This is a paper by Christopher Pincock, a philosopher at Ohio State University, tackling the interesting issue of whether, and in what sense, mathematical explanations are different from causal / empirical ones. Here is the abstract:

This article focuses on a case that expert practitioners count as an explanation: a mathematical account of Plateau’s laws for soap films. I argue that this example falls into a class of explanations that I call abstract explanations. Abstract explanations involve an appeal to a more abstract entity than the state of affairs being explained. I show that the abstract entity need not be causally relevant to the explanandum for its features to be explanatorily relevant. However, it remains unclear how to unify abstract and causal explanations as instances of a single sort of thing. I conclude by examining the implications of the claim that explanations require objective dependence relations. If this claim is accepted, then there are several kinds of objective dependence relations.

And in what follows are some of the highlights from the paper, which we thought were particularly interesting while reading it. We have alerted Prof. Pincock of this, so hopefully he will chime in during the discussion.

In the philosophy of science, discussions of explanation tend to assume that most explanations are causal explanations. Disagreements arise concerning what a cause is and how the explanatorily relevant causes are to be identified.

…

This methodology more or less guarantees a certain kind of satisfying result: there turns out to be only one kind of explanation. However, the worry remains that this unified category of explanation is more an artifact of the tools used than an underlying unity.

…

The case study for this article is Plateau’s laws for soap-film surfaces and bubbles. …

The power of Plateau’s laws is that they work for any such soap-film system. The frame can be any shape. In fact, there might not be a frame at all. An unconstrained soap film may form a bubble that encloses a given volume. Such a system almost trivially meets Plateau’s laws as it has only one smooth surface. A more interesting case involves more than one bubble. These systems obey Plateau’s laws as well

…

Taylor’s solution was to develop a new mathematical theory of surfaces that incorporated these complexities. … Prior to Taylor’s ground-breaking work in the 1970s, mathematicians were forced to resort to experiments with soap films to discern the structure of this or that surface. … With these definitions, the key result is that ‘any such configuration of surfaces must of mathematical necessity conform exactly to the three geometric principles stated at the beginning’ (Almgren and Taylor [1976], p. 86), namely, Plateau’s three laws.

…

We think we have an explanation when we have found a (1) classification of systems using (2) a more abstract entity that is (3) appropriately linked to the phenomenon being explained. Whenever an explanation has these three features I will say that we have an abstract explanation. … An easy way to see that causal dependence is not involved would be by emphasizing the highly mathematical character of the Taylor case. As nobody thinks that causal relations obtain in pure mathematics, we have a non-causal explanation. … Woodward is at pains to allow for explanations via causal generalizations that are not laws. These generalizations may lack the necessity or universal scope that many require laws to have, but yet they can still explain. For Woodward (writing with Hitchcock), these generalizations explain because they say how an object would change under this or that intervention

…

An attractive aspect of Woodward’s approach to causal explanation is that he can trace the value of explanations to the description of causal dependence relations. We can generalize Woodward’s approach by taking the essential features of abstract explanation to correspond to an abstract dependence relation. That is, we can say that a soap-film surface obeying Plateau’s laws depends on its being an instance of an almost minimal set. As with causal dependence, there can be subtle questions about exactly how we should interpret talk of abstract dependence … Strevens allows important explanatory contributions from more abstract entities like mathematical objects. But he ultimately requires these entities to represent underlying causal processes: ‘The ability of mathematics to represent relations of causal dependence—wherever it comes from—is what qualifies it as an explanatory tool’

…

Jackson and Pettit distinguish between a causally efficacious property and a causally relevant property. A causally efficacious property is one whose bearer thereby gains certain causal powers, for example to bring about a certain effect in a given situation. Clearly, one sort of causal explanation would explain that effect by noting the presence of the appropri- ate causally efficacious property. However, Jackson and Pettit insist that not all causally relevant properties are causally efficacious.

