This discussion got quite huge (link, and continuation of link, and continuation again), and eventually has led to me wanting to take a few minutes to elaborate on the foundations of mathematics and the meaning of existence (meaning: the meaning of the word "existence"). For good or for ill, this will probably be quite long. Apologies.
My claim, up front, is that Platonism is bogus. In fact, I think that reifying ideals (or abstractions in general) is a recipe for problems. We see it with religions (Christianity and Islam are ultimately (neo)-Platonist in their philosophical basis), and we see it with politics (hard Libertarianism is a reification of the ideal of Liberty). I think it's easier to see the problem with politics like Libertarianism, where because Liberty has been reified, it is held as more important than the flourishing and suffering of real sentient beings, but the problem is more tenacious with religions.
|In fact, this remarkable picture was shared by The Thinking Atheist today.|
In fact, I suspect that confusion of the Platonist sort is a primary reason that religions are so tenacious. For me, it has become transparently obvious that "God" is a certain kind of abstraction (and I'm starting a book fleshing this idea out fully). The confusion between whether or not "God" exists, then may rest entirely in the confusion of Platonism--the "unsettled" question about the "existence" of abstractions. Further, I suspect the fact that we use the word "exist" both for ideas like "baseballs exist" and "democracy exists" is a holdover from Platonism that constrains and confuses our thinking in a Platonist direction--problematically.
Not all "exists" are intended equally
Here, I'll offer a short series of examples that hopefully reveal just how ludicrous it is to accept that "exists" means one thing (whether for real things or abstractions). This series of paragraphs is a comment that appears in the discussion referred to at the beginning. (Link to comment).
Do numbers exist? Can you show me three? Not three of something. Show me three. Can you do it? Mathematicians say "the number three exists," meaning "there is an abstract notion called 'three' that describes the property of 'threeness,' which can be defined explicitly as the unique property shared in common among all collections of three things." But can you show me three? No! All you can show me is collections of objects that exhibit threeness. Is this the same meaning of "existing" as we use for the idea that "trees exist"? Of course not!
Do dragons exist? People have talked about them for centuries. There is complex and detailed literature available about them. Because someone thought up dragons and literature came up about them, must we say that they exist? Do dragons only exist in the abstract world of imagination? Is that the same kind of "existing" as we would use if they were a real animal? Of course not!
Then we can get weird. Suppose someone imagines a monster of some kind, writes it down, and never shares it. Does that monster exist? What if he never writes it down? Does it exist? What if he thinks it when drifting off to sleep one night, forgets about it by morning, and never thinks of it again? Does it exist?
Or weirder. Do potentially imagined things exist? Meaning, do things that could be imagined but that haven't been and perhaps never will be exist? Do they start existing only when someone imagines them for the first time? How odd, if so. What about those potentially imagined things that will never actually be imagined by any mind? Do they exist? In what sense?
Platonism can't deal with these problems except to assert an unqualified "yes" with very little nuance. Is this the same as the lusted-for "logical argument that Platonism is false"? Of course not! Like I mentioned, I don't think such an argument can be formulated because Platonism is based upon the acceptance of a bizarre set of unfalsifiable axioms (e.g. "There exists a realm of ideals in which the forms of all objects and ideas have reified existence," "Within the realm of ideals, the quintessential form of every thing and idea exists," "Human thought is the process of navigating this abstract world and discovering, not inventing, an expression of the forms contained therein.")
That's why I've dedicated so much time to his objections. He's committing one of the same errors that theists commit, at the foundation: he's engaging in non-parsimonious thinking that relies upon unfalsifiable axioms to fill in some attributional gaps that his psychology seems to need for some reason.
[At this point, people looking only to the thrust of this essay--about Platonism and the meaning of existence--can stop. The curious can read on for more information: background thoughts that led to this and answers to some particular objections.]
What kinds of objections does this answer?
To keep this shorter, it's probably best for the interested to see the actual series comment that I hope the above closes. (Start here.) I'll try to pull out some highlights here, though.
