More on Frisch

February 12, 2012

More puzzlement about something in Frisch’s book. On p. 17:

These is disagreement between those who think that the domains of applicability of all scientific theories are essentially limited and those who have a hierarchical conception of science according to which the ultimate aim of science is to discover some universal theory of everything. My claim that classical electrodynamics is (and to the best of our knowledge will remain) one of the core theories of physics is independent of that debate… For, first, we need to distinguish between the content of a theory and our attitude toward that content. Even if we took the content of classical electrodynamics to be given by universal claims with unrestricted scope about classical electromagnetic worlds, our attitude can be that we accept or endorse those claims only insofar as they concern phenomena within the theory’s domain of validity.

Unlike Frisch, I do not see the point (other than the obvious rhetorical one of avoiding terminological disputes) of distinguishing between the content of a theory and our attitude towards it. Under Frisch’s account, that part of the content of the theory that encompasses claims about what the entire universe is like is irrelevant to our knowledge of the physical world, because we accept only claims of the theory that fall within the theory’s domain of validity. What, then, is the purpose of attributing these useless claims, which have no bearing on our knowledge of the world, to the content of the theory?

It may sound here like I am just arguing about terminology, but I do think this particular use of language, which is deeply entrenched in philosophy of physics, is pernicious. It is pernicious because by elevating some particular construal of the mathematical structure of the theory to be straightforwardly “the content” of the theory, one is led to an overemphasis on the mathematical structure as being informative about the world, while overlooking the informativeness inherent in how that structure fails to perfectly map onto the world. This terminology in effect provides a licence to focus solely on formal features of the mathematical structure as being the “essence” of the theory without seriously considering how the structure hooks on to the actual world, as opposed to how it hooks on to the philosopher’s possible worlds.


Frisch on reliable theories

February 12, 2012

There’s a really confusing passage in p. 42 of Mathias Frisch’s book on inconsistency in classical electrodynamics. He suggests, in response to the “problem” of inconsistency in classical electrodynamics, that we modify our account of theory acceptance:

this problem disappears if in accepting a theory, we are committed to something weaker than the truth of the theory’s empirical consequences. I want to suggest that in accepting a theory, our commitment is only that the theory allows us to construct successful models of the phenomena in its domain, where part of what it is for a model to be successful is that it represents the phenomenon at issue to whatever degree of accuracy is appropriate in the case at issue. That is, in accepting a theory we are committed to the claim that the theory is reliable, but we are not committed to its literal truth or even just of its empirical consequences. This does not mean that we have to be instrumentalists. Our commitment might also extend to the ontology or the ‘mechanisms’ postulated by the theory. Thus, a scientific realist might be committed to the reality of electrons and of the electromagnetic field, yet demand only that electromagnetic models represent the behavior of these ‘unobservables’ reliably, while an empiricist could be content with the fact that the models are reliable as far as the theory’s observable consequences are concerned.

If acceptance involves only a commitment to the reliability of a theory, then accepting an inconsistent theory can be compatible with our standards of rationality, as long as inconsistent consequences of the theory agree approximately and to the appropriate degree of accuracy… our commitment can extend to mutually inconsistent subsets of a theory as long as predictions based on mutually inconsistent subsets agree approximately.*

What confuses me about this is that I do not know what Frisch could mean by a theory being reliable apart from its consistently producing predictions that agree with experiment. Frisch wants to avoid instrumentalism by claiming that in accepting a theory, all we are committed not just to the observable consequences of the theory, but also possibly to the reality of the ontology and mechanisms of the theory. That is, in accepting the theory of electrodynamics, we might also be committed to the claim that electromagnetic models represent the behavior of ‘unobservables’ like ontology and mechanisms reliably. But what does it mean to represent reliably, apart from being a representation that reliably leads to predictions that agree with experiment? What does Frisch mean in the excerpt above by “represents the phenomenon at issue to whatever degree of accuracy is appropriate”? How can degrees of accuracy be attributed to representations over and above the accuracy of their experimental predictions?

Incidentally, I’m appalled at how expensive Frisch’s book is now. I bought it for $9 on Amazon when OUP slashed prices after having decided to stop printing it. Now it costs $60. The Kindle Edition costs $53.72!