…

Lange is clear that the value of these explanations is that they do something that causal explanations cannot do: ‘these [distinctively mathematical] explanations work not by describing the world’s network of causal relations in particular, but rather by describing the framework inhabited by any possible causal relation’ … Lange discusses the explanation for why a person cannot carry out a certain crossing over the bridges of Konigsberg. The purely mathematical part of the explanation pertains to abstract topological structure (Lange [2013], p. 489). But the rest involves ‘various contingent facts presupposed by the why question that the explanandum answers, such as that the arrangement of bridges and islands is fixed’

…

According to Salmon’s classic discussion, conceptions of explanation can be divided into epistemic, modal, and ontic approaches … Few defend an epistemic conception today, primarily because the link between explanation and prediction seems too confining. Salmon himself advocates an ontic conception that ties explanations to features of the world: ‘The ontic conception sees explanations as exhibitions of the ways in which what is to be explained fits into natural patterns or regularities’ (Salmon [1998], p. 320). The more specific ontic approach that Salmon defends is of course a causal approach. … On a modal approach ‘scientific explanations do their jobs by showing that what did happen had to happen’

Categories: notable

I don’t think it’s true that “most” explanations in physics are causal explanations. Take, for example, the very common explanations in terms of energy or momentum being conserved. Physics students are always taught to think in such terms, since applying conservation of energy or conservation of momentum can be a powerful way of figuring out what happens.

Yet, such explanations are not “causal”. Nobody thinks that there is some daemon that goes around keeping an accounting ledger, and then issues instructions to particles to ensure that the accounting balances.

Rather, it is presumed that the low-level causation operates such that, overall, energy and momentum are always conserved. Thus, it will be the case that there is an equivalent explanation that is causal, but the explanation in terms of conservation of energy or momentum is not in itself causal.

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“As nobody thinks that causal relations obtain in pure mathematics, we have a non-causal explanation.”

Don’t mathematical platonists think that causal relations obtain in pure mathematics? If one is discovering an already existing Form, surely there is some causal relation between the Form and the mathematician. I heard a podcast with Cedric Vilani who said he believes that he is discovering what is there, not inventing.

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‘scientific explanations do their jobs by showing that what did happen had to happen’

Aka, inertia.

I think that part of the issue is that our minds are not built to digest energy, but information. We perceive reality as sequences of discrete events and concepts, otherwise it would all flow into white noise. Much as what we see is like a sequence of movie frames, that our vision extracts from the visible light. Otherwise it would be like the shutter left open and would be a whited out frame.

So the form, the information we extract, is descriptive, but only when we try to assemble the entire dynamic input into an entity or event, do we have some degree of explanation for that particular feature. Which we still have to edit and structure into a mentally digestible form, or it does revert to that white noise of too much information.

We like to think everything is information, but as with computers, where would those 1s and 0s be, without the electrons racing about the circuits?

By being “conserved” energy simply exists. It has no reason to cease existing. It is those constantly changing forms it manifests which are transient and while physics likes to think all information is preserved; How? It takes energy to manifest that information and if the information were permanent, then every bit of new information would need additional energy to be recorded. Yet information is static and energy is dynamic.

Now obviously energy can record enormous amounts of information. Consider Moore’s Law. Yet any energy we extract from nature and use to record those digits, was in some prior form, before we put it to our uses and so that form had to be transformed into the form we put it in. All of which requires more energy to create that configuration. Just as the production of mass out of energy radiates out enormous excess energy and even the manufacture of a car creates excess waste and other byproducts, including the salaries and profits which are the form of energy those involved are most concerned with.

As Deep Throat said in Watergate; “Just follow the money.”

To paraphrase; Just follow the energy.

Energy goes from prior to succeeding form, thus past to future, as these forms coalesce and dissolve, thus future to past. Just as we as individuals go from birth to death, future to past, while the species goes from prior generations to succeeding ones, past to future. Much as the cars in that factory go from initiation to completion, while the process goes the other direction, consuming material and expelling product.

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Following one of the references in this paper, there is this:

Juha Saatsi

– http://juha-saatsi.org/research/work-in-progress/

Mathematics and program explanations

– http://juhasaatsidotorg.files.wordpress.com/2014/03/maths_and_pe.pdf

“The only option, it seems, is to say that mathematics is involved in the programming relation, not in and of itself, but as an indispensable part of some kind of physical-cum-mathematical property complex. What is such complex like? How does mathematics get involved in programming via such complex? I have no idea.”

