Sunday, September 14, 2014

Step 2: The Absolute Simplicity of God (Updated)

This is the second step in a proof for the existence of God that has been the subject of an ongoing series. In the First Step, we deduced the existence of at least one unconditioned reality. This argument draws heavily on Robert Spitzer’s New Proofs for the Existence of God.

In the first step, we saw that if any reality exists—any reality at all—there must be at least one unconditioned reality. In this article, we will be drawing out the consequences of this with respect to simplicity. We will see that an unconditioned reality must be absolutely simple.

The term “simplicity” is a term of art. In common parlance, simplicity often means something like the lack of content or what is easily understood. We naturally consider “1”, for instance, to be simpler than the operation “1+1” or the number “32.” “Simplicity,” as we will use the term here, will not mean what is easy to understand or what lacks a richness of content. Simplicity will be used in an ontological sense to mean that which is without parts, boundaries, or incompatible states.


An Unconditioned Reality Lacks Parts


Let’s begin with the proof for the following claim:

2.1 An unconditioned reality, considered in itself, cannot have parts.

A part is defined as follows:

2.1a A part is any aspect of a reality that is distinct from any other aspect in any way.

It is important to note how broad the definition of a part is. A part could be something that exists at a different location, has a different function, or a different modality (actual instead of potential, for example).
The principle in 2.1 follows swiftly from the definition of an unconditioned reality (1.2). Consider the following indirect proof.

2.1.1 A part is either necessary to the existence of the whole, or not. (Bifurcation)

Assume an unconditioned reality, “UR.” If “UR” has a part necessary to its existence, UR depends for its existence on another reality (i.e., condition). But then UR is not an unconditioned reality. (1.2) This is a contradiction. Therefore, it cannot be the case that a reality is both unconditioned and depends for its existence on some part. Thus we can conclude:

2.1.2 An unconditioned reality cannot have a part necessary to its existence.

Now let us see if an unconditioned reality, considered in itself, can have a part on which it does not depend for its existence. Assume an unconditioned reality, “UR.” Assume that UR has a part, “p,” on which it does not depend. UR exists even if p does not. But if UR’s existence is independent of p, UR considered in itself, does not include p. Therefore we can conclude:

2.1.4 An unconditioned reality, considered in itself, is a reality independent of unnecessary parts.

This establishes 2.1. UR cannot have a necessary part. (2.1.2). If UR has an unnecessary part, that part is distinct from UR in itself. (2.1.4) Therefore, an unconditioned reality, in itself, does not have parts.

From this simple proof, we can draw several sweeping conclusions. First, an unconditioned reality cannot be a spatial reality. A spatial reality is either extended or non-extended. Any extended spatial reality has spatial extension, and any extended thing has parts. (If A is spatially extended, it has an extension from location 1 to 2, which is distinct from location 2 to 3.)

A non-extended spatial reality is a point. It has a location in space, and is therefore limited by space, but it is not extended, and therefore has no parts. However, no unconditioned reality can be a point, for to be a point, there must be the reality of space. Any non-extended spatial reality depends upon space, and is therefore conditioned. Thus, a spatial reality either has parts (and for this reason cannot be unconditioned) or it has no parts, in which case it is conditioned by the reality of space.

We can therefore conclude:

2.2 An unconditioned reality, considered in itself, is not a spatial reality.

Similarly, an unconditioned reality cannot be a temporal reality. A temporal reality either consists of a duration or it doesn't. If it is a duration, it extends through space and has parts. (For example, if A is temporal, its existence stretches from time 1 to time 2, which is distinct from the stretch from time 2 to time 3.)

What of an instant in time? If any non-extended instant exists in time, at this point in time and this point alone, it would depend upon the reality of time. But an unconditioned reality is by definition not dependent. Therefore, no unconditioned reality could be extended (because it would have parts) or non-extended (because it would be conditioned by time). Thus, we can conclude

2.3 An unconditioned reality, considered in itself, is not a temporal reality.

From 2.2 and 2.3 we know that any unconditioned reality is super- or extra- spatio-temporal. This allows the deduction of the immutability of unconditioned reality.

The proof for immutability runs as follows. Any change occurs in time: A thing has property x at time 1, and property y at time 2. However, an unconditioned reality is not a temporal reality. (2.3) Therefore an unconditioned reality, considered in itself, does not suffer change. So we can conclude

2.4 An unconditioned reality, considered in itself, is immutable.

Note that none of this entails that an unconditioned reality could not have conditioned, non-essential parts, such as, for example, the Eastern Orthodox concept of the divine energies. Furthermore, it could be the case that an unconditioned reality could become conjoin with conditioned realities in such a way that it takes on spatially limited properties. All that is proved here is that an unconditioned reality, considered in itself, is not spatially limited, immutable, and so on.