"Not a single one of you can provide a logical argument why Platonism is wrong."
I claimed he is looking in the wrong place here (using the analogy of a "you are here" star on a map and then looking for the star on the ground and arguing because it isn't there). As I clarified more later (in the comment above), it's not a matter of a logical argument that proves Platonism is wrong, it's a matter of the fact that it isn't useful for anything and is decidedly problematic. Platonism rests upon reifying abstractions. That's a problem because reified abstractions are no longer treated like abstractions (see Libertarianism--the importance of the abstraction is held above salient concerns about flourishing and suffering because the abstraction has been reified, i.e. taken to be real in an important sense). This confusion is at the heart of many of our deepest social ills including religion and bad politics. Why is this looking in the wrong place? Because such a logical argument almost certainly doesn't exist. You want an answer to a question that doesn't mean anything, however profound it seems to you.
"The purported "killer" of Platonism, Kurt Gödel, remained Platonist until his death, so I would assume you must believe your own mind to be greater than his, so please by all means provide evidence of this claim."
Those interested in Gödel's work, it's advised to go read this blog essay I wrote about him a couple of months ago. A cleaner, tighter version of this argument will appear in Dot, Dot, Dot, my next upcoming publication.
My response: This is another ridiculous charge. We know more about the fallout of Kurt Gödel's work now than he did. In fact, he's a character a bit like Tesla--held up on a pedestal now that sweeps under the rug the fact that he was kind of crazy. Also, as a Platonist, Gödel had a particular faith-based bent to believe in and vindicate Platonism, so of course he adhered to it! It's like C.S. Lewis and his "liar, lunatic, or lord (leaving out legend)" and concluding "lord." He wanted it to be true, and he never turned his back on it although he provided a key insight that makes Christianity far less believable.
Gödel's revelation was that our axiomatic systems can only be complete and coherent when they're trivial, which means that no matter how we decide to try to describe the world (mathematically, philosophically, via our own worldview), we are forced to choose axioms to do it. Not all choices are equally salient, of course, but on down the line, when we get into the transfinite stuff, we have no reason to believe that any of these axioms "make sense" against reality. It really uncovers just how human the whole thing is. If we want to call it "discovery" in a "realm of ideals," fine--but we have to know what we're doing! We're navigating a mental space of ideas, not something real. Otherwise, we obfuscate and contribute to an enormous lack of clarity that leads to some pretty serious problems, and what for? So we can feel better about nearly meaningless questions of ontology?
"Do you think just because you can't point to something that it doesn't exist?"
No. I believe that "exist" in the sense of abstractions, mental constructions, means something completely different than "exist" in the sense of physical objects or energy. It's a bit unfortunate (and maybe a consequence of Platonic thinking) that our language doesn't provide two different words for these things. If it did, I doubt you'd be confused on this point. On what other grounds might people think that theology is in any way different than mythology except that theology has its own special word?
"Where does the 'mental' come from? Randomness?"
Too blinded to see. Mental comes from minds. It exists in minds--only in minds. Again, star on the ground. The star is on the map (the map now is in your mind, it is imaginary), and you're looking for it on the ground. Randomness? By your use here, I'm not sure you even know what that word means, but see the previous paragraph in which I talk about billing you for your time.
"Do you think just because you can't point to a 'mental' object, such as a dimensionless point on a number line or grid, that these points don't exist and are simply 'made up'?"
Yes. They exist in minds as useful constructions defined by axioms which are statements made by people with minds. "Simply 'made up'" straw mans the situation a little bit, though, because it seeks to put it on par with Harry Potter. It's more like being on par with Newton's laws, a set of models that allow us to approximate values that give us predictive power concerning the behaviors of real objects. That's what the models are for: explanation and prediction. You're talking about the models as if they are real. They aren't. They're imaginary maps. This is the fundamental confusion of Platonism.
"Do you think all of reality is made up by language and that consensus, which determines language, also determines reality?"