On Mathematics’ ‘Indispensable Explanatory Role’

– http://juhasaatsidotorg.files.wordpress.com/2014/06/explanatory-role.pdf

“If mathematics does not play a programming role, but is nevertheless explanatorily indispensable, what other roles are there? A natural alternative is to argue that mathematics only plays the role of representing some non-mathematical features of the world that themselves play the programming

role.”

On explanations from “geometry of motion”

– http://juhasaatsidotorg.files.wordpress.com/2015/01/geometry-of-motion.pdf

“It really matters to science that we can recognize and are able to conceive of different kinds of scientific explanations: some straightforwardly dynamical and causal; others geometrical, non-local, and (explanatorily) independent of the dynamics.”

Finally, in the paper itself:

“There is clearly still much to be learned about explanation by reaching back into the practice of science and mathematics.”

It is odd to me that of what I have seen here that the articles on program explanation do not appear to “reach back” into the models of causality and levels of abstraction that have been developed from the theory of programming semantics:

Mathematical Foundations of Programming Semantics

– http://events.cs.bham.ac.uk/mfps31/?lang=en

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This issue seemingly encompasses three sub-issues: the distinctions of three sets of concepts.

I1, Underlying reality (UR) vs explanation: UR will be there with or without explanation.

I2, Causality: by law vs by event sequence. 1) ALL laws can be written with math-language, 2) event sequence causality can be further divided into two subgroups, a) sequences loosely governed by laws, b) just happenstances.

I3, Abstract entity (AE) vs empirical phenomenon (EP): EP is the expression of UR, AE is written with math-language.

To make the issue simpler, we should first remove the human agent (the trouble maker) out of the picture first (at least, temporary). So, there is a UR doing its DANCING, with its own CHOREOGRAPHY which can be described with some kind of language. When UR (EP) can be DESCRIBED with AE, AE has an ISOMOPHIC structure the same as EP and is a suitable language for it. If a choreography of a UR cannot be described with any means (language), the chance is that we (human) do not know the details of that choreography, not because that that choreography is wrong or not in existence.

So, what is the problem?

Christopher Pincock: “… As nobody thinks that causal relations obtain in pure mathematics, we have a non-causal explanation.”

What is this? Is this very important? Absolutely not.

After the choreography of a UR is described with a way (languages), we can call it an explanation (causal or non-causal).

Is that LANGUAGE a human invention, having nothing to do with the choreography of the UR? Why are we getting so big head of ourselves all the time? All languages (including the speaking language) which we invent are already parts of Nature, and this is the key point of the book “Linguistics Manifesto”.

The entire math system is just a subset of Nature. We (human) construct our OWN math system by using preexist math lego pieces.

Someone claimed that many math-concepts exist in mind only, without physical references. Of course, this is wrong, but it is a long story. The easy answer is that the brain is the carrier for mind, and the intelligent part of brain (not bodily control part) is a white slate without anything on it. Without the burnt-in with external info (structure of Nature), that brain will know absolutely nothing, let alone about math-concepts (see http://www.prequark.org/inte001.htm ).

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The paper seems to be saying that soap bubble explanations are somehow different because they use abstract mathematics. Many fields of science use abstract math.

All I get out of this is that philosophers have a deep mistrust of anything mathematical. If a lot of math is involved, then somehow it is not truly an explanation, or it is not causal, or not objective, or not real. This is all nonsense. Mathematical reasoning has been essential to science for millennia.

The paper acts as if mathematical soap bubble work in the 1970s was some great philosophical break from the past. Plateau’s laws are not new. Plateau died in 1883.

It also acts as if explanations can be mathematical (ie, abstract) or causal, but not both. It seems to me that all the good explanations are both mathematical and causal. I don’t see any examples that match his ideas.

