= 27d567bc2d48d9f40e9ccc20ea370b15)
endoself comments on What do professional philosophers believe, and why? - Less Wrong Discussion
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (249)
I think Jack meant the sort of modern platonism that philosophers believe, not Tegmark-style platonism. Modern platonism is the position that, as Wikipedia says, abstract objects exist in a sense "distinct both from the sensible external world and from the internal world of consciousness", while in Tegmark's platonism, abstract objects exist in the same sense as the external world, and the external world is a mathematical structure.
Wikipedia's fine, but I'd rely more on SEP for quick stuff like this. The question of what makes something 'mathematical' is a difficult one, but it's not important for evaluating abstract-object realism. What makes something abstract is just that it's causally inert and non-spatiotemporal. Tegmark's MUH asserts things like that. Sparser mathematical platonisms also assert things like that. For present purposes, their salient difference is how they motivate realism about abstract objects, not how they conceive of the nature of our own world.
If I understand this correctly, I disagree. Modern philosophical platonism means different things by 'abstract' than Tegmark's platonism. In philosophical platonism, I accept your definition that something is abstract if it is causally inert and non-spatiotemporal. For Tegmark, this doesn't really make sense though, since the universe is causal in the same sense that a mathematical model of a dynamical system is causal, and it is spatiotemporal in the same sense that the mathematical concept of Minkowski spacetime is spatiotemporal, since the universe is just (approximately) a dynamical system on (approximately) Minkowski spacetime. The usual definition of an abstract object implies that physical, spatiotemporal objects are not abstract, which contradicts the MUH. I don't think we really have a precise definition of abstract object that makes sense in Tegmark's platonism, since something like 'mathematical structure' is obviously imprecise.
I don't think that means that abstract objects in the ordinary sense don't make sense. It just means that he counts a lot of things as concrete that most people might think of as abstract. We don't need a definition of 'mathematical structure' for present purposes, just mathematically precise definitions of 'causal' and 'spatiotemporal'.
The abstract/concrete distinction is actually a separate ontic axis from the mathematical/physical one. You can have abstract (platonic) physical objects, and concrete mathematical objects.
Example of abstract physical objects: Fields
Example of concrete mathematical objects: Software
My definitions:
Abstract: universal , timeless and acausal (always everywhere true and outside time and space, and not causally connected to concrete things).
Concrete: can be located in space and time, is causal, has moving parts
Mathematical: concerned with categories, logics and models
Physical: concerned with space, time, and matter
My take on modern Platonism is that abstract objects are considered the only real (fundamental) objects. Abstract objects can’t interact with concrete objects, because concrete objects don’t actually exist! Rather, concrete things should be thought of as particular parts (cross-sections, aspects of) abstract things. Abstract objects encompass concrete objects. But the so-called concrete objects are really just categories in our own minds (a feature of the way we have chosen to ‘carve reality at the joints’).
This isn't modern Platonism.
A program is an abstract object. Particular copies of a program stored in your hard drive, are concrete.
Ok, then its Geddesian Platonism ;) The easiest solution is to do away with the concrete dynamic objects as anything fundamental and just regard reality as a timeless Platonia . I thought thats more or less what Julian Barbour suggests.
http://en.wikipedia.org/wiki/Platonia_(philosophy)
The actual timeless (abstract) math objects are the mathematical relations making up the algorithm in question. But the particular model or representation of a program stored on a computer can be regarded as a concrete math object. And an instantiated (running) program can be viewed as a concrete math object also ( a dynamical system with input, processing and output).
These analogies are exact:
Space is to physics as categories are to math
Time is to physics as dynamical systems (running programs) are to math
Matter is to physics as data models are to math
This seems to be a question of "How are we allowed to use the word 'exist' in this conversational context without being confusing?" or "What sort of definition do we care to assign to the word 'exist'?" rather than an unquoted question of what exists.
In other words, I would be comfortable saying that my office chair and the number 3 both plexist (Platonic-exist), whereas my office chair mexists (materially exists) whereas 3 does not.
