Tuesday, September 20, 2005

Existence Confusion

We sometimes paraphrase meaningful propositions in ways that are not strictly meaningful.

Take the proposition all Carbon 14 atoms will eventually decay. Literally, this proposition can never be tested. However, physicists would accept this as meaningful because they can translate it into a meaningful proposition, namely, the mean lifetime of Carbon 14 is 5,500 years. Technically, a Carbon 14 atom need never decay (though it would be extraordinarily improbable).

When you provide me with a philosophical proposition, I can try to squeeze it into a meaningful context, or paraphrase it so it does. I can almost always do this, as I demonstrated.

However, some propositions are designed to be resistant to this sort of reformulation. Suppose you give me just such a proposition:

A necessary, uncaused being exists.

If you accept my claim that a proposition must be part of a logical model and a choice of symbols to be meaningful, then we have to identify what that context is.

Here, you use the term "exists". You might mean this in a way that is different from when we say that "this cup of tea exists." We'll rewrite your verb as $exists until we know what it means.

For everyday, physical objects, existence is predicated on a specific definition of what empirical attributes the objects have. They are said to exist not when we can imagine them, but when we observe them.

For example, if you say that "a cup of tea exists on the table", and I look at the table and find that there is only a bowl of sugar on the table, then I have falsified your claim. Without these tests the verb to exist would be useless because elephants could exist on the table just as well.

So in your proposition, what are the specific, observable qualities of this being that would afford its existence if we observed them?

If you don't have any such qualities, then the verb you are using is just $exists not normal exists.

In the latter case, what does $exists mean? Perhaps, it is the fictional interpretation of exists, e.g., Chewbacca's third heart exists if we could only do an MRI on him in the Star Wars Universe. I doubt this because you have not shown what experiment, real or fictional would validate your claim.

Your claim is that this being (whatever a being is in this context) has a property of $existence which is as yet undefined. This is what I mean when I say it is meaningless.

The fact that confused people, some philosophers among them, feel they "understand" your proposition is not adequate to make your case. People think they understand a lot of things that they don't. In this specific case, people have an intuitive sense of what existence is. In their brains there is a cluster of neurons that fires when the concept of existence is triggered. This region forms as we grow up, using the verb to exist in the coffee cup sense. However, once we have a word for this existence property, it is tempting to trigger this region of the brain out of context. It is tempting to say that existence is just an attribute of a thing that makes it real.

This is confusing to us because we intuitively think things can exist independently of their properties. Next, we start saying X exists where X is something unobservable. It sounds grammatically correct, and it seems intuitively possible, but it is actually nonsense. It is a psychological illusion.

Now, your proposition may still form part of a logical structure, but unless you can define $exists in some rigorous way, you really aren't saying anything about the world.

Suppose you provide me some other interlocking propositions. Maybe "If a being A $exists, then there is a being B that does not $exist". (I have no idea what this means, but it would seem to logically relate to your proposition.) Even in that case, none of your interlocking propositions have any empirical consequences except for their own computational self-consistency. What makes such a proposition about the world? Nothing, I would say.

7 comments:

leibniz said...

If you don't have any such qualities, then the verb you are using is just $exists not normal exists.

I don't think we can define existence, ordinary or otherwise. But suppose for the sake of argument that I were to define existence as the property of having actual attributes. On this definition, fictional things would not exist, because not being actual, they would not have actual attributes. Ordinary material things would exist, because they would have actual attributes, which would just so happen to be empirical attributes. But immaterial things might also exist. For example, there might be a divine being who has some actual attributes, such as omnipotence, which he cannot be observed to have. This is really much closer to our ordinary conception of existence.

The fact that confused people, some philosophers among them, feel they "understand" your proposition is not adequate to make your case.

Yes it is, actually. Remember that the case I was trying to make was a very modest one: I was trying to show that there is prima facie evidence for the existence of a third category of statement to which metaphysical claims belong. The mere fact that most philosophers and philosophically minded people, including most of the people to whom your argument is presumably directed, acknowledge this third category is enough to make the point I was trying to make.