Coel, a great many common conservation arguments are causal. If you ask, what caused the baseball motion, I might say the cause is conservation of momentum when the baseball bat hit it. (Or cricket bat if you prefer.) If you ask, why does the Earth keep spinning, I might say the cause is conservation of (angular) momentum.

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Pondering the nature of the concept of explanation is very important. Yet, to brandish mathematics as unfathomable sorcery, would be a strange streak

Indeed, when an explanation can be fully mathematized, it is finished. Far from being “abstract”, it has become trivial, or so suppose those with minds for whom mathematics is obvious.

Warning to philosophers.

Mathematics is just like 2 + 2 = 4, written very large. Very large, for very complicated situations, sometimes. In particular, soap bubbles are all about minimizing energy. As those who know of energy would guess. So the field is eminently clear. The mathematics deal with the devilish iridescences in evidence. Among other subtleties.

How is a soap bubble more abstract than the mathematical arsenal that had to be elaborated over three centuries to explain it? Because a child can make a soap bubble, but a child does not understand a partial differential equation?

Or because a child can make a soap bubble, but is not aware of the concept of energy? Energy was figured out by Emilie du Châtelet; Newton had confused it with momentum.

In a soap film, any point p ∈ M has a neighborhood with least energy relative to its boundary. Yes, there are a lot of prickly details, as the necessity of defining appropriate energy such as Dirichlet’s energy.

Soap bubbles are more complicated than films, as the inner pressure is different from the outer one.

Anyway, I pretty much support what Schlafy said. Schlafy is a rigorously trained mathematician. Mathematicians are used to make elaborate demonstrations, and then, to their horror, discover somewhere something that cannot be causally justified. Then they have to reconsider from scratch.

To claim that mathematics is not causal is beyond belief. Mathematics is all about causality. Causality, by the way, reflect the axonal geometry of the brain. (The full logic of the brain is much more complicated, as it involves much more than axons, such as dendrites, neurotransmitters, glial cells, etc.)

“Causes” in mathematics are also called axioms. In practice, well known theorems are used as axioms to implement mathematical causality. A mathematician using a theorem from a distant filed may not be aware of all the subtleties that allow to prove it.

Mathematics, though, is causation. And the ultimate explanation. As it makes causation limpid. Precisely.

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I agree exactly with the words Patrice Ayme wrote — but with “mathematics”→”programming”, “mathematical”→”programmatical”, etc.

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I like this lecture a lot, Dr Shrimplin makes several interesting points:

1) This Sistine Chapel ceiling was originally painted with a depiction of the stars or the religion was always closely linked to cosmology, which was the tradition of all Western Religion going back to the Greeks.

2) The ideas of Copernicus were widely known and known by scholars in the Church before his official work was published in 1543 after his death, so Michelangelo was influenced by the Heliocentric teachings.

3) Heliocentric teaching conflicted with theology because of the concept of hell being below, which Dante solved later on with a dualistic approach to God, Heaven and Hell. It was actually the Protestants later on who rejected the geocentric teachings which appeared to conflict with scripture. As we know the Church scholars did not scientifically reject Galileo’s works later on, but wanted it recanted and suppressed in the climate of Protestant Europe.

4) Michelangelo was quoted as saying, “I paint with my brain, not my hands”.

5) Michelangelo was a sculptor, not a painter——-and he looked down on painters as lesser artists.

My own take is that sculptors work in a three dimensional world and are less inclined to the ‘cognitive illusions’ which painters are skilled at. Temples, Cathedrals, caves of worship have always held cosmological significance, so the Pope’s choice of Michelangelo was really a desire to build a sculpture from within as opposed to just beautiful painted murals. Being the Renaissance, with new scientific teachings at hand, there was an influence in Michelangelo to make this a truer scientific and mathematical depiction of the universe; which was the main point of her lecture. So if you listen to the lecture she discusses the mathematical and of course cosmological influences on his thinking.

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There are several things I don’t quite understand here.

First, who is the author of the essay? In the sentence “I have alerted Prof. Pincock of this”, who is the “I”, why weren’t they acknowledged, where are their credentials, etc? Is it just me, or does this essay appear somewhat half-baked?