Absolute Simplicity


We have established that an unconditioned reality, in itself, is simple in the sense that it has no parts. Let’s extend this notion of simplicity further to include its limit: absolute simplicity.

2.5 “Absolute simplicity” means that reality which utterly lacks a) boundaries and b) incompatible states with other realities.

This definition of absolute simplicity clearly turns upon the twin notions of boundaries and incompatible states. The two notions are closely connected, as a few examples will show.

Consider the boundaries of a given square: it has four equilateral sides and four right angles. The boundaries of a square conflict with the boundaries of a circle, giving rise to an incompatible state: no X can be both square and circular at the same time and in the same respect.

Note that boundaries operate as restrictions. The boundaries of a square restrict the kinds of angles a square can have qua square. No square can have a 72 degree angle.

Examples from Contemporary Physics


Let’s move from geometry to physics. One of the electron’s boundaries is its repulsion of other other electrons. An electron qua electron repulses other electron. Protons, on the other hand, attract electrons. The boundary conditions of protons and electrons conflict with one another. This means that protons and electrons are incompatible states: nothing can be both a proton and an electron at the same time and in the same respect, if for no other reason that nothing can both attract and repel an electron at the same time and in the same respect. Boundaries give rise to incompatible states.

Although a proton and an electron are incompatible states, they can interact with each other through a simpler reality—the electromagnetic field. The greater simplicity of the electromagnetic field’s state entails not only the compatibility between the electron and the field, but also permits the interaction between the electron and the proton. Beings with incompatible states or boundaries can interact through simpler realities.

The Tree of Being: An Illustration


Fr. Spitzer uses the notion of the “tree of being” as a way of representing the relations of exclusion, incompatible states, and simplicity. The tree of being is one way of illustrating the principle of simplicity, rather than being part of the argument.

A simpler reality has fewer boundaries than does a less simple reality. Spatial extension, for example, is more simple than a square, for it has fewer boundaries. Spatial extension is compatible with a square, but it is also compatible with a circle. Spatial extension is a simpler reality than the square and the circle, being compatible with both but not having the limits (boundaries) of either. Furthermore, the square and the circle, though they are incompatible states, can relate to each other through the simpler reality of the spatial field (for example, by being side by side).

We can represent these relationships of boundaries and simplicity as forming a tree:

              Spatial extension
                        / \
                      /     \
              Square   Circle

Fr. Spitzer calls this the tree of being. The example he uses, however, is that of the proton and the electron. As we saw, the boundaries of the proton and the electron means that they are incompatible states. However, protons and electrons are both compatible with electromagnetic fields. Electromagnetic fields are, therefore, simpler realities in this respect, because they have fewer boundaries, and thus fewer incompatible states. Due to the greater compatibility of an electromagnetic field, lower realities can interact with one another.

This can be represented as follows 

               Electromagnetic field
                           / \ 
                         /     \
                 Proton   Electron

There are two ways of distinguishing realities that can be seen visually on the tree of being. One is through greater simplicity—e.g., the proton can be distinguished from the electromagnetic field by greater simplicity—and the other is through incompatible states—e.g., the proton and electron.

There are two types of simplicity: simplicity in act and simplicity in potency. Simplicity may be had by either lack or plenitude. For example, 0 is a simple reality, but its simplicity is that of potentiality or lack. It is simple, because it lacks actualities that give rise to boundaries or incompatible states. As Fr. Spitzer puts it, “Zero has no boundaries because it signifies ‘the absence of reality in which boundaries can inhere.’” Such simplicity is had in the absence of reality. Thus:

2.7 Absolute simplicity in potency utterly lacks any reality or actuality.

Simplicity in act, on the other hand, does not have boundaries because it does not have limitations on its act or power. Absolute simplicity in act, as Fr. Spitzer puts it, “would then refer to act or being without any intrinsic or extrinsic parameters, boundaries, or restrictions, that is a being capable of acting in any and all non-contradictory ways.” Simplicity in act arises as the plenitude of unbounded reality.

A simpler reality (in act) will have fewer boundaries and therefore greater compatibility or inclusivity with other realities lower in the tree of being. An absolutely simple reality is, by definition, utterly without boundaries or incompatible states, and therefore is compatible with all other realities. (The question remains, at this point, whether there is any absolutely simple reality.) 

Boundaries: Intrinsic and Extrinsic


We are now reaching the latter part of Step 2, namely, the question of whether an unconditioned reality is absolutely simple. In order to approach the question of whether an unconditioned reality is utterly simple, we need to determine whether it has any intrinsic or extrinsic boundaries.

An extrinsic boundary is a boundary that separates a reality from another (external) reality. An intrinsic boundary is a boundary internal to that reality. An intrinsic boundary gives rise to parts. For example, the boundaries of my heart exclude the boundaries of my liver (in terms of spatial location, function, material composition, and so on), and so the two are distinct parts. However, we discovered that an unconditioned reality, considered in itself, does not have parts. (2.1) Therefore, an unconditioned reality cannot have intrinsic boundaries.

Can an unconditioned reality have extrinsic boundaries? That is, can an unconditioned reality have boundaries that distinguish it from other realities? The answer is no. This can be shown by the following indirect proof.

Assume that an unconditioned reality, UR, does have extrinsic boundaries distinguishing it from a given reality, R. UR and R are incompatible realities. R’s existence entails a state of ~UR, just as a square’s existence entails a state of ~circle. However, if there is a state ~UR, it must either be the case that ~UR obtains everywhere or is spatially or temporally limited. If ~UR obtains everywhere, then we have a contradiction. It can’t be the case that both UR and R exist.

But it also cannot be the case that the state of ~UR is limited to one place or time where R exists, while elsewhere there is a state UR—for then UR would be limited by space or time. But we saw that no unconditioned reality is limited spatio-temporally. (2.2 and 2.3). We can conclude that UR can have no extrinsic boundaries with any existing realities:

2.8 No unconditioned reality has extrinsic boundaries excluding any existing reality.

Notice this argument does not demonstrate that an unconditioned reality has no boundaries whatsoever, for it may have boundaries that exclude a potential entity. But this is easily proven false along similar lines. Assume UR, which has boundaries that exclude a possible reality, P. If P were possible, then it must be possible that ~UR. However, if ~UR were locally the case, it would be universally the case, as we saw above. Thus, the assumption of UR having an incompatible state with a possible reality entails the non-existence of UR, which is a contradiction. Therefore, we can conclude:

2.9 No unconditioned reality has extrinsic boundaries.

Conclusion


Now we can wrap up the argument. An unconditioned reality is necessarily without parts (2.1), outside space and time (2.2 and 2.3), and immutable (2.4). Furthermore, an unconditioned reality is absolutely simple (as defined in 2.5) because it lacks intrinsic and extrinsic boundaries (2.8 and 2.9), and is therefore absolutely simple. We can therefore conclude: 

2.10 Any unconditioned reality is absolutely simple.

Furthermore, we know that there exists at least one unconditioned reality. (1.10) From 1.10 and 2.10 we can conclude:

2.11 There exists at least one absolutely simple unconditioned reality.

Finally, we know that any existing unconditioned reality must be absolutely simple in terms of act. For anything that absolutely simple in terms of potency is non-existent. (2.7) Thus, we can conclude:

2.12 There exists at least one unconditioned reality that is utterly without boundaries or incompatible states.

It is clear that an unconditioned reality must be infinite. For anything finite is so by a limitation—a boundary. But we have shown that an unconditioned reality has no boundaries. (2.5 and 2.10). Therefore:

2.13 Any unconditioned reality is infinite.

Finally, unconditioned realities must be eternal. For if they exist, but they do not exist in time (i.e., at one time but not another), then they are eternal.

2.14 Any unconditioned reality is eternal.

The jump from Step 1 to Step 2 is considerable. In Step 1 we deduced the existence of an unconditioned reality (or realities). But the nature of that unconditioned reality was left vague. We knew that it did not depend on any other reality, but little beyond that. Could a fundamental particle be unconditioned? What about the universe as a whole? Those questions were not answered in Step 1.

In Step 2 we established that any unconditioned reality is absolutely simple, is not spatial or temporal, is infinite and immutable. This means that no fundamental particle could be unconditioned, nor could any field with any sort of extension or duration. The host of physical entities are conditioned realities that ultimately depend on a reality outside time and space. Only two steps into the argument, and we’ve gone a good way toward proving the truth of theism.

This post has been updated due to a lacuna pointed out by Singring. The text of the original post can be viewed here.

29 comments:

KyCobb said...

Not really

Singring said...

'From this simple proof, we can draw several sweeping conclusions. First, an unconditioned reality cannot be a spatial reality. Any spatial reality has spatial extension, and any extended thing has parts. (If A is spatially extended, it has an extension from location 1 to 2, which is distinct from location 2 to 3.) We can therefore conclude:'

I fail to see how a spatial reality with 'spatial extension' necessarily has parts.

I can easily conceive of a reality with the spatial extension of the planck length, for example, which - at least in my understanding of current physics - cannot consist of parts (by definition).

'From 2.2 and 2.3 we know that any unconditioned reality is super- or extra- spatio-temporal. '

Where did this 'sweeping conclusion' suddenly come from. Again I fail to see how this follows from 2.2 or 2.3 and you give no indication of how it would.

Your argument of immutability also doesn't make much sense to me - my objection would be analogous to my objection to 'spacelessness', simply substituting planck time for planck length.

Your mention of 'divine energies' doesn't help either...

'A simpler reality has fewer boundaries than does a less simple reality.'

How does this follow?

'...the proton can be distinguished from the electromagnetic field by greater simplicity...'

It is misleading to posit the proton and the electric field as realities. Charged particles like protons generate an electric field, so one is simply the product of the other.

I give up here.

I respect the amount of effort you invest in these posts, Thomas, but I hope you can see how they do little to convince someone not already ideologically committed.

Thomas M. Cothran said...

Since it's late, I'll just address the spatial extension part.

A planck length is 1.61619926 × 10-35 meters. Half a planck length is (1.61619926 × 10-35)/2 meters.

So if you have an reality, A, that is measured at one plank length, you would have two segments, each measuring (1.61619926 × 10-35)/2 meters.

These segments are parts, just as if I had a string two feet long, the first foot would be a part of that string.

Thomas M. Cothran said...
This comment has been removed by the author.
Thomas M. Cothran said...

I should point out that nothing in the argument assumes that all physical realities are spatially extended. There could well be conditioned realities that are not spatial or temporal. But whether there are or there aren't doesn't affect this argument.

Singring said...

I strongly suggest you read up on the significance of the Planck length.

It most certainly it's not like a length of string two feet long.

Thomas M. Cothran said...

Singring,

A planck length is the shortest measurable length it is theoretically possible to measure. But it's still spatially extended: it's 1.61619926 × 10-35 meters.

I can't tell if your argument is that it's so small it's a point (i.e., it is not extended) or if it is so small that nothing shorter could exist independently, sort of like a quantum.

If you're saying that that a planck length is so small that you won't find e.g., some elementary particle smaller than that length, that does not demonstrate that a reality with the length of 1.61619926 × 10-35 meters has no parts. A part need not exist independently of the whole. For there to be two parts of something 1.61619926 × 10-35 meters in length, it is sufficient that there be two segments of (1.61619926 × 10-35)/2 meters. If you deny that there are two segments (1.61619926 × 10-35)/2 meters in length, you are simply denying that half of a planck length is (1.61619926 × 10-35)/2 meters. That is to say, what you would be denying is that [(1.61619926 × 10-35)/2 m] + [(1.61619926 × 10-35)/2 m] = 1.61619926 × 10-35 m. Which I'm guessing you don't want to do.

I think the confusion comes from your reading too much into the term part. I'm just using it in the broad sense, which the OED defines as "a piece or segment of something used to make up the whole."

On that definition, it can easily be shown that anything that measures a planck length has parts. Consider this:

Suppose the existence of F, a fundamental particle, which has the length of a Planck lenght. It must either be the case that there exists a distance running along the first half of F, F1, that measures half a planck length, (1.61619926 × 10-35)/2 meters, or not. Suppose there exists no distance F1. In that case, it would be false that half the distance of F is F1, or (1.61619926 × 10-35)/2 m. But if it is false that 1/ of F is (1.61619926 × 10-35)/2 m, then it is also false that F is [(1.61619926 × 10-35)/2 m] + [(1.61619926 × 10-35)/2 m] in length. In which case, it is false that F is 1.61619926 × 10-35 m in length. Thus it cannot be true that there is no distance F1. But if there is a distance F1, then F has parts.

Thomas M. Cothran said...

"It is misleading to posit the proton and the electric field as realities. Charged particles like protons generate an electric field, so one is simply the product of the other."

A truck is a reality. It is a product (of a complex production process), but I presume you would step out of the way should one come straight at you.

Singring said...

'A truck is a reality. It is a product (of a complex production process), but I presume you would step out of the way should one come straight at you.'

My apologies, I left out a word in my original post. I meant to say:

'It is misleading to posit the proton and the electric field as separate realities.'

My objection to your argument should be clear from that.

'If you're saying that that a planck length is so small that you won't find e.g., some elementary particle smaller than that length, that does not demonstrate that a reality with the length of 1.61619926 × 10-35 meters has no parts.'

I apologize again for having to resort to Wikipedia (a very poor source) to clarify my point, but I don't have the time to find a more in-depth discussion that I (or you, I presume) would be able to follow:

"According to the generalized uncertainty principle (a concept from speculative models of quantum gravity), the Planck length is, in principle, within a factor of order unity, the shortest measurable length – and no theoretically known improvement in measurement instruments could change that."

So what this suggests is that the term '(1.61619926 × 10-35)/2 meters' is a meaningless one. It is a length that cannot - even theoretically - be measured.

So I can imagine a reality with the spatial extension of one planck length that does not consist of parts in the sense of your argument.

Even if you posit that a length shorter than the Planck length exists and is a meaningful concept, but is simply unmeasurable, this is conjecture.

At the very least this casts significant doubt on your argument.

KyCobb said...

So God is a singularity?

Thomas Cothran said...

Singring,

Your argument assumes that the smallest measurable distance is the smallest possible distance. That's not too far away from saying that Mt. Everest only exists when someone is looking at it. Reality is not dependent upon what we can perceive or measure.

Aside from that, you're using a different definition of "part," because you keep assuming a part or segment would have to be able to exist independently. Even if it were utterly impossible for there to be an independent entity that measures less than a Planck length, it doesn't change the two half segments of a Planck length amounts to a whole Planck length. None of this need imply that these segments could exist on their own or that one segment is qualitatively different than another. Again, I'm using part in the broadest dictionary definition.

I think what you're getting at would be better if we consider the possibility of an entity being a point, which has no extension. The idea would be that there is a reality which is located in space (and thus limited by space), but is not extended and has no parts.

Even if that were possible, such a non-extended spacial reality could not be an unconditioned reality, for the obvious reason that it has, as one of its conditions, the existence of the spacetime field. No space, no point (i.e., no non-extended spatial reality). From this it would follow that unconditioned realities are not spatial. (Remember that reality was defined in 1.1 in its broadest scope. Anything we can say is in some way is a reality.)

Thomas Cothran said...

A few more points.

1. You ask how it follows that a reality has fewer boundaries. The answer is by way of definition--see 2.5.

2. You say that "it is misleading to posit the proton and electron field as realities ...." I continue to use the definition of realities in 1.1 to include anything that is in any way. The quick and easy test is that if it is true in any way to say that "there is an x ..." or false in every way to say "there's no such thing as an x", then x is a reality.

You later amended your objection to say that it's hard to see how they are "separate" realities. But it's hard to see how that is an objection to my argument. Even if realities A, B, and C are the cause of reality B, reality B could still be simpler. Perhaps you would say such simplicity would be by privation rather than act. That might be right, but whatever the case is, it doesn't affect the argument and the example. That was an illustration of simplicity.

I do think you're correct that there was a hole in the argument about non-extended spatial realities. The previous comment adjusts the argument for those, and I'll do a follow up post summarizing and responding to objections.

Thomas Cothran said...

Kycobb,

If by singularity you mean one, it would be the case than an unconditioned reality is singular. If you mean it in the sense of physics, I think the argument makes clear the answer would be no.

Singring said...

'Your argument assumes that the smallest measurable distance is the smallest possible distance.'

And your argument assumes that the smallest measurable distance is not the smallest possible distance. The difference is that I'm not trying to derive a 'proof of the existence of God' from uncertain premises.

'Aside from that, you're using a different definition of "part," because you keep assuming a part or segment would have to be able to exist independently.'

No, I am not assuming that it be able to exist independently at all. The question is how can one possibly argue that a spatially extended reality can always be divided into parts when in fact there is a physical length we know of that - even theoretically - cannot be measured. This is quite different from whether or not Mount Everest ceases to exist when we stop looking at it.

I very clearly stated that my objection does not depend on there being a length smaller than the Planck length in reality - just that we cannot be certain of this at the moment. This (for the moment) defeats any deductive argument based on the premise that there is, that much should be obvious.

'... it doesn't change the two half segments of a Planck length amounts to a whole Planck length.'

Now you are just playing semantics. In your original argument, you clearly state:

'First, an unconditioned reality cannot be a spatial reality. Any spatial reality has spatial extension, and any extended thing has parts.'

You are clearly speaking of a reality, not abstract numbers. And as I have stated, current physics suggests that the Planck length is the smallest possible length. Saying 'a reality of half a Planck Length' - whether proposing it exists independently or not of an actual Planck length - is as meaningful as saying there's a 'massless mass' in the universe.

Singring said...

'Even if realities A, B, and C are the cause of reality B, reality B could still be simpler. Perhaps you would say such simplicity would be by privation rather than act. '

This does clarify your point. I was referring to your use of the electron, proton and electric field as contrasting realities due to their different number of boundaries, which was confusing me as an analogy.

'I do think you're correct that there was a hole in the argument about non-extended spatial realities.'

Remember that this objection also applies to temporal reality - there is a shortest possible Planck time as well.


Thomas Cothran said...

Singring,

The same argument in the comment above would apply to time as well. Just as anything that measures a planck length depends on the reality of space can't be unconditioned, so anything that measures a planck time depends on the reality of time, and so can't be unconditioned. The non-spatiality and non-temporality of an unconditioned reality can be established on those grounds.

You happen to be wrong about whether a plank length is extended, but I'm happy to bracket it for the sake of argument, given the independent grounds above.

Thomas M. Cothran said...

I've updated the post to allow for both extended and non-extended temporal realities. Singring is credited in the italics at the end of the post, and I've also linked to a page that has the original text.

I probably won't do an additional "Objections and Responses" like I did for the first step unless I get more objections.

Singring said...

'Just as anything that measures a planck length depends on the reality of space can't be unconditioned, so anything that measures a planck time depends on the reality of time, and so can't be unconditioned.'

This reminds me of the ontological argument in that you are engaging in wordplay. You are treating our concept of a dimension of space (i.e. the Planck length) as if it were somehow to be treated separate from space itself.

I don't see any reason for doing so. In fact it strikes me as absurd to do so.

A space of the diameter of one Planck length does not 'depend' on space, it is space. The Planck length is merely our way of describing a feature of this space, an abstract concept that does not 'depend' on space in the way you seem to be suggesting.

To make this explicit: I can imagine a reality with the diameter of a Planck length existing without any humans there to measure it and it would just be space - no parts, and not dependent on space because it is space.

I might as well say the unconditioned reality you are positing is dependent on the reality of the unconditioned reality. Which means it is not unconditioned.

I understand the Aristotelean urge to introduce various different, separately considered aspects (or 'causes') of a reality, but I think you were party to previous discussions on this blog where I and others clearly expressed that arguments involving such approaches can only be convincing to those already metaphysically committed.

The argument remains unpersuasive. As I said before, I respect the work you invest in these posts and I'm sure the argument will sound reasonable to some believers or deistically/theistically inclined philosophers, but you shouldn't expect to convince any skeptic using this approach.

Thomas Cothran said...

Singring,

I did not say that a Planck length depends upon space; I said that something that is as long as a Planck length depends on space.

Is it your position that nothing exists smaller than a Planck length?

Singring said...

'I did not say that a Planck length depends upon space; I said that something that is as long as a Planck length depends on space.'

I did not spot the distinction, my apologies. However, my original response applies as this is still wordplay.

You are treating this 'something' (as long as a Planck length) as if it were some object in space - but you should be considering space itself.

Let's leave the Planck length aside for a moment, as it speaks to your argument on 'parts', but not directly to the issue of 'conditionality'.

A ruler like the one on my desk that is one meter long, made of plastic, is a 'thing' that depends on space, I agree. But a space of the extent of one meter is just space - it is not a 'thing' that depends externally on space for its existence, because it is space.

What you are essentially trying to argue is that a space (or 'reality') is dependent on space for its existence, thus making it a conditioned reality.

This is analogous to me saying that an unconditioned reality is dependent on an unconditioned reality for its existence, thus making it a conditioned reality.

You are defeating your own argument.

'Is it your position that nothing exists smaller than a Planck length?'

My position is that the Planck length is the smallest possible length, based on our best current understanding of the universe and how it operates (at least to my understanding).

This suggests to me that it is very unlikely that some 'thing' or even some space exists with smaller dimensions (at least as far as we currently understand and define 'things' and 'reality').

I may be wrong. None of this is certain and I am fully prepared to be shown otherwise by additional data. I am going with the best information available currently.

With this in mind, I am currently in no position to accept a deductive argument attempting to prove the being of an unconditioned, spaceless, timeless reality when it is built on premises that a) don't seem to mesh with the best current data and/or b) are internally incoherent.

Because of this, I am not inclined to accept the stronger claims you will proceed to derive from this argument, culminating (as you have announced) in the proof of the theistic God of the Bible.

Moreover, I would be very surprised if this line of argument were to convince anyone who takes the time to seriously interrogate your premises.

Thomas Cothran said...

Singring,

I am certainly no physicist, but I believe that fundamental particles such as quarks are, in contemporary quantum theory, extensionless points.

As to the argument about space, there's a reason I've phrased the argument as I have, so that it is independent of any particular view of physics or philosophy of science.

I didn't argue that a spatially extended reality depends on space, I said it has parts. What would depend on space would be a point, since it would not be extended but it would it depend on there being someplace for it to be. (A reality that would not be extended and not located at any place would be extra-spatial.)

Now this could be applied to Aristotelian physics (which doesn't view space as a reality distinct from entities), Newtonian physics (which views space as an indifferent set of coordinates), or contemporary cosmology (which says space is dynamic and has an origin).

It appears you tend to agree with contemporary cosmology. On that view, there is a spacetime field which is extended. Things that exist within spacetime depend on this field. And the spacetime field is conditioned--it even has an origin billions of years ago.

Anything that exists within spacetime, anything made up of fundamental particles, is, on the account of contemporary cosmology, conditioned. Spacetime itself is conditioned, and cosmologists study some of those conditions.

If you're going to assume the view of the world offered by contemporary cosmology, it's clearly the case that the spacetime, and everything in it, is a conditioned reality.

Singring said...

'I am certainly no physicist, but I believe that fundamental particles such as quarks are, in contemporary quantum theory, extensionless points.'

True quarks and other subatomic particles can be treated as extensionless points in physics, but that doesn't necessarily mean they actually are extensionless points, nor does it mean that they have an extension less than a Planck length. To my understanding, at the scales we are talking about they are better thought of as waves anyway. If you want to call a wave a 'thing', feel free to do so. I fail to see how this negates any of the objections I have raised. The smallest possible spatial extension is the Planck length (as far as we know).

'I didn't argue that a spatially extended reality depends on space, I said it has parts.'

And I have argued that a spatially extended reality with the diameter of a Planck length cannot have parts. I feel we are going in circles at this point.

'And the spacetime field is conditioned--it even has an origin billions of years ago. Anything that exists within spacetime, anything made up of fundamental particles, is, on the account of contemporary cosmology, conditioned. Spacetime itself is conditioned, and cosmologists study some of those conditions. '

I'm getting the awful feeling that your argument amounts to nothing more than a restatement of the Cosmological or 'First Cause' argument, just using different language.

Just because you replace 'cause' by 'condition' an 'unconditioned' by 'uncaused' doesn't actually improve the argument.

In this sense, I would submit there are plenty of physicists today who would propose that the universe is, in fact, 'unconditioned' and (though I might be overextending myself here...) that the unconditioned element is the quantum field/quantum vacuum.

It is at this point that I have to appeal to authority - but at least this time it's the New Scientist, a slightly better source than Wikipedia.

http://www.newscientist.com/blogs/nstv/2011/07/how-the-universe-appeared-from-nothing.html

Now, maybe I'm misunderstanding your entire argument and you would be quite happy to accept the quantum field as an 'unconditioned reality'. In that case, we might still have some disagreement on the form of the argument, but I think we'd at least agree on what you are arguing for (at least in this part of the argument).

Thomas Cothran said...

"The smallest possible spatial extension is the Planck length (as far as we know)."

Wikipedia disagrees

As to the rest, if the word "part" is confusing toward you, I could put a specific definition in the argument. Define part as any aspect of a reality that may be distinguished in any way from another aspect of that reality, and the confusion should lift. Any object that has the length of a Planck length would clearly have parts in this sense, for one end can be distinguished from the other by being located 1.61619926 × 10-35 meters away. That's more than enough for the argument to work.

Singring said...
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Singring said...

'Wikipedia disagrees'

Using a point particle that 'lacks spatial extension' to support an argument about a space having a spatial extension less than the Planck length is not very productive in my view.

How exactly would something that has no spatial extension be considered a part of something that has spatial extension in the sense of subdividing this spatial extension into smaller parts? If it is extensionless, it clearly can't be a part of the extension of that which is supposed to be part of.

But all of this is beside the point anyway, because Wikipedia reiterates my earlier point regarding the 'particles' in the very first sentence of the entry:

'A point particle (ideal particle[1] or point-like particle, often spelled pointlike particle) is an idealization of particles heavily used in physics.'

Clearly the words 'ideal', 'point-like' and 'idealization' should give a clue that these particles are possibly or even probably not actually extensionless points in reality, but rather are just treated as such for ease of calculation.

The next paragraph makes this even clearer:

'A point particle is an appropriate representation of any object whose size, shape, and structure is irrelevant in a given context. For example, from far enough away, an object of any shape will look and behave as a point-like object.'

I should have pointed out that the Planck length is so small, it has never been approached in terms of actual measurement (I think the record is somewhere around 10 to the minus 15 meters). It is a theoretical boundary. Hence why 'particles' that may have considerably greater extension than a Planck length (but less than that which would significantly affect calculations) are treated as extensionless points.

'As to the rest, if the word "part" is confusing toward you, I could put a specific definition in the argument. Define part as any aspect of a reality that may be distinguished in any way from another aspect of that reality, and the confusion should lift.'

This is a different way of expressing this statement, but I'm not sure it's any clearer or that it solves the problem. I don't think I was confused by your earlier version. It is just that, at the Planck level, these 'distinctions' as you now say become irrelevant and - in fact - impossible to even make.

A spatial extension of the Planck length can have no parts to be distinguished from each other or from the space of a Planck length itself, because measurement - and thus resolution - of time and space become theoretically impossible at this point. To speak of a part of reality at this level is absurd. The Planck length is the smallest part of reality there can theoretically be and yet it has spatial extension.

'Any object that has the length of a Planck length would clearly have parts in this sense, for one end can be distinguished from the other by being located 1.61619926 × 10-35 meters away. That's more than enough for the argument to work.'