Well it is certainly the case that knowing how to use the word "exist" is helpful for answering the question: "what exists?" And a consistent application of the usage of the word "exist" is how the modern platonic argument get's its start. We look at universally agreed upon cases of the usage of "exist", formulate criteria for something to exist and apply those criteria. The modern Platonist generally has a criteria along the lines of "If and only if an entity is quantified over by our best scientific theories then it exists." Since our best scientific theories quantify over abstract objects the modern Platonist concludes that abstract objects exist.
Once can deny the criteria and come up with a different one or deny that abstract objects meet the criteria. But what advantage do these neologisms give us? Does using two different words, plexist and mexist, do anything more than recognize that material objects and abstract objects are two different kinds of things? If so why isn't calling one "material" and the other "abstract" sufficient for for making that distinction? Presumably we wouldn't want to come up with a different word for every way something might exist: quark-exist, chair-exist, triangle-exist, three-exist and so on.
Why not just have one word and distinguish entities from each other with adjectives?
Because what we're saying about our descriptions of things is different. For some nouns, saying that it "exists" means that it has mass and takes up space, can be bumped into and such. For other nouns, "exists" means it can be defined without contradiction, or some such.
The verb "exist" is being used polysemously, even metaphorically — in the manner that "run" is used of sprinters, computer programs, and the dyed color of a laundered shirt. A sprinter, program, and dye are not actually doing anything like the same thing when they "run", but we use the same word for them. This is a fact about our language, not about the things those three entities are doing. If there were any confusion what we meant, we would not hesitate to say that the program is "executing" and the dye is "spreading" or some such.
The whole Platonist position begins from a definition of "exists" that works equally well for abstract and concrete objects. You alternative definitions are bad: "has mass and takes up space, can be bumped into and such" isn't even a necessary set of criteria for a wide variety of concrete objects. Photons and gluons for instance.
We don't know that it "works equally well", since we don't have omniscient knowledge about the existence of abstract objects. If abstract objects don't exist, then the quantification criterion is too broad, and therefore does not work.
This straight-forwardly begs the question. I say "What it means to exist is to be quantified over in our best scientific theories". Your reply is basically "If you're wrong about the definition then you're wrong about the definition."
Your claim was "If we are right about the definition, we are right about the definition".
I'm yet to see such a definition. Do you mean the "definition" (a postulate, really) such as the one on Wikipedia? (SEP isn't any better.)
If so, then it's a separate definition, not something that "works equally well". Besides, I have trouble understanding why one needs to differentiate between the abstract world and "the world of consciousness".
It's just a way of categorising Platoniists. Conceptualists think 3 is just a concept in their mind, Ptatonists don't.
No, I don't mean that. I've given a definition/criterion like eight times in this thread include two comments up :-).
In other words, theories about the world generally make reference to entities of various kinds. The say "Some x are y" or "There is an x that y's" etc. These x's are a theory's ontological commitments. To say "the number the 3 is prime" implies 3 exists just as "some birds can fly" implies birds exist. Existence is simply being an entity posited by a true scientific theory. Making anything more out of "existence" gives it a metaphysical woo-ness the concept isn't entitled to.
What does "Sherlock Holmes is a bachelor" imply?
"Sherlock Holmes is married" is false. But the truth of "Sherlock Holmes is a bachelor" doesn't imply much about his existence.
A lot of lifting seems to be being done by the "scientific" in "scientific theory".
"Sherlock Holmes is a bachelor" implies that Sherlock Holmes exists. But when you say that you're simply taking part in a fictitious story. It's story telling and everyone knows you're not trying to describe the universe. If the fiction of Arthur Conan Doyle turned out to be a good theory of something-- say it was an accurate description of events that really took place in the late 19th century-- and accurately predicted lots of historic discoveries and Sherlock Holmes and the traits attributed to him were essential for that theory, then we would sat Sherlock Holmes existed.
I am rightly shifting the criteria of "what exists" to people who actually seem to know what they're doing.
That is not uncontentious.
In which case SH is not implied to exist. But I knew that it is a fictitious story. The point was that "the number the 3 is prime" doens't imply that 3 exists, since properties can be correctly or incorrectly ascribe to fictive entities. There is no obvious implication from a statement being true to a statement involving entities that actually exist. Mathematical formalism and fictivism hold 3 to be no more existent than SH, and are not obviously false.