Second, I don’t get what Plateau’s laws have to do with an “explanation”. It would be more natural to consider them a “description” of soap films, describing certain generic properties, that always hold (given certain assumptions).

Coelgave another nice example — conservation of energy is also a description of certain generic property of a system, that also always hold (bar gravitational effects). Neither really deserve to be called “explanation”, despite the fact that we regularly employ them to infer certain properties of physical systems. So somehow I fail understand, what is the whole essay (let alone the paper) actually about? Can anyone specify what *problem* are the author and Chris Pincock trying to address?Third, I fail to understand philosophers obsession with causality. It is being approached as something profoundly important or mysterious in philosophy, whereas in physics it is merely an emergent property of (approximate) deterministic dynamics. My impression is that people seem to be so stuck on causality because they are used to thinking in terms of Newtonian mechanics, where a ball moves because some other ball has hit it, so the collision is the “cause” of the ball’s motion, etc. But to a physicist, such a view on the world appears too naive, since there are lots of phenomena in Nature which cannot be interpreted in such terms. Therefore, causality is just a mirage, a consequence of thinking in deterministic terms. Establishing causal chains can certainly be very useful in practice (since a lot of properties of Nature of our everyday reality can be approximated with deterministic models), but deep down it is still just a mirage. I fail to see any profound, fundamental, conceptual, metaphysical, philosophical, or otherwise, importance of causality. So why is causality (or lack thereof) considered to be such a big deal in philosophy?

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Marko

I think causality is important to philosophers (at least to me – an armchair philosopher) because it is often where the direct perception ends and the theorizing about what is seen begins. It seems to me that a big part of science involves isolating/controling the variables so that we can know what is causing something.

You say:

“My impression is that people seem to be so stuck on causality because they are used to thinking in terms of Newtonian mechanics, where a ball moves because some other ball has hit it, so the collision is the “cause” of the ball’s motion, etc. But to a physicist, such a view on the world appears too naive, since there are lots of phenomena in Nature which cannot be interpreted in such terms. Therefore, causality is just a mirage, a consequence of thinking in deterministic terms.”

Do you think that because there are lots of phenomena in nature which can not be interpreted in deterministic cause and effect terms that deterministic causation is always a mirage? Or do you think some phenomena does follow deterministic causality?

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HI Coel,

But the passage you quoted does not say that they are.

Hi Marko,

Actually there are so few philosophers who are “obsessed” or even interested in causality that it would probably be possible to phone them all up and ask them yourself.

Mainstream philosophers have regarded ‘causality’ as being nothing more than a manner of speaking since Hume pointed out the problem with the concept.

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I couldn’t read the whole article yet, but on the basis of the exposition above, I am also a bit confused. As Marko stated Plateau’s Laws are a description of an observable regularity. I don’t see that they explain anything much at all. I guess Taylor’s work can count as an “abstract explanation”, but then any mathematical proof can.

The author makes much of the seemingly “universal applicability” of Plateau’s Laws on the basis of Taylor’s geometrical proof, but I am not quite sure how this licenses talk of a “new (uncausal) kind of explanation”.

I could also understand soap films as dynamical systems and Plateau’s Laws as describing some structural properties of a powerful attractor in phase space. In this light there is a causal narrative (explanation) for each trajectory in phase space and a “meta-explanation” for why most/all trajectories lead to this attractor. Is that what an “abstract explanation” is supposed to capture?

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Marko,

“It is being approached as something profoundly important or mysterious in philosophy, whereas in physics it is merely an emergent property of (approximate) deterministic dynamics.”

I see it as the opposite. That determination is emergent from causality. While the physical properties of a process will yield a determined outcome, but since the input into an event only arrives with its occurrence and its arrival is limited by the finite speed of light, the outcome cannot be determined prior to the occurrence. So the input has to come together and effect a result for determination to occur and much of this process is the physical effect of energies striking each other.