Recall that you made an argument against metaphysics, which took the form of a dilemma. I criticized this argument by pointing out that friends of metaphysics (presumably the people you are trying to persuade with your argument) recognize a third possibility that you have simply ignored in your argument, thus making it a false dilemma. In response to this, you claimed that it was the metaphysician's burden to show that this third option is a real possibility. I denied this on the ground that you are the one setting up the dilemma, so that you must bear the burden of showing that this third option, which is widely accepted as possible, isn't really possible.

You still haven't really provided us with any reason that would be accepted by anyone not sharing your logical positivist prejudices for the claim that there can be no statements that are both non-empirical and not about the world. This, again, is what needs to be shown in order for your argument against metaphysics to have any force for the people who don't already accept your conclusion

Doctor Logic said...

I don't think we can define existence, ordinary or otherwise.

Ah, but we have to. It must at least have some operational or computational meaning.

I think this has a lot to do with knowledge and understanding in general. Here's where I'm going with this.

My friend Robin posted a comment about this while back along the lines of: does a thermometer know the temperature?

Well, a thermometer has no intellect, so we are hesitant to say that it knows or understands anything. It certainly responds to temperature in a consistent manner (when it's working right). I think what constitutes intelligence and knowledge, is meta-knowledge: knowing that you have knowledge. An intelligent machine will have to be able to create theories about what it knows, and must be able to determine when it knows something and when it doesn't. It has to be able to tell when its pre-programmed knowledge is garbage programmed in by its creator as opposed to actual facts. That is, it has to be able to verify it in some way.

As humans, our memories and our reasoning are imperfect. We may not recall a witnessed event with perfect clarity. A chain of reasoning is itself a sequence of events or steps, and we may not recall these perfectly either. So when we say we know something, it must go deeper than simply recalling that the answer to question X is Y.

Confidence in knowledge comes from analysis and repeatability of the steps we took to derive the knowledge, and in confirming the knowledge with predictions (empirical or computational confirmation).

It should be of great concern if we cannot define the symbols we are using. If we cannot define our symbols, it is impossible to verify meaning.

When you give me a proposition, I can only know what it means if I can decide on a recipe by which the proposition can be verified or falsified. That recipe could be mathematical, i.e., involve consistency relations with other propositions or axioms. Or, the recipe could be empirical, i.e., involve the observation of physical phenomena (actually, computation is a subset of this). Could there be a third kind of recipe? I don't see how.

Let's give some examples.

234 times 56 is 13104

We know what this means because we know how to verify it, both computationally and with correspondence with empirical objects, e.g., by counting widgets out of 234 crates containing 56 widgets each.

The universe came into existence a finite time ago.

We can create an acceptable, empirical definition of the universe as containing all events and all phenomena. Coming into existence is a tricky one because there is no concept of time before the beginning of the universe. However, we can formulate some model in which we know what propositions might be consistent with our thesis.

We can break these examples by using symbols for which we have no corresponding recipe.

salamander times frog is giraffe

What happens when we try to determine the meaning of this proposition? We come up with theories like there is a symbol scoring mechanism wherein the animal names correspond to numbers and the operations are mathematical.

Or perhaps there is some biological operation in which sharing genes from two species yields the third.

Or these words are just colorful symbols in some set of mathematical relations, like a.b=c.

We really can't say we know what this means until we have the recipe for verifying that we know what it means.

Returning to your original proposition:

A necessary, uncaused being exists.

You really can't say you know what this means if you can't say what the word "exists" means, or what the word "being" means, or in what way the being is "necessary".

As it stands, I would agree that people have an emotional reaction to this proposition. It certainly sounds deep and profound. Yet, if we cannot say what it means, we must either discard it as a confusion, or admit that how a string of symbols makes us feel is equivalent to its content (i.e., it is poetry).

leibniz said...

I don't think we can define existence, ordinary or otherwise.

Ah, but we have to. It must at least have some operational or computational meaning.