But we are not discussing 'objects' the length of a Planck unit. We are discussing space itself of an expanse of one Planck unit. In this context, at the Planck length, speaking of one point in space being so and so many meters away from another becomes meaningless, because these distances can't be (even theoretically) measured. But even if they could, those points may well be conditioned by the space 'containing' them, but the space itself would not be conditioned.

I go back to my earlier point - it is (at least in my view) absurd to assert that space is conditioned by space. Space is space.

Singring said...

PS:

From later on in the Wikipedia entry:

'For example, for the electron, experimental evidence shows that the size of an electron is less than 10-18 m.[6] This is consistent with the expected value of exactly zero.'

So the lower threshold seems to be 10 to the minus 18 meters. And I freely confess I may be wrong and current physics may actually expect the electron to have zero spatial extension, as this sentence would seem to indicate. (Though I am not sure if by 'zero' they are implying the Planck scale).

However, in my previous post I point out that this does not circumvent my objection. I can grant that an electron has zero spatial extension and, as part of space time is conditioned on space time. In fact that would seem quite obvious to me.

That does not mean, however, that space itself - which has a boundary at the Planck scale - is conditioned.

Thomas Cothran said...

Singring,

Remember the definition of part I'm using: a part is any aspect of a reality that can be distinguished in any way from another aspect of that reality.

Say that space is made up of atomic units which measure Planck lengths. (It doesn't, but I'll go ahead and assume that for the sake of argument.)

Anything that measures a Planck length has parts. It is analytically true that for any x that measures a Plank length, one end is distinct from the other end in terms of location.

This can be shown by an indirect proof. Suppose there is an X (which can be any reality, including space) which measures a Planck length. Suppose further that the X is simple. If X is simple, no aspect of X is distinct from another aspect in any way. It follows that no aspect of X is 1.61619926 × 10-35 m apart from any other aspect of X. From that it follows that X does not measure a Planck length. Which is, of course, a contradiction.

If "part" is defined as any aspect that is distinct from any other aspect of a reality, it necessarily follows that it cannot be extended in space. For something to be extended in space, one aspect must be distinct from the other in terms of location. If no aspect is distinct from any other in terms of location, the reality is either a point (assuming there are such things) or is extra-spatial--by which I mean neither extended nor located at a point in space.

(There are also the possibility of one dimensional entities that have no extension, are located in space, but do have parts, such as strings.)

The confusion is probably due to my not defining "part" in the original post. Now that I have done so, however, the argument is perfectly lucid.

Singring said...

'If "part" is defined as any aspect that is distinct from any other aspect of a reality, it necessarily follows that it cannot be extended in space. For something to be extended in space, one aspect must be distinct from the other in terms of location. '

You are going back to old problems: within a Planck length, it is absurd to speak of distinct locations as they are theoretically unmeasureble.

'Remember the definition of part I'm using: a part is any aspect of a reality that can be distinguished in any way from another aspect of that reality.'

Here is the heading to the relevant part of your argument:

'2.1.4 An unconditioned reality, considered in itself, is a reality independent of unnecessary parts.'

So far, you have not explained (at least in my view) how a space of the extension of one Planck length (or of any extension, really!) 'depends' on - as you now put it - 'two distinct ends' (or 'aspects' or whatever you want to call it), which we may see as 'unnecessary parts'.

As I have said before, I can see how one might argue that some object within space or even some point within space can be considered to depend on or be conditioned by the space that contains it - for without that space it could not be a point or object in space.

I believe my gripe with your argument lies in this section:

'Now let us see if an unconditioned reality, considered in itself, can have a part on which it does not depend for its existence. Assume an unconditioned reality, “UR.” Assume that UR has a part, “p,” on which it does not depend. UR exists even if p does not. But if UR’s existence is independent of p, UR considered in itself, does not include p.'

Here, you intend to show that UR cannot have parts if it is unconditioned.

I maintain that using points in space (whether they be actually 'measureable' or not) as 'aspects' or 'parts' in this context is spurious as I see no reason to consider these abstract notions (extensionless point A in space and point B in space) as anything that can be seen as distinct from space as 'UR (space) + p (point in space)' would require.

I cannot see how a spatial extension of some diamater has to be conditioned just because we can, for example, pick out points in it on which it, in fact, does not depend for its existence.

Thomas Cothran said...

Singring,

I'm not sure I see what your argument is. My argument doesn't purport to say that an Unconditioned Reality can't have parts non-essential parts--the only claim is that an Unconditioned Reality, considered in itself (or essentially) is without parts. Nothing in your argument even touches on that claim.

I have no issue with saying that an unconditioned reality can have accidental parts, just that when considered in itself it can't have parts.