Archived

Aseity

Read 14781 times

MorleyMcMorson

  • ***
  • 2603 Posts
    • View Profile
Platonism vs. Fictionalism
« on: October 22, 2012, 04:34:21 pm »
This is mainly for Jubilee, but all may respond.

Jubilee writes,

Quote
However, there is a revised version of the indispensability argument, defended best by Alan Baker, which evade all of these criticisms. Baker’s argument avoids them by arguing that mathematics plays more than just a representational role in science, but also plays an explanatory role.  This revised argument also helps platonists in the fight against hard road nominalistm too. Although some of our theories can be nominalized, they do so by losing explanatory power.

The argument is analogous to the scientific realist’s argument for quirks and electrons via their explanatory power.  Baker’s example comes from biology. One of the puzzles facing biologists is why a certain insect, called the periodical cicada, has prime life cycles. A common explanation is that prime lifecycles cut down on intersection with predators. In this explanation, a property of numbers themselves, that prime numbers have the least multiples, plays an essential part of the explanation and does genuine explanatory work. Just like the scientific realist would argue, you can't have a genuine explanation without the explanans existing.

Sometimes we posit entities that don’t play a causal explanatory role, but a mere logical explanatory role. For example, regardless whether you think this is the best explanation, some use the multiverse to explain the fine-tuning of the universe for intelligent life. It is argued that if there are multiple universes, a fine-tuned universe is really like a win of a cosmic lottery. Notice this explanation is purely logical, there is no causal contact between other universes for this explanation to work. Alan Baker suggests mathematical explanations are like that--they provide logical, not causal explanations.

There are a number of things I'd like to say to this, but I'll start with a few observations.

1. It seems to me very difficult to run an indispensability argument out there as far as abstract objects go.  Basically, indispensability says, "If you get rid of this, everything goes crazy."  The problem, as I see it, is that this smuggles in causality, at least if causation is counterfactual.  If you say, "Take X away, and you lose Y," then X is a cause of Y.  If not, how could that conditional hold?  You could say that Y is a part of X, and thus if you took X away you'd lose Y, but this is a rather trivial case and not one of causation (unless one wants to consider everything self-caused, but I digress).  Balaguer points this out, more or less, in his book.  Abstracta are not indispensable; you can take them away and it won't change anything at all.  If per impossibile removing them caused external changes, that would mean they had some causal impact.  But, ex hypothesi, they don't.  Therefore, indispensability arguments really only make sense for concreta, for things which can stand in causal relations.

2. Explanations are tricky things.  What is a good explanation in one person's eyes might not be good in another's.  One also has to consider the whole explanation-truth relation: do good explanations have to be realist, or can they be fictionalist?  Fictionalists explain things using numbers and other abstracta; they simply believe explanations can have merits which might override failure to correspond with how things are.  So, as such, this argument begs the question against fictionalists since fictionalists can agree (a la Balaguer, at least in theory) that there can't be (or we can't create, anyway) any good explanations without reference to abstracta.  But fictionalists are okay with this, so the argument for Platonism is a bit murky, to say the least.

3. Your examples are questionable, as well.  Take your multiverse example.  You say it is a "purely logical" explanation.  In a sense this is true.  But you have to consider that there can be explanations of different aspects of things.  The multiverse qua explanation for fine-tuning does explain the fine-tuning, but it explains it qua abstractum (low odds).  It would then reduce to a relation between abstracta.  If you want to say, on the other hand, that it explains the nitty-gritty physics of our world, I'd have to say that it's not a logical explanation you need but a physical one, one explaining, say, universe-generation within a multiverse.  It would, then, be either abstractum explaining abstractum or concretum explaining concretum.  The latter is irrelevant; the former gives nobody who doesn't already believe in abstracta any reason to believe in them.
"We have no past, we won't reach back..."
-Ardent A-theorist Cyndi Lauper in her song "All Through the Night", singing about the impossibility of time travel on her presentist metaphysic.

1

Jubilee

  • ***
  • 1237 Posts
    • View Profile
Re: Platonism vs. Fictionalism
« Reply #1 on: October 22, 2012, 06:53:30 pm »
YAY! Finally someone cares enough to talk about this stuff ^_^

Quote
1. It seems to me very difficult to run an indispensability argument out there as far as abstract objects go.  Basically, indispensability says, "If you get rid of this, everything goes crazy."  The problem, as I see it, is that this smuggles in causality, at least if causation is counterfactual.  If you say, "Take X away, and you lose Y," then X is a cause of Y.  If not, how could that conditional hold?  You could say that Y is a part of X, and thus if you took X away you'd lose Y, but this is a rather trivial case and not one of causation (unless one wants to consider everything self-caused, but I digress).  Balaguer points this out, more or less, in his book.  Abstracta are not indispensable; you can take them away and it won't change anything at all.  If per impossibile removing them caused external changes, that would mean they had some causal impact.  But, ex hypothesi, they don't.  Therefore, indispensability arguments really only make sense for concreta, for things which can stand in causal relations.

In the original indispensability argument, mathematical objects were idealizations and place holders--so it's not too hard to see how we could just retain the nominalized content and dispense with the platonic content. Let's specifically talk about the explanatory argument and specifically the case of the periodical cicada. Alan Baker points out that a property of numbers, primeness, is an essential part of the explanation. Only when you combine this piece of pure mathematics with a biological law and ecosystem constraints to you yield an explanation of the lifecycles of the cicada.

Without the piece of number theory, the explanation cannot get off the ground. Assuming talk of counterpossibles is meaningful, if there were no numbers, then this biological phenomenon would be inexplicable because there would be no property of primeness to help explain the data. So, yes, if you took away mathematical entities, then there is no reason why the cicada's lifecycle must be 13 or 17 years--a loss in explanatory power.