For instance;

“My impression is that people seem to be so stuck on causality because they are used to thinking in terms of Newtonian mechanics, where a ball moves because some other ball has hit it, so the collision is the “cause” of the ball’s motion, etc. But to a physicist, such a view on the world appears too naive, since there are lots of phenomena in Nature which cannot be interpreted in such terms.”

Maybe you should tell the operators of the Large Hadron Collider that their method of smashing things into each other is too naive. Possibly just a chalk board is all that is necessary. We can even get multiverses from that.

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Hi victorpanzica

What this lecture delivers is a lot of astounding ignorance of a kind I thought had disappeared from academia.

She drags out the obscure 6th century monk Cosmas Indicopleustes to claim that the Christians in the 6th century believed in a flat Earth cosmology..

Nonsense. Nearly every educated person from at least 300 AD onward would have held to a Ptolemaic cosmology which had a spherical Earth at the centre.

You can read this in many places, for example Augustine and the Venerable Bede.

Dante was simply describing a theatrical version of what was commonly believed at the time and had commonly been believed for centuries.

And Dante was not seriously suggesting that Hell was in the middle of the Earth and that Satan was really wedged right at the centre so that you could crawl down his midriff and (changing orientation) up his legs to get the the other side. He is simply presenting an allegorical picture and it would have been understood by his audience that way.

In passing I note that the infinitely small, infinitely bright point of light on which Beatrice gazes for an infinitely short period of time is not identified as the Sun, but as Aristotle’s Prime Mover and hence (from the beliefs of the time, God.

Hell has never been literally considered as a place underground in Christian tradition, in fact it is a common theme that heaven and earth are supposed to be swept away and a new world put up in their place.

It was not a belief of the Church that God exists in space and time or that Hell or God’s kingdom are places in space and time.

She refers a few times to a Medieval belief in the flat earth – this is a myth created in the 19th century by people like Washington Irving and John William Draper I thought the myth had finally been laid to rest. Apparently not.

The change that came in that period was not a move from a flat Earth to a spherical Earth, but from a geocentric Universe to a non-geocentric Universe.

OK, this is as off topic as victorpanzica’s post to which I am replying. These myths are a pet peeve of mine.

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Having read the article, I don’t have too much of a problem with it apart from a few subtle points pertaining to Platonism and the relationship of causality to mathematics.

However, like some others, I’m not all that sure what the fuss is about: nothing in the paper seems to my layman’s eyes to be especially insightful or to extend beyond the relatively obvious. It may be that the paper is an important contribution to the literature simply because it reminds us that not all explanations are causal, something which the ongoing academic conversation on causality has perhaps glossed over.

It seems rather obvious to me what an explanation is. I wonder is there anything wrong with the following:

An explanation is simply an account of how an observed state of affairs must obtain (or is likely to obtain, or is in any event unsurprising) given certain assumptions. A correct explanation is when the account and the assumptions are all correct.

Some explanations are causal, because the assumptions they depend on pertain to causal events that may or may not have happened. Some explanations are more abstract, because what they they assume is an abstract model of a system and show that the observed state of affairs is logically entailed by the model.

I think this view is broadly compatible with the thesis in the paper, though stated differently. In any event, the nature of ‘explanation’ really doesn’t seem to be much of a problem to me.

Schafly:I think your reaction to the article is somewhat off-base. The paper is not an attack on science or mathematics. It is an an argument from a philosopher, addressed to the community of fellow philosophers, making the point that some popular philosophical accounts of the nature of explanation are too narrow, focusing only on causation (e.g. event A caused event B) and not on mathematical relationships.

> The paper acts as if mathematical soap bubble work in the 1970s was some great philosophical break from the past.

No it doesn’t. It only uses Plateau’s laws as a case study to point out to philosophers how Taylor’s work doesn’t fit well with some philosophical accounts of explanation. It is a good case study precisely because it is an example of a well-established and mainstream scientific explanation.

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Occam’s beard> Don’t mathematical platonists think that causal relations obtain in pure mathematics?

It depends on how that question is interpreted. Mathematical objects are changeless, whereas causation usually implies time and change. But causation can be given a mathematical account.