* Frisch, M. (2005). Inconsistency, Asymmetry, and Non-Locality: A Philosophical Investigation of ClassicalElectrodynamics. Oxford University Press, USA.


What is a ‘fundamental theory’?

March 20, 2011

‘Fundamental theory’ is a phrase that is often used by philosophers and scientists alike, but I’m not sure what they mean by that. In this paper, Mathias Frisch writes:

In the case of non-fundamental theories, domain restrictions may also include restrictions to certain length- or energy-scales.

This suggests that fundamental theories are supposed to apply to all length- and energy-scales.

In the paper that Frisch is replying to, Gordon Belot writes:

We will of course need further principles that demarcate the domain of applicability of each theory — but every non-fundamental theory involves such principles.

Do fundamental theories, then, have no such restrictions on their domains of applicability? If so, does that mean that fundamental theories are just ‘theories of everything’? Does it also mean that we have no real examples of fundamental theories for our world, since all of our theories apply only to limited kinds or arrangements of matter?

Elena Castellani gives a quite different account of ‘fundamental physics':

“fundamental physics” is the physics concerned with the search for the ultimate constituents of the universe and the laws governing their behavior and interactions. Fundamentality, on this view, is the prerogative of the physics of smaller and smaller distances (or higher and higher energies), and, accordingly, particle physics and cosmology are currently identified as the fields where the quest for the “final theory” takes place.

I find the quick move from ‘fundamentality’ to ‘finality’ in her last sentence quite intriguing. But that aside, note that Castellani here takes fundamental physics to refer to the study of the “ultimate constituents” of the universe and their behaviour. This characterisation is quite different from Frisch’s — Castellani’s ‘fundamental physics’ may involve a restriction to certain length scales (the very small). But perhaps she has a notion of ‘fundamental theory’ that is distinct from that of ‘fundamental physics’.

In fact, although they never explicitly state this, the discussion between Frisch and Belot regarding the consistency of classical electrodynamics often refers to a certain subset of the equations of classical electrodynamics as characterising the ‘fundamental theory’, with other subsets being non-fundamental theories of classical electrodynamics. But we know that classical electrodynamics has a limited domain of applicability. So I’m not sure what they mean by ‘fundamental theory’ in this context.

There is also a notion of ‘fundamental’ at work that talks about theories being more or less fundamental than other theories, but may not call any one theory ‘fundamental’ tout court. Stephan Hartmann, for example, characterises one theory as ‘more fundamental’ than another if it covers a broader range of energy scale which includes the energy scales at which the ‘less fundamental’ theory is valid. In the same paper, Hartmann quotes Steven Weinberg as claiming that a more fundamental theory is ‘on a level closer to the source of the arrows of explanation than other areas of physics’. However, this characterisation doesn’t mesh so well with debates in philosophy of science about whether a less fundamental theory can explain phenomena better than a more fundamental theory. If theories are to be defined as more fundamental according to the ‘arrows of explanation’, then it is simply by definition that there are no phenomena that can be explained better by less fundamental theories.

Next, we have Carlo Rovelli, who suggests that a limited domain of validity renders a theory non-fundamental, yet claims that QFT is “the fundamental theory of motion” (p. 257 of the linked book):

General relativity cannot be seen as a ‘fundamental’ theory since it neglects the quantum behavior of the gravitational field, but many of the directions that are explored with the aim of finding a quantum theory of the gravitational field and/or extending the Standard Model — perhaps to a theory of everything — are grounded in QFT. Thus, one may regard QFT as the fundamental theory of motion at our present stage of knowledge — playing the role that Newtonian mechanics and its Lagrangian and Hamiltonian extensions played in the eighteenth and nineteenth centuries.

Rovelli seems to be implying here that a ‘fundamental’ theory is one that proves to be fruitful in a large number of ways — at least that’s what I take his comparison with Newtonian mechanics, and his quip about the current role of quantum field theory, to imply. Yet he disqualifies GR as a fundamental theory on account of its neglect of quantum behavior.

So, what is a fundamental theory?