You're assuming a causal account of explanation, which is very contentious at best and question begging against the platonist at worst. Since we are dealing with a new type of relationship between objects, I don't see any reason to suspect other examples of this type of explanation should be available. Nevertheless, that crucial dependence between explanadum and explans still exists in my example.

Your response to my multiverse example seems sound to me, but I'd like to think about it more.

Quote
Explanations are tricky things.  What is a good explanation in one person's eyes might not be good in another's.  One also has to consider the whole explanation-truth relation: do good explanations have to be realist, or can they be fictionalist? 

We have to look at what makes an explanation a good one and Alan Baker reports that most biologists accept this explanation of the lifecycle of cicadas. An object can't do genuine explanatory work if it doesn't exist--this is the same point scientific realists make. If you retort that the difference between scientific unobservables and abstracta is their causal role, I'd repeat that in both cases if the objects didn't exist and have their properties, they couldn't account for the data.

You should read through Baker's original article:
http://www.swarthmore.edu/Documents/academics/philosophy/Baker%20math%20expl%20cicada%20Mind.pdf

and his response to criticism:
http://www.swarthmore.edu/Documents/academics/philosophy/Baker%20math%20expl%20sci%20BJPS.pdf
« Last Edit: October 22, 2012, 06:59:58 pm by Jubilee »
There are more things in heaven and earth, Horatio,
Than are dreamt of in your philosophy.

2

MorleyMcMorson

  • ***
  • 2603 Posts
    • View Profile
Re: Platonism vs. Fictionalism
« Reply #2 on: October 23, 2012, 12:07:51 pm »
Quote
In the original indispensability argument, mathematical objects were idealizations and place holders--so it's not too hard to see how we could just retain the nominalized content and dispense with the platonic content. Let's specifically talk about the explanatory argument and specifically the case of the periodical cicada. Alan Baker points out that a property of numbers, primeness, is an essential part of the explanation. Only when you combine this piece of pure mathematics with a biological law and ecosystem constraints to you yield an explanation of the lifecycles of the cicada.

Right, it's an essential part of that explanation.  But if non-realist (fictionalist) readings of the explanation are fine, then this doesn't count against fictionalism.  The hallmark of the fictionalist, after all, is the acceptance of explanations for reasons other than literal truth.  Fictionalists believe explanations/theories can have overwhelming merits even apart from truth.

Quote
Without the piece of number theory, the explanation cannot get off the ground. Assuming talk of counterpossibles is meaningful, if there were no numbers, then this biological phenomenon would be inexplicable because there would be no property of primeness to help explain the data. So, yes, if you took away mathematical entities, then there is no reason why the cicada's lifecycle must be 13 or 17 years--a loss in explanatory power.

I'm glad you brought counterpossibles up, since I was planning on doing so as well.  From everything I know we do not yet have a successful semantics for discussing counterpossibles, and as such an argument which requires such a thing is at least undercut.

Quote
You're assuming a causal account of explanation, which is very contentious at best and question begging against the platonist at worst. Since we are dealing with a new type of relationship between objects, I don't see any reason to suspect other examples of this type of explanation should be available. Nevertheless, that crucial dependence between explanadum and explans still exists in my example.

I'm not assuming a causal account of explanation: I'm a fictionalist---I don't think explanations even need to feature exclusively existing entities, let alone causally relevant ones!  What I'm assuming, on the other hand, is a counterfactual analysis of causation.  These are distinct.

Quote
We have to look at what makes an explanation a good one and Alan Baker reports that most biologists accept this explanation of the lifecycle of cicadas. An object can't do genuine explanatory work if it doesn't exist--this is the same point scientific realists make. If you retort that the difference between scientific unobservables and abstracta is their causal role, I'd repeat that in both cases if the objects didn't exist and have their properties, they couldn't account for the data.

Why not accept all this but simply take a fictionalist stance towards the explanation?  You've given no reason other than that, if we did this, this wouldn't do "genuine explanatory work."  Who says it has to do so?  That biologists accept the explanation is fine, but biologists probably, most anyway, have never even heard of fictionalism or scientific anti-realism.

I'll look over those articles should this discussion stagnate.
"We have no past, we won't reach back..."
-Ardent A-theorist Cyndi Lauper in her song "All Through the Night", singing about the impossibility of time travel on her presentist metaphysic.

3

Jubilee

  • ***
  • 1237 Posts
    • View Profile
Re: Platonism vs. Fictionalism
« Reply #3 on: October 23, 2012, 12:46:14 pm »
Hey, MorleyMcMorson :DD

I'm running a little low on time right now but I can respond later. Even apart from that, I recommend reading Baker's paper anyway because I'm not going to say anything original and he writes with much more precision than I do. He addresses pretty much everything you said. Tell me what you think: http://www.swarthmore.edu/Documents/academics/philosophy/Baker%20math%20expl%20sci%20BJPS.pdf

I think you'll find section 3 and on particularly pertinent. If you don't feel like reading, I'll respond tomorrow or the next day. Cheers :D
There are more things in heaven and earth, Horatio,
Than are dreamt of in your philosophy.

4

MorleyMcMorson

  • ***
  • 2603 Posts
    • View Profile
Re: Platonism vs. Fictionalism
« Reply #4 on: October 23, 2012, 09:23:07 pm »
I'm really only interested in addressing your specific concerns, so I'll just wait for your personal responses to my points, plus anything else you might want to add (quotes from Baker?).
"We have no past, we won't reach back..."
-Ardent A-theorist Cyndi Lauper in her song "All Through the Night", singing about the impossibility of time travel on her presentist metaphysic.