Jimmy_sanfrancisco wrote:“The number three is prime”
Meinongianists claim that the sentence is true, and that, therefore, the number three is prime, but the number three doesn’t exist. Therefore, there is an object that doesn’t exist and is prime.
First, I think this is probably not an accurate presentation of what Meinongianism holds.
As I understand it, Meinongianism is the thesis that there are things/facts that do not exist.
Now, for any comments about this idea to be meaningfully intelligible, we have to define what we mean when we use certain words... such as [facts] and [exist]. If we carefully restrict the meaning of [exist] to [physical existence], then it seems to me that your argument is pointless-since by definition ideas do not exist. Your simply providing a very long argument to show that [that which does not exist] does not exist.
If, on the other hand, we assume that non-physical things like [ideas] and [mental concepts] are capable of existing, then your argument is deeply flawed, for many reasons.
So first, what is Meinongianism really trying to say? My suspicion is that it is simply another way of saying that [there are some facts which are only ideas] and [ideas are not physical]. I can't see how any other interpretation could be meaningful. (If you think it means something else, let me know what and I may comment further on that line of reasoning.)
Second, is your presentation of Meinongianism correct? Let's look at the presentation again:
Jimmy_sanfrancisco wrote:“The number three is prime”
Meinongianists claim that the sentence is true, and that, therefore, the number three is prime, but the number three doesn’t exist. Therefore, there is an object that doesn’t exist and is prime.
I think you have probably mischaracterized what the meinongians would hold. I believe they would hold that "The number three is prime" is a [fact that is true]. The number [3], however, is not a fact. It is a physical object which exists, or (at the very least) we can show physical instances of it. Thus, in the framework of this presentation, it is not the number three that does not [physically exist], it is the idea that "the number three is prime". That is the fact which does not physically exist. There is no object that we can point to and say "this is
The number three is prime". Yet we know that the number [3] is an instance of a prime number, and so "the number three is prime" is a fact.
It seems to me that when we present the meinongian POV in a meaningfully accurate way, your argument is revealed to be pointless, by definition. However, let us look at the argument more closely:
Jimmy_sanfrancisco wrote:The refutation:
(P1) There is an object that doesn’t exist, or there isn’t.
(P2) If there is an object that doesn’t exist, then it is something or nothing.
(P3) An object that doesn’t exist is something only if it has some features that nothing doesn’t have.
(P4) An object that doesn’t exist has all the same features that nothing has: they both have no features at all.
...Therefore,
(C1) an object that doesn’t exist is nothing.
(P5) Nothing is an object that doesn’t exist is the same as its not being the case that there is an object that doesn’t exist.
...Therefore,
(C2) it is not the case that there is an object that doesn’t exist.
The first problem with this refutation is that it is far too imprecise to be meaningfully relevant. If we presume that [x] is a physical object that isn't a physical object... what exactly does that even mean? Only that [x] is [not x]. We need go no further. The proof of falsehood is in the premise. Which is another way of saying the premise is necessarily false.
On the other hand, I think if we state it in a meaningful, meinongian way, it becomes:
(P1) There is a "fact" which is either [physically real] or [not physically real].
Again, your (P2) seems to be saying, "If [x] is [something which physically exists] and it [doesn't physically exist], then it is [something] or [nothing].
Using the same logic, we can show this premise is trivial, (if not false). For your saying, "If [x] is [not x], then it is [something] or it is [nothing]. Again, vagueness plagues us, for in a sense, [nothing] is clearly [something]... it is an [idea], or a [mental concept]. Therefore, you have not given us a [one or the other] scenario. This also invalidates the premise and the conclusions drawn from it.
Your (P3) appears to be absurd and meaningless to me. Given my interpretation, it appears to be saying, "An object that [doesn't physically exist] has [physical existence] only if it has some feature that [nothing] doesn't have.