This is tricky to pick apart. No. I'm a realist. I think reality exists, and I think people exist and try to explain it for their own purposes. We build mental models that allow us to make decisions. You're going Pyrrhic skeptic here, in a sense, taking the nuclear option. On the other hand, our language does determine how we experience reality. I gave one example of this above, but a far more profound example is available from the Himba Tribe in Africa. Their language is built completely differently around how they describe colors, and it has been demonstrated that they literally see the colors differently than people who speak, say, English. Their experience of reality, which is a model itself created by their brains, are dependent upon language in a very fundamental way. Given a spectrometer, though, they'd get the same numbers we get regarding various colors of light, and so their experience isn't changing reality. Our language helps make our brains, our brains determine how we experience reality, and reality, being non-agent, doesn't care a whit.
This is an incredibly deep, probably insurmountable bias that only a data-driven field like science has any hope of overcoming.
"Do scientists decide reality by consensus?"
No. Scientists determine the explanatory and predictive power of the models by consensus, although scientific consensus is a special kind of consensus that relies upon them having independently examined and cross-examined the evidence. Already, the forefronts of theoretical physics are putting out ideas that could possibly provide two or more fundamentally different descriptions of reality beyond our capacity to test. It's conceivable, given natural limitations like the Planck scale, that this could happen without the possibility of better resolution. Scientific consensus is really about the usefulness of the models. Imminently useful and elegant models with no essential contradictions via observation can be called "a description of reality," and are, for all intents and purposes, but the description is never the thing itself. Maybe try Buddhism on for a couple of years until you get this point in your head.
"What are our probabilities describing?"
The likelihoods of seeing certain outcomes in the world.
"Are you saying the actual patterns that the probabilities describe are themselves made up because we made up the language to describe them?"
There's a lot to untangle here. First, probability is a model that assigns likelihoods to the various potential outcomes. It's mental stuff too. What probability ultimately means is still hotly debated (in fact, it's probably the most bitter debate going in the philosophy of mathematics). This speaks to the fact that we're assigning the meanings, though (meanings also are mental models--the universe itself has no need or use for meanings, only thinking beings that care about them do).
Second, your "because" is broken all to pieces. I hope I've already clarified the difference here. In a sense, the probabilities are made up because they're a construction by which we attempt to describe what we see in the world. The randomness underlying it on the macroscopic scale (e.g. rolling dice) is usually assumed to be simply deterministic chaos, i.e. the physical system we're trying to model is too complex to reliably make predictions about, so a probability model with the assumption of randomness is more useful. Deterministic chaos is usually not regarded to be at work in quantum mechanics, although no one yet knows what is going on there. It could be deterministic at a scale smaller than the Planck scale, for instance. It could be that our binary logical system is bogus from the get-go, demanding a fuzzier type of logic to really understand what's going on. At any rate, the language of probability theory (which we invented starting in the 17th century) is something we invented to try to describe these things and to make useful predictions regarding them. The probability itself is "made up" (a phrase I seriously regret using with you now because you're taking its most extreme meaning, as if it is a farcical throw-away thing).
Third, patterns. Are there "actual patterns" at all? If no one was there to see the pattern, would it be a pattern? I'd probably argue that structures would exist, but that a "pattern" requires a mental model, so probably not. I bring this up not only because it's interesting but because it paints a clear picture about how confused your basic assumptions are. You're willing to assert that "patterns" exist independently of minds to interpret them that way, and you're not examining that assumption. If you lose that assumption, does your Platonism start to fall apart?
Mostly, and finally, I think you're really busy looking for something that is important to you for some reason, that being answers to questions that appear meaningful and deep but that are actually just confused. Christians think that the idea of the Trinity is meaningful and deep because it's so confused. As John said in his Outsider Test for Faith "Faith is a parasite on the mysterious." Here, you've assigned a meaningful-to-you mystery to the ontology of mathematics, and your faith (in the reification of abstract ideas) in Platonism is a parasite on that manufactured mystery.
"How do we tell 'reified abstractions' from abstractions?"
You tell me. I don't think they have any meaning. I'm not the Platonist.