You are not, because you are ignoring them when they say centres don't exist. You are trying to read ontology from formalism, without taking into account the interpretation of the formalism, the semantics. "
Sorry, I should have looked first.
Ah, I see. How is it different from "we define stuff we think about that is not found in nature as "abstract""?
I guess that's where I am having problems with this approach. "Number 3 is prime" is a well-formed string in a suitable mathematical model, whereas "some birds can fly" is an observation about external world. Basically, it seems to me that the term "exist" is redundant in it. Everything you can talk about "exists" in Platonism, so the term is devoid of meaningful content.
Hmm, where do pink unicorns exist? Not in the external world, so somewhere in the internal world then? Or do they not exist at all? Then what definition of existence do they fail? For example, "our best scientific theories" imply that people can think about pink unicorns as if they were experimental facts. Thus they must exist in our imagination. Which seems uncontroversial, but vacuous and useless.
I can talk about a Highest Prime. Specifically, I can say it doesn't exist.
Would a Platonist think that a tulpa exists?
Ah, fair point. I went too far. Still, I'm dubious about conflating the logical and the physical definition of existence. But hey, go wild, it's of no consequence.
I would say pink unicorns do not exist at all. The term, for me, describes a concrete entity that does not exist. "The Unicorn" could be type-language, which are abstract objects-- like "the Indian Elephant" or "The Higgs Boson" but unlike the Indian Elephant the Unicorn is not something quantified over in zoology and it is hard to think of a useful scientific process which would ever involve an ontological commitment to unicorns (aside from studying the mythology of unicorns which is clearly something quite different). "3 is prime" is a well-formed string in a suitable mathematical model-- which is to say a system of manipulating symbols. But this particular method of symbol manipulation is utterly essential to the scientific enterprise and it is trivial to construct methods of symbol manipulation that are not.
Our best scientific theories imply that people can think about pink unicorns as if they were experimental facts. So thoughts about pink unicorns certainly exist. It may also be the case the unicorns possibly exist. But our best scientific theories certainly do not imply the actual existence of unicorns. So pink unicorns do not exist (bracketing modal concerns).
So to conclude: it's different in that the criterion for existence requires that the entity actually figures in scientific explanation, in our accurate model of the universe, not simply that it is something we can think about.
So, if a theory of pink unicorns was useful to construct an "accurate model of the universe" (presumably not including the part of the universe that is you and me discussing pink unicorns?) these imaginary creatures would be as real as imaginary numbers?
But if "plexists" means something like "I have an idea of it in my head", then there is no substance to the claim that 3 plexists..3 is then no more real than a unicorn.
The number 3 has well-defined properties; such that I can be pretty sure that if I talk about 3 and you talk about 3, we're talking about the same sort of thing. Sources on unicorns vary rather more broadly on the properties ascribed to them.
I don't see what that has to do with existence. We could cook up a well-defined fubarosco-juno unicorn.
I agree that this is useful, but it is essential to recognize that these words are just wrapping up our confusion, and that there are other questions that are still left unanswered when we have answered yours. It can sometimes help to determine which things plexist and which mexist, but we still don't really know what we mean when we say these, and having words for them can sometimes cause us to forget that. (I suppose I should refer to phlogiston here.) I think that Tegmark-platonism is probably a step towards resolving that confusion, but I doubt that any current metaphysical theory that has completed the job; I certainly don't know of any that doesn't leave me confused.
We can wonder about the nature of concrete objects and the nature of abstract objects without quarreling about whether or not one exists.
I don't think we really can. The categories of concrete and abstract objects are supposed to carve reality at its joins: I see a chair, I prove a theorem. You can't really do this sort of analysis without reference to the chairs and the theorems, and if you do make those references, you must have already settled the question of whether a chair is concrete, and a fortiori whether concrete objects exist. The alternative, studying concepts that were originally intended to carve reality at its joins without intending to do so yourself, has historically been unproductive, except to some extent in math.
Right, so accept that both abstract and concrete objects exist.. While you're not doing science feel free to think about what abstraction is, what concrete means and so on.
I don't think I've been clear. I'm saying that the categories of abstract and concrete objects are themselves generated by experience and are intended to reflect natural categories, and that it's not useful to think about what abstraction is without thinking about particular abstract objects and what makes us consider them abstract.