> surely there is some causal relation between the Form and the mathematician

I personally would not say so. I would say there is a logical relation. The physical events of the world are sufficient to give a causal explanation for the mathematician’s actions, but there is a certain logical or structural similarity between the world and the Form. I don’t think most modern Platonists conceive of themselves as directly perceiving Forms with some kind of mathematical sense.

> I heard a podcast with Cedric Vilani who said he believes that he is discovering what is there, not inventing.

Sounds about right to me.

Patrice Ayme,> To claim that mathematics is not causal is beyond belief.

I think you are just interpreting that claim differently to how it is intended. For you, an axiom is a kind of cause. That is not necessarily how everyone conceives of these terms.

Marko,>In the sentence “I have alerted Prof. Pincock of this”, who is the “I”, why weren’t they acknowledged, where are their credentials, etc?

You seem to be confused because you haven’t noticed that Massimo has been posting a paper every week with a few notes for the past few weeks. The “I” is Massimo.

> Is it just me, or does this essay appear somewhat half-baked?

It’s not an essay. It’s a link to a paper for discussion with a few notes.

> It would be more natural to consider them a “description” of soap films

And you would be right. The explanation is not Plateau’s laws themselves but Taylor’s explanation/derivation of the laws.

I agree with much of what you say on causality, except without the assumption that determinism is false. On that we disagree (I am agnostic, with a leaning towards MWI determinism).

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Coel,

“Yet, such explanations are not “causal”. Nobody thinks that there is some daemon that goes around keeping an accounting ledger”

I find the idea that any scientific explanation is not causal hard to wrap my mind around. That, seems to me, is what science is in the business of doing: explaining the causes of natural phenomena. And I have no idea where this daemon thing comes from. You think that when biologists, for example, invoke natural selection as a cause of biological adaptation they are invoking a daemon??

“it will be the case that there is an equivalent explanation that is causal, but the explanation in terms of conservation of energy or momentum is not in itself causal.”

But if there is a lower explanation that is causal then by definition all higher level explanations are causal too, regardless of whether the causes are expressly addressed or not.

brodix,

“I think that part of the issue is that our minds are not built to digest energy, but information.”

As usual, I find this sort of statement unhelpful. Our “minds”? Built for a purpose?

“We like to think everything is information”

I don’t, in fact I find that attitude highly, ahem, uninformative.

“As Deep Throat said in Watergate; “Just follow the money.” To paraphrase; Just follow the energy.”

I find the analogy deeply uninformative.

Tienzen,

I must admit that your comments, while looking formally impressive, rarely add to my understanding of what you are saying. I wonder if you could come down to earth a bit and speak in language that we mortals can actually understand.

schlafly,

“The paper seems to be saying that soap bubble explanations are somehow different because they use abstract mathematics. Many fields of science use abstract math.”

The paper doesn’t deny that. Indeed, it builds on it.

“All I get out of this is that philosophers have a deep mistrust of anything mathematical.”

How on earth did you get that out of this paper?

“This is all nonsense. Mathematical reasoning has been essential to science for millennia.”

You interpretation of the paper is nonsensical, I’m afraid.

“Plateau’s laws are not new. Plateau died in 1883.”

Your point being?

“It also acts as if explanations can be mathematical (ie, abstract) or causal, but not both”

Actually, not, it doesn’t.

Patrice,

“Warning to philosophers.”

To quoque?

“How is a soap bubble more abstract than the mathematical arsenal that had to be elaborated over three centuries to explain it?”

Where did you get the idea that the author was making any such claim?

“Anyway, I pretty much support what Schlafy said.”

I find that unfortunate, since he clearly hasn’t understood the paper. Which I in turn explain to his irrational disdain for philosophy.

“To claim that mathematics is not causal is beyond belief. Mathematics is all about causality.”

It most obviously isn’t. What’s causal about Fermat’s Last Theorem? Causality implies physicality, and most of pure math has absolutely nothing whatsoever to do with physicality.

““Causes” in mathematics are also called axioms.”

You either don’t understand what causality means or what axioms are. Or both.

Philip,

“I agree exactly with the words Patrice Ayme wrote — but with “mