geoff

Three of you replied to my OP with similar sentiments, as the following quotes show:

"I await your proof that abstract entities independent of physical processes are logically necessary."

"I see no reason to grant that abract entities are logically necessary immaterial objects."

"...I don't think it is necessary to demand of abstract objects that they exist independent of any physical state."

Are you serious? (This is not a rhetorical question).

To those who deny or are agnostic about the logical necessity of abstract objects, can you imagine a possible world where first order logic did not apply? Or where numbers, sets, and collections did not exist? Can you really be serious in supposing that these things (and a whole host of other abstract objects) are not logically necessary? I cannot not imagine that to be the case.

Both Wyrdsmyth and James Still side-stepped the issue by ostensibly trying to clarify matters by distinguishing between various forms of atheism. That might be helpful for other discussions but not for this one. Taking "naturalism" as it is defined by a friend of naturalism (cf. Augustine, "A Defense of Naturalism", infidels.org library), I am claiming that logically necessary abstract objects cannot exist. As I stated in the OP, naturalism cannot account for these things.

Owleye's response, when you break it down to its essentials, re-states the problem I posed in my OP (but he doesn't answer it).

The paper Vorkosigan referenced in no way seeks to reconcile either explicitly or implicitly how naturalism can account for abstract entities. If anything, the paper reinforces my original contention that abstract entities are really just the physical by-products of our physical brains. Thus, they cannot be logically necessary (because they depend on contingent beings for their existence). Therein lies the rub.

[ May 24, 2002: Message edited by: geoff ]

[ May 24, 2002: Message edited by: geoff ]</p>

geoff

Wyrdsmyth wrote:

"So, let's see the proof. The evidence. The burning bush."

For starters, see my response in your "God behind the curtain" thread. (That seems like the most appropriate place to respond).

Wizardry

Yes. You asserted that there exist logically necessary immaterial abstract objects. You need to prove that assertion.

Can you prove that the use of first order logic is dependent on logically necessary immaterial abstract objects? If not, then this is a non sequitur.

Again, you need to prove that these things are dependant on logically necessary immaterial abstract objects.

What you can or cannot imagine is not germane to the point at hand, what is relevant is what you can prove.

Did I misread something? I thought you were arguing that abstract entities are not physical by-products of physical brains and that they were logically necessary. This appears to say the opposite.

Peace out.

Ierrellus

This is from a diehard evolutionist.

geoff,

Why would it not be possible for evolution over eons to arrive at a species capable of manipulating matter by virtue of phenomenal consciousness in ways that agree with its own operative, experential physics? The computer came about because the human brain operates on a similar basis. All human discoveries tend to simulate human experience. Too many in fields of science or philosophy set the standards of human phenomenal consciousness at a pinnacle which its humble origins could never reach. There is an abundance of room in what is physical to include all that we consider mental abstractions, even the need, for some of us, of a God.

Ierrellus

(edited for spelling. I still can't spell shite.)

[ May 24, 2002: Message edited by: Ierrellus ]</p>

James Still

<strong>To those who deny or are agnostic about the logical necessity of abstract objects, can you imagine a possible world where first order logic did not apply? Or where numbers, sets, and collections did not exist? Can you really be serious in supposing that these things (and a whole host of other abstract objects) are not logically necessary? I cannot not imagine that to be the case.</strong>

Geoff, you are assuming two things. Your first assumption is Platonic -- you implicitly treat numbers and concepts as real existents. Second, you assume that it is an a priori intuition shared by everyone that these objects are real existents in every logically possible world. I for one do not share that intuition. It seems to me that numbers are not real but instead constructed in our minds as we impose relations upon the world around us. Or take the concept of Justice. Is Justice something independent of us? Is it something out there by which we measure particular acts of justice? Or is it the case that we construct the concept of Justice as a useful tool and measure our particular acts of justice against that concept? These are the questions that must be addressed before you can go on to claim that naturalism must "account for abstract entities." In the absence of a clear problem, no accounting is necessary.

snatchbalance

Vorkosigian,


Just that without abstractions, we would only be left with particulars.

For example, if I say "chair", you can form a mental picture of what you consider to be a chair. I don't have to show you a particular chair for you to know what I'm talking about.

All chairs have some chairness(the abstraction), or it's not a chair.

SB

Wizardry

Actually, to be honest, I consider the notion that there exists an actual Justice "object" to be a bit silly.

So much for proof by "you can't actually believe that, can you?".

[ May 24, 2002: Message edited by: Wizardry ]</p>

geoff

(1) James Still wrote: "Reductionism aside, if it is an abstract entity and an emergent property of the physical brain, who would deny that it is not also a naturalistic phenomenon?"

Sure, there can be physical explanations, but not exclusively so. I still maintain that abstract entities (numbers, sets, laws of logic and so on) are logically necessary and, thus, they cannot be dependent upon contingent beings.

(2) Wizardry wrote: "You asserted that there exist logically necessary immaterial abstract objects. You need to prove that assertion."

My reply: First, I should have omitted "immaterial". "Logically necessary" can stand alone. I really don't know if I can prove that which, at least I find, is impossible to not think. Consider the basic laws of logic (identity, excluded middle, contradiction): can we truly think of a world in which these things would not apply? I cannot. It's difficult to prove (At least I can't. Any logicians in the house?), but why would something that intuitively seems axiomatic be proveable?

(3) Again, from Wizardry: "I thought you were arguing that abstract entities are not physical by-products of physical brains and that they were logically necessary."

My reply: That is what I'm arguing for. I mistyped. Thanks for catching that. For the sake of clarity, I am arguing that N&E cannot account for abstract entities (that are logically necessary).

(4) James Still wrote: "Geoff, you are assuming two things. Your first assumption is Platonic -- you implicitly treat numbers and concepts as real existents. Second, you assume that it is an a priori intuition shared by everyone that these objects are real existents in every logically possible world. I for one do not share that intuition. It seems to me that numbers are not real but instead constructed in our minds as we impose relations upon the world around us."

My reply: I'm not saying anything about the properties of abstract entities other than that they are logically necessary (one need not be Platonic to hold to that).

A rejoinder:

Take numbers (as just one abstract object). If the friends of N&E are correct, then numbers depend upon human intellectual activity. But how can that be? There are too many of them to have arisen as a result of human intellectual activity. An unlimited mind would need to be thinking them, else we will get caught up in many irresolvable conundrums. (And that's just taking numbers into consideration. Think about the conundrums we would run into if we actually considered the laws of logic as not applying to all possible worlds).

One last note. A respondant wrote: "This [post]is from a diehard evolutionist." So what? Nothing I have being arguing for denies the possibility of evolution. The argument might, through extrapolation, mean the denial of naturalistic evolution, but it doesn't rule out evolution by other means (theistic, e.g.).

[ May 24, 2002: Message edited by: geoff ]</p>

snatchbalance

geoff,

I think abstractions are convenient tools. People need to group and order to make sense of the physical world. dealing in particulars would overwhelm our sensory and computational capabilities.

We hear and see what we need to hear and see.

SB

Vorkosigan

Sure, there can be physical explanations, but not exclusively so. I still maintain that abstract entities (numbers, sets, laws of logic and so on) are logically necessary and, thus, they cannot be dependent upon contingent beings.

That's fine that you "maintain" this, Geoff, but what everyone wants to see is a demonstration of why abstract entities are logically necessary AND cannot be dependent on contingent beings. Both forks of your assertion require proof. That would include a definition of "logically necessary," and an argument showing how it applies to the cognitive processes of H. sapiens.

Vorkosigan