Tyndall on the Value of Science

February 15, 2011

The old applications vs intrinsic value debate again. But I just love the way Tyndall writes:

Thus, in brief outline, have been brought before you a few of the results of recent enquiry. If you ask me what is the use of them, I can hardly answer you, unless you define the term use. If you meant to ask whether those dark rays which clear away the Alpine snows, will ever be applied to the roasting of turkeys, or the driving of steam-engines — while affirming their power to do both, I would frankly confess that they are not at present capable of competing profitably with coal in these particulars. Still they may have great uses unknown to me; and when our coal-fields are exhausted, it is possible that a more ethereal race than we are may cook their victuals, and perform their work, in this transcendental way. But is it necessary that the student of science should have his labours tested by their possible practical applications? What is the practical value of Homer’s Iliad? You smile, and possibly think that Homer’s Iliad is good as a means of culture. There’s the rub. The people who demand of science practical uses, forget, or do not know, that it also is great as a means of culture — that the knowledge of this wonderful universe is a thing profitable in itself, and requiring no practical application to justify its pursuit.

But while the student of Nature distinctly refuses to have his labours judged by their practical issues, unless the term practical be made to include mental as well as material good, he knows full well that the greatest practical triumphs have been episodes in the search after pure natural truth. The electric telegraph is the standing wonder of this age, and the men whose scientific knowledge, and mechanical skill, have made the telegraph what it is, are deserving of all honour. In fact, they have had their reward, both in reputation and in those more substantial benefits which the direct service of the public always carries in its train. But who, I would ask, put the soul into this telegraphic body? Who snatched from heaven the fire that flashes along the line? This, I am bound to say, was done by two men, the one a dweller in Italy,* the other a dweller in England,** who never in their enquiries consciously set a practical object before them — whose only stimulus was the fascination which draws the climber to a never-trodden peak, and would have made Caesar quit his victories for the sources of the Nile. That the knowledge brought to us by those prophets, priests, and kings of science is what the world calls ‘useful knowledge’, the triumphant application of their discoveries proves. But science has another function to fulfil, in the storing and the training of the human mind; and I would base my appeal to you on the specimen which has this evening been brought before you, whether any system of education at the present day can be deemed even approximately complete, in which the knowledge of Nature is neglected or ignored.

That was from Fragments of Science, vol. 1, pp. 94-5.

*Volta.
**Faraday.


Metaphysics and Effective Theories

February 11, 2011

I’ve lately been finding it really difficult to get myself interested in alleged metaphysical issues stemming from assuming that a certain physical theory applies to the entire universe. Many of the ‘philosophical’ problems of quantum mechanics, for example, are of this ilk, as are many in algebraic quantum field theory and general relativity.

The standard practice in philosophy of physics is to use a so-called fundamental theory for your metaphysical inferences. Effective theories are for the most part ignored. The intuition is that the ‘fundamental theory’ describes ‘what is really out there’ while effective theories are somehow more phenomenological, or derivative of the fundamental theory (and hence need not be considered in addition to the fundamental theory).

A question arose in class today as to why is it that people who worry about entanglement in quantum mechanics typically worry about it in relation to special relativity rather than general relativity. The standard answer is that gravity is an effect that is negligible in the entanglement experiments we are considering, so we do not have to worry about what a quantum theory of gravity would have to say about the issue.

That got me wondering about how far someone could use that answer and still maintain that it is useful to figure out what the metaphysics of our world is by supposing that quantum mechanics applies to the entire universe. My worry is this. By using the ‘gravity is negligible’ reason, one is admitting that quantum mechanics is really just another effective theory — it has a limited domain of application. If so, then either

  1. One thinks that in general it is legitimate to derive metaphysical conclusions using effective theories, or
  2. One thinks that there is something special about quantum mechanics as an effective theory, which allows one to derive metaphysical conclusions from it, as opposed to other effective theories that are typically ignored (e.g. effective field theories).

If one goes with 1., then it seems to me that the right way to do scientifically-informed metaphysics is to take the various theories we have as each being informative about their respective domains of applicability. This has the implication that we should not be applying quantum mechanics to the entire universe and taking the metaphysical implications of that seriously. For it is classical theories that are most effective at large size scales, not quantum mechanics.