It must have a meaning, but that doesn't mean we can define it. Is it your view that all meaningful terms must be capable of being defined? It is an old philosophical truth that not everything can be defined. For if we do not allow circular definitions, supposing that every word can be defined sets us off on an infinite regress. At some point we come to words that we regard as meaningful that aren't defined. This happens in physics as much as in mathematics and metaphysics.

I would be inclined to agree with you that intelligence is something like knowledge that we have knowledge. This is close to the traditional idea that intelligence requires self-consciousness (awareness of one's own beliefs, desires, and mental states). (Incidentally, you say that "what constitutes intelligence and knowledge, is meta-knowledge: knowing that you have knowledge." But you should strike 'and knowledge' from this: knowledge cannot consist in knowing that you have knowledge.)

What I don't get is how you slide from this claim:

Intelligence consists in knowing that we have knowledge.

to this one:

Intelligence (knowledge?) requires knowing how to verify what one knows (or "knows").

This is just more logical positivist prejudice being sneaked in without argument. Why couldn't I know that I know P, without knowing how to verify P?

When you give me a proposition, I can only know what it means if I can decide on a recipe by which the proposition can be verified or falsified.

I think I'd be willing to agree with this, understood in a certain way. Consider the claim 'God exists'. I can only know what this means if I can say something about how it might be verified or falsified. It can't be verified or falsified empirically, of course, but it might be verifiable or falsifiable by other metaphysical beliefs that I might have. For instance, I know that if it were true that there are no immaterial objects, then 'God exists' would be false. Likewise, I know that 'God exists and roses are red' entails the truth of 'God exists'. Isn't this basically the sort of thing you're talking about when you say that "we can formulate some model in which we know what propositions might be consistent with our thesis"?

leibniz said...

Duplicate post:

I don't think we can define existence, ordinary or otherwise.

Ah, but we have to. It must at least have some operational or computational meaning.

It must have a meaning, but that doesn't mean we can define it. Is it your view that all meaningful terms must be capable of being defined? It is an old philosophical truth that not everything can be defined. For if we do not allow circular definitions, supposing that every word can be defined sets us off on an infinite regress. At some point we come to words that we regard as meaningful that aren't defined. This happens in physics as much as in mathematics and metaphysics.

I would be inclined to agree with you that intelligence is something like knowledge that we have knowledge. This is close to the traditional idea that intelligence requires self-consciousness (awareness of one's own beliefs, desires, and mental states). (Incidentally, you say that "what constitutes intelligence and knowledge, is meta-knowledge: knowing that you have knowledge." But you should strike 'and knowledge' from this: knowledge cannot consist in knowing that you have knowledge.)

What I don't get is how you slide from this claim:

Intelligence consists in knowing that we have knowledge.

to this one:

Intelligence (knowledge?) requires knowing how to verify what one knows (or "knows").

This is just more logical positivist prejudice being sneaked in without argument. Why couldn't I know that I know P, without knowing how to verify P?

When you give me a proposition, I can only know what it means if I can decide on a recipe by which the proposition can be verified or falsified.

I think I'd be willing to agree with this, understood in a certain way. Consider the claim 'God exists'. I can only know what this means if I can say something about how it might be verified or falsified. It can't be verified or falsified empirically, of course, but it might be verifiable or falsifiable by other metaphysical beliefs that I might have. For instance, I know that if it were true that there are no immaterial objects, then 'God exists' would be false. Likewise, I know that 'God exists and roses are red' entails the truth of 'God exists'. Isn't this basically the sort of thing you're talking about when you say that "we can formulate some model in which we know what propositions might be consistent with our thesis"?

7:49 PM

Doctor Logic said...

I think I'd be willing to agree with this, understood in a certain way. Consider the claim 'God exists'. I can only know what this means if I can say something about how it might be verified or falsified. It can't be verified or falsified empirically, of course, but it might be verifiable or falsifiable by other metaphysical beliefs that I might have. For instance, I know that if it were true that there are no immaterial objects, then 'God exists' would be false.

I think this is progress! We might be getting to a consensus on what our disagreement is. :)

There is no problem of infinite regress. Circularity is permissable. If I have a mathematical system, is it not also circular? I suspect that it is. Any proposition in the system can be converted into others using the defined operations of the system, yet we never escape the system itself, and we're always led back to the axioms.

