity is real. I can weigh all the grains of rice in a sack, and verify that the heaviest 25% of the grains weigh noticeably more than the lightest 25% of the grains. I can verify that the machine is better than I am at weighing things.

In contrast, human-trained machines can't outperform their trainers in subjective fields. I don't think that a committee or a technical analysis is a more precise judge of beauty or gastronomic taste than the "best" human judge. Likewise, I don't think that the justice system or a religious authority has demonstrated higher moral precision than a good individual human. I think this is a clue that our inventions in these spaces are mere approximations to our subjective feelings.

Similarly, in a subjective field, I cannot verify that another person can work better as external comparator. Suppose you wish to use your friend Plato as an external comparator for the beauty of women. Suppose that 90% of the time, Plato agrees with you. When Plato disagrees, how will you settle the argument? There's no mechanism you can use to verify that Plato is right or wrong.

The same goes for morality. No other person can act as a verifiable external comparator. If God is taken to be an external comparator, then not only must you have faith in his existence, but you must also have (double) faith that he is an accurate external comparator because you certainly can't verify that his is right and you are wrong.

Based on my definition, we are forced to conclude that morality and aesthetics are subjective, whereas mathematics and physics are objective.

Can we find an alternate definition that will hold morality objective, but maintain the subjective-objective distinction? Well, I can't rule out that possibility, but I can't think of a viable alternative. This is because I think that one can't claim objectivity of an attribute if it's observer-dependent, so the tests I have outlined appear to be minimum requirements of objectivity.

8 comments:

Wedge said...

doc,
What about the law of non-contradiction? Modus Ponens? 2+2=4?

These things are objectively true regardless of the fact that there is no independent comparator to confirm that they are. Their objectivity rests in our universal human intuition that they cannot be otherwise. We "just know" it.

If this is the case, there is no clear reason to write off all shared moral intuitions (like "torturing babies for fun is wrong") as obviously subjective.

Doctor Logic said...

Wedge,

We have to assume the pillars of rationality (e.g., non-contradiction) or else we can't argue anything. In contrast, we don't have to assume that theorems objectively follow from axioms. If logic always worked albeit subjectively, I don't see why that would pose a problem for the subject in question.

Indeed, if arithmetic were subjective, we could both coincidentally believe that 15 + 20 = 35, and we might not notice the lack of objectivity.

Of course, we can show by the method above that theorems do actually follow objectively from axioms, e.g., by using computers and notational mechanisms.

Wedge said...

doc,
You seem to be saying that since the fundamentals of logic and mathematics are foundational to everything we do, and since we all agree on them, it doesn't matter whether they are objective or subjective - and, in fact, they are subjective according to your definition. A couple of thoughts:

1) The idea that something like weight is objective but the fundamentals of logic are not is wildly counterintuitive. It seems a high price to pay to declare moral statements subjective by definition.

2) Any independent verifier that we build for a physical property like weight (it appears that only physical properties can be objective under your definition) will need to be designed by an engineer. In the design process, the engineer will make extensive use of both mathematics and logic. How can the end-product tell us anything about objectivity if its proper function depends upon subjective principles?

Doctor Logic said...

Wedge,

Technically, I said that the foundations of rationality are not provable, which isn't the same thing as saying that logic is not objective.

Every mathematical system is built upon axioms. If I assume the axioms of Euclidean geometry, I get the theorems of geometry. If I don't assume them, I may not. Indeed, non-Euclidean geometry gives theorems which contradict theorems of Euclidean geometry. Yet neither system of geometry is actually better than the other. We cannot objectively say that the axioms of Euclidean geometry are the correct ones. However, we can say that the conclusions that follow are objective. This can be done with computers.

So, I'm not really saying anything counterintuitive about mathematics.

In the design process, the engineer will make extensive use of both mathematics and logic. How can the end-product tell us anything about objectivity if its proper function depends upon subjective principles?

I think there's a confusion here about the meaning of subjective in this context. Here, a subjective attribute is one that is painted onto the objective facts by the self.

For example, the "curativeness" of penicillin is not in the penicillin itself. The curativeness of penicillin is in its reaction with our individual biochemistry. It's not that penicillin is objectively curative and that an allergic patient is out of touch with reality. Thus, curativeness is subjective.

I have another test of objectivity that I will write up in a new post.

Wedge said...

doc,
The fact that we need to assume certain principles in order to get anywhere does not make it a matter of indifference whether or not those principles are true. It certainly doesn't mean that no system of axioms is better than another. If the foundational axioms of rationality and mathematics are not objective, observer-independent truths, then we can have no knowledge whatsoever about the nature of the world. We can only derive what follows from our axioms (which you don't seem to think have any knowable truth value).

Doctor Logic said...

Wedge,

The fact that we need to assume certain principles in order to get anywhere does not make it a matter of indifference whether or not those principles are true.