I realize this isn't what you're trying to say, but I don't think there is any way to intelligibly say [what you are trying to say]. First, we have the same [x is not x] problem. Secondly, [nothing] is necessarily an idea that cannot be physically actualized--so it necessarily shares at least one feature with the [non-physical x]: Neither [exists in the physical sense]. Given this obvious truth, why would we then turn around and assume that [x] should reject the relevant features that make it [not physical]. Clearly, since [x] and [nothing] are not the same idea, there will be some features that they do not share. [x] is the idea of [primeness]; while [nothing] is the [absence of some
thing]. These are clearly very different ideas... yet they both lack the property of being physical.
It should be rather clear that my above argument completely undoes (P4). The key word is [all]. Something that doesn't physically exist will share one feature with nothing... and that is the fact that [
nothing doesn't physically exist].
By extention, (C1) is clearly flawed. Just because two things share certain properties doesn't necessarily make them the same thing. Only if they share ever possible property are they the same. [x and nothing] do not share every possible property. In fact, they share only one significant property. We can, however, restate (C1) in a manner that does make sense.
(C1) ...Something that doesn't physically exist is nothing physical
But again, we didn't need any of the rest of your proof to demonstrate this fact. It is self evident, by definition.
Given all of the above, (P5) is such a garbled jumble as to be devoid of any meaningful meaning. I have a vague notion of what you're trying to say, but it is extremely vague, and mostly nonsensical. One attempt to restate it plainly, while keeping to your implied meaning, might go something like:
(P5) ...saying 'there is no [thing] which is a [physical object] and yet is [not physical] ... is the same as saying 'it is not the case that there is a [thing which physically exists] that [does not physically exist]
While this may be true, it is nothing more than a (very complicated, but none-the-less) trivial tautology.
The final conclusion is much easier to reinterpret:
(P5) ...it is not the case that there is [something physical] which is [not physical].
Once again, however, this is a trivial, self evident truth. No 'proof' is needed to show it's truth. (Or, if it is needed, it is not possible.)
Jimmy_sanfrancisco wrote:A Meinongian reply:
Reject 4th premise: Because there is an object that doesn’t exist that has some feature that nothing has: the number three doesn’t exist and it is prime.
My assumption is that this is not a valid presentation of the Meinongian counter-argument. However, (with a little tinkering to give clarity), it can be seen as a fairly accurate way to state (at least one of) my strategy(-ies) for dealing with (P4). For as I showed, [nothing] does share some features with the fact in question--but certainly not all.
Jimmy_sanfrancisco wrote:My reply:
(P1) Meinongianists claims that there are objects that don’t exist that are not prime, for example, the number four ...
...Therefore,
(C1) not existing and being prime are independent features of objects that don’t exist: having [not existing] does not require having [being prime].
(P2) not existing is a feature that the number three has independently of its having being prime.
(P3) the number three is an object that doesn’t exist, or it is not the case that it is an object that doesn’t exist.
(P4) In either case, it follows that: it is not the case that it is an object that doesn’t exist.
...Therefore,
(C2) it is not the case that the number three doesn’t exist and is prime.
Given my comments above, you may already be able to see what I believe to be the flaw in this line of reasoning.
First, (P1) is inaccurately stated. It should be:
(P1) ...M's claim there are [facts that do not physically exist] and which [are not prime]. For example, "The number 4 is not prime". is such a fact.
So is the fact that, "The number three is prime." This fact is clearly not itself a prime number. It states something about a [number] and about [being a prime]... but the fact is not a [number] or a [prime].
...Therefore
(C1) ...[not existing physically] and [being prime] are not inter-dependent features of things that do no exist physically. And having the property of [not existing physically] does not require something to also have the property of [being prime].
This is redundant and obvious; and I would suggest does not require (P1) for its truth. All that is necessary is the realization that [x] is not [y]. And [not existing physically] is not the same idea as [being prime]; therefore, they cannot be reciprocally inter-dependent features. They are not identical. One can depend on the other (as primes depends on being non-physical) but they can't both depend on the other, without being the same thing.
(P2) restates (C1) and (P3) basically says "Either [3]
exists physically or it doesn't". While (P4) basically says,
(P4) ...In either case, it follows that the [object that does or doesn't physically exist] is not an object that [doesn't exist physically].
This is the same as saying:
If [x or not x] then [not x].
I think it's pretty obvious this is not correct--and the assumption that it is correct invalidates the conclusion, (C2).