Physical systems are just like mathematical ones, so they too have some circularity. The difference is that we continuously add new axioms to the system through observation instead of fiat.

So you have at least mathematical meaning by way of interlocking consequences:

God has the property of existence

X has the property of existence iff X also has property of being material

God does not have property of being material

I don't dispute that these propositions have meaning in this minimal sense.

The question remains whether this says more than

p(G,E)

p(X,E) iff p(X,M)

~p(G,M)


That is, can we bridge any of these symbols with those used in the context of empirical science? Note, I am not begging the question here by saying that the propositions have empirical consequences. Rather, I am asking whether the symbols we use in the physical world mean the same thing outside that context.

Here is an analogy. Consider what it means to perform an integral in calculus. Suppose I have a proposition in this purely mathematical calculus:

Integrate function F over x

Then I create a physical theory by appending calculus to physical observation, and I have physical propositions:

Energy is conserved, so the change in potential energy equals the work done.

Work done is the Force integrated over the distance.


One might ask, does the verb to integrate mean the same thing in both systems?

As it happens, it does. The mechanical recipe for integration is identical in both systems.

Returning to your metaphysical propositions, we have to ask whether the verb to exist means the same thing in

God exists

as it does in physical systems like

Gorillas exist.

My claim is that it does not because the recipe for the meaning of existence in one system does not apply in the other.

Metaphysical propositions give the appearance of being about the world because they use verbs that apply in the physical world, but they really have only mathematical content because the meaning of those verbs is lost out of context. Lost because the recipe for the meaning of those verbs cannot be applied in the metaphysical context.


Likewise, I know that 'God exists and roses are red' entails the truth of 'God exists'. Isn't this basically the sort of thing you're talking about when you say that "we can formulate some model in which we know what propositions might be consistent with our thesis"?

Do you see why your 'roses are red' example has nothing to do with the meaning of 'God exists'?

Suppose I have an algebraic system, Q, over integers with addition (+), subtraction (-) and multiplication (*) defined. I provide you with this proposition:

Prop 1: G % 12

Without knowing the meaning of the % symbol, I must give you more information. For example, I could say

Prop 2: x % y => (x + 2) * 3 = y

That would give you plenty of meaning for the % operator within Q. You could derive from this the fact that G = 2.

Let's suppose I refuse to give you a proposition like Prop 2.

Instead, I give you Prop 3:

Prop 3: (x % y) and (z + 16 = 256) => (x % y)

you would still have no idea what the % operator does or what (G % 2) means in Q.

If I add more propositions about G and the % operator, I still don't really get anywhere in the context of Q. For example, I add propositions 4 and 5 as:

Prop 4: (x % 2) => ~ (x $ 5)

Prop 5: (G $ 7)

From this we could derive ~(G $ 5), but we don't know the formula for % or $ in terms of our standard algebraic operations in Q.

Are we justified in saying that % or $ have meaning in terms of Q? Are % and $ about Q? We have no reason for claiming as much. No theorem of algebra contradicts propositions 1, 3, 4, and 5. The truth of (G % 2) has no consequences in Q for G, and % and $ have meaning only within the isolated set of propositions 1,3,4,5.

You might object on grounds that we can declare G to be an element of our algebraic system, Q. We would then have meaning, G simply being underdetermined. This objection would be valid if such a declaration were made. However, there the analogy with metaphysics breaks.

If G is declared as a symbol in principle beyond determination in Q, then we are not justified in regarding G as an element of Q. Neither are we justified in claiming that (G %2) is about Q.

P.S. I really hope this post makes sense in the morning. :)

leibniz said...

I'm afraid I have lost interest in this dispute, Dr. Logic. Sorry.

Doctor Logic said...

leibniz,

Well, I can't say I'm not disappointed, but thanks for participating here. I found our exchange quite helpful.

I come away with the the idea that what I'm trying to say should be expressed more precisely, more rigorously, and perhaps, more concisely. I'll add this to my list of projects!

Cheers,

doctor(logic)