Without the axioms, there is no truth at all. Your demand is a bit like saying that there's no point in having a Superbowl champion if we're not certain that the rules/laws of football are absolutely true. Yet we cannot prove that the laws of football are absolutely true. We merely assume that the laws of football are what they are because, if we didn't, there would be no such thing as the truth of a winner. Truth requires a test of truth, and there's no such test for the axioms of logic.

If the foundational axioms of rationality and mathematics are not objective, observer-independent truths, then we can have no knowledge whatsoever about the nature of the world.

This is overreaching. The correct statement is:

If no subset of experiences have a structure which is logical and discoverable, then we can have no knowledge whatsoever about the nature of the world.

Fundamentally, there's no reason why parts of the world can't be acausal or inconsistent (indeed, quantum mechanics can be interpreted as saying this). It's just that if all the world was like that, we couldn't have any knowledge of it. So, I don't see how we get from a statement like "some of the world is logical" to the absolute truth of the axioms of logic.

We can only derive what follows from our axioms (which you don't seem to think have any knowable truth value).

I didn't say that theorems have no knowable truth value. The truths that follow from assumed axioms are objective, frequently knowable, and valuable. The theorems have truth values because the axioms show us how to say whether a theorem is true or false. Truth values can and do follow from assumptions.

Wedge said...

doc,
I claim that certain axioms, like those that underlie logic and mathematics, are necessary truths. That is, they are true in all possible worlds. They could not be otherwise, and you don't need a proof to know it.

Not all axioms are like this. Consider the assumption that my memories are (mostly) reliable accounts of my past experiences. Could this be false? Absolutely. It is possible that evolution or a malignant deity might have rigged me with an unreliable memory. But is there a possible world in which the law of non-contradiction is false? Or 2+2=5?

I don't know how to respond to your comparison between the axioms of rationality and the rules of football. It seems clear to me that the rules of football are contingent, while the rules of reasoning are necessary.

Truth requires a test of truth
I deny that this is the case. And, since affirming it leaves us with no real connection to the world outside ourselves, I think I have good reason for doing so.

If no subset of experiences have a structure which is logical and discoverable, then we can have no knowledge whatsoever about the nature of the world.
I don't think your “subset of experiences” alteration really weakens my point. If the axioms which allow us to carry out logical discovery are imposed on the world in order to allow us to cope, then they have no necessary connection to it. We cannot examine the world to see if it is rational because we use rationality to examine the world. We may discover that rationality is useful or valuable, but that is all that we can say.

I didn't say that theorems have no knowable truth value. The truths that follow from assumed axioms are objective, frequently knowable, and valuable.
I understand that theorems can follow “objectively” from assumptions. But you don't think assumptions/axioms themselves have any truth value. You admit as much when you say Truth requires a test of truth, and there's no such test for the axioms of logic.

You seem to think that this is just the way it has to be – that everyone must just accept that no axioms have truth value, and move on. But this is not the case. There are worldviews which offer positive reasons for thinking that rationality is not a convention but a fundamental truth about the world. Yours is just not one of them.

Doctor Logic said...

Wedge,

I claim that certain axioms, like those that underlie logic and mathematics, are necessary truths. That is, they are true in all possible worlds. They could not be otherwise, and you don't need a proof to know it.

They could not be otherwise in any consistent world, right? The force of necessity derives from the need for consistency, does it not? That seems circular to me.

Also, I think that reliability of memory is as necessary for rational thought as the law of non-contradiction. The law of non-contradiction is useless if I misremember X as ~X.

Truth requires a test of truth
I deny that this is the case. And, since affirming it leaves us with no real connection to the world outside ourselves, I think I have good reason for doing so.


In what way does this sever any such connection? What is and isn't the self is pretty well defined by what we can test, and anything that is in principle untestable is irrelevant to experience.

If the axioms which allow us to carry out logical discovery are imposed on the world in order to allow us to cope, then they have no necessary connection to it. We cannot examine the world to see if it is rational because we use rationality to examine the world.

Well, I think we can say that the world appears to be mostly rational, and we can ask what the irrational bits of the world might look like to us. That's why I think 19th century scientists and philosophers could have predicted quantum effects had they asked what the universe might have been like if it were partially inconsistent.

We may discover that rationality is useful or valuable, but that is all that we can say.

What more is there to say that is of any value? :)

But you don't think assumptions/axioms themselves have any truth value. You admit as much when you say Truth requires a test of truth, and there's no such test for the axioms of logic.

Technically, I don't think they have absolute or determinate truth values, which is slightly different.

There are worldviews which offer positive reasons for thinking that rationality is not a convention but a fundamental truth about the world. Yours is just not one of them.

But this is a sort of confusion. In order to justify your assumption of rationality, you (1) assume that it is possible for a thing to guarantee rationality, then (2) assume that such a thing actually exists. It's all rather contrived, especially since the other two assumptions can't be proven either. Why have faith in (1) and (2) when you can just have faith in rationality itself?