As for 2., I am still struggling to imagine what could be special about quantum mechanics that licenses us to treat it in a different way from other effective theories. One possible reason is that one thinks that the most important aspects of quantum mechanics will still persist in a ‘final theory’ which applies to the entire universe. But whatever these preserved aspects are, it’s not clear to me that they are the same aspects as those that lead to the traditional philosophical problems in quantum mechanics. It might be that the mathematics of the final theory is such that the problems with locality and whatnot that manifest themselves in quantum mechanics are somehow dodged. One can apply the same consideration to other issues in philosophy of physics. Maybe underdetermination in general relativity won’t actually translate to an underdetermination problem in the final theory.

In addition, if you look at the history of physics, it doesn’t seem to me that the aspects of older theories that are preserved in newer theories are those which tend to preserve philosophical problems in the older theories. It doesn’t seem to me as though any of the aspects of classical physics that are preserved in quantum mechanics are those that are philosophically problematic for either theory. In other words, the robust aspects of physical theories often aren’t those that lead to traditional philosophical problems.

Someone help me out here. I seem to be missing out on a lot of fun by being so pessimistic about this enterprise of reading metaphysics off ‘fundamental’ theories.


Epistemic opacity in simulations

January 10, 2011

This post is the result of reading Wittgenstein and the philosophy of simulation literature in close temporal proximity.

Here is Paul Humphreys on epistemic opacity in computer simulations:

a process is epistemically opaque relative to a cognitive agent X at time t just in case X does not know at t all of the epistemically relevant elements of the process. A process is essentially epistemically opaque to X if and only if it is impossible, given the nature of X, for X to know all of the epistemically relevant elements of the process. For a mathematical proof, one agent may consider a particular step in the proof to be an epistemically relevant part of the justification of the theorem, whereas to another, the step is sufficiently trivial to be eliminable. In the case of scientific instruments, it is a long-standing issue in the philosophy of science whether the user needs to know details of the processes between input and output in order to know that what the instruments display accurately represents a real entity.

The charge is that simulations bring something new to philosophy of science because they are epistemically opaque, unlike, say, the process of solving an equation analytically.

However, I’m not sure I understand how simulations are any more epistemically opaque than physical experiments or non-automated calculations in mathematics. First, consider experiments. It seems to me that the checks we make to ensure that the results of experiments are reliable are almost completely analogous to those we make to ensure that the results of simulations are reliable. Allan Franklin has a good list of the kinds of checks we make to ensure that experiments produce reliable results. All the seven criteria he describes there seem to be used to validate simulations as well as physical experiments. We do check that the simulation reproduces known results and artifacts. We do try to eliminate plausible sources of error. If the simulation produces a striking pattern that can’t be explained by plausible sources of error, we do use that pattern itself to argue for the validity of that pattern as a legitimate result. If multiple independently corroborated theories account for the results of a simulation, that does add to the validity of the results. Simulations are often based on well-corroborated theories. Finally, statistical arguments are used to argue that patterns seen in simulations are real.

So what is epistemically relevant in simulations that humans cannot know, that can be known in the case of physical experiments and mental or pen-and-paper mathematical calculations? I’m guessing that what Humphreys takes to be epistemically relevant in simulations but inaccessible to human knowledge is something like the results of each computational step in the simulation, or whether the mechanistic workings of the simulating apparatus produces mathematically correct results. But are the results of each computational step epistemically relevant? Here is one reason to think not. In a physical experiment, one never has a complete working theory of the apparatus that tells us the exact consequences of every step in the experiment. It seems to me that demanding that the result of every computational step in the simulation be epistemically accessible to humans is analogous to demanding that every step in the experiment be justified by a theory that describes every aspect of the apparatus.

What if Humphreys considers the reliability of the simulating apparatus, that is, whether it is producing mathematically correct results, as the epistemically relevant aspect of simulations that is essentially inaccessible to humans? As noted above, the same way one can validate the reliability of experiments without having a complete theory of the experimental setup, we have ways of validating the reliability of simulations. But they are not foolproof of course. Suppose we take seriously the possibility that our methods of validation still leave out epistemically relevant information. It is possible that even though our checks show that the results are reliable in a large variety of situations, some hocus-pocus is going on which can be discovered only by going through every single step in the simulation, which humans cannot do. But there is an analogous “problem” when it comes to mental or pen-and-paper arithmetic. One’s belief that one is calculating 2098×98723 correctly, if one is doing it for the first time, is based on one’s past success in calculating various other things correctly. Of course some hocus-pocus could be going on just this time, for the new calculation, a kind of hocus-pocus which did not show itself in previous calculations. But this possibility does not lead us to say that there is something epistemically missing from the new calculation. If one really wants to be paranoid, one could always doubt the results of mental or pen-and-paper calculations, because after all we do not know, mechanistically, how the human mind consistently applies arithmetical rules, and whether it always correctly applies them. We act as though it always consistently applies them because of prior evidence of its reliability, but these do not suffice to ensure with certainty that it will always consistently apply them. How is this different from the case of simulations? In simulations, we also only have the prior results of simulations, and the backing of mathematics and physical theories relating to the mechanics of the simulation, to assure us that this time the simulation will also be reliable.

Humphreys’ ascription of epistemic opacity to machine calculations but not human calculations is an interesting inversion of one point of view that Wittgenstein discusses at various points in his philosophy of mathematics. Wittgenstein identifies the philosopher of mathematics’ love for axiomatic reductions of mathematics due to the idea of “mechanical insurance against contradiction” (RFM, p. 107e, his emphasis). The idea is that by reducing mathematics to a set of rules that even a machine can follow, one excludes mistakes from mathematics:

We may trust ‘mechanical’ means of calculating or counting more than our memories. Why? — Need it be like this? I may have miscounted, but the machine, once constructed by us in such-and-such a way, cannot have miscounted. Must I adopt this point of view? — “Well, experience has taught us that calculating my machine is more trustworthy than by memory. It has taught us that our life goes smoother when we calculate with machines.” But must smoothness necessarily be our ideal (must it be our ideal to have everything wrapped in cellophane? (RFM, 106e)

ResearchBlogging.org
Humphreys, P. (2008). The philosophical novelty of computer simulation methods Synthese, 169 (3), 615-626 DOI: 10.1007/s11229-008-9435-2
Wittgenstein, L. (1967). Remarks on the Foundations of Mathematics, ed. G. H. von Wright, R. Rhees, and G. E. M. Anscombe, trans. G. E. M. Anscombe. MIT Press.


Yes

October 23, 2010

It says something about Thomas Bernhard that one of his more upbeat novels ends with a suicide.

I have been stuck in this rut in my fiction reading habits, where I find most characters in most books alienating. Thomas Bernhard’s are an exception, but it’s not clear that reading the monologues of depressives and master procrastinators adds to my quality of life.

I had to nearly coerce myself to finish reading The Limeworks because the entire thing is nothing but the inner thoughts of a procrastinator who isolates himself and his invalid wife in an inaccessible abode, ostensibly so that he can carry out his research in peace, but never actually manages to write down any of his research results, and most days barely gets any experiments done. Right at the start of the book you’re told that the protagonist has killed his wife and gone crazy and is now in police custody. The rest of the book consists almost entirely of his maniacal habits and thoughts preceding that event. Most of Bernhard’s books are that way — heavy on monologues, light on events.

Which was why I was pleasantly surprised by Yes. It is similar to The Limeworks in also having a protagonist who is a master procrastinator and has not been able to get any research done for several months. But things actually happen in Yes. The protagonist meets a mysterious Persian woman whose life story is gradually revealed. They briefly help each other out of depression. Then they get bored, realise they are only reinforcing each other’s foibles, and stop meeting. The woman locks herself in a half-built house and starts decomposing. The protagonist visits her against his better judgment and is told to never do it again. He doesn’t. She eventually throws herself under a lorry.

That’s actually an upbeat ending. I was expecting it to end with just her continued wasting away, which would have been more depressing. Also, unusually for Bernhard, the positive development in the middle of the story actually led to some rather lyrical writing. Finally, it’s rare to see intensely expressed emotions in Bernhard that aren’t negative. One can’t help but wonder if any events in Bernhard’s life paralleled the writing of this relatively positive book.

I wonder why Bernhard hates Linz so much. Many of his books contain rants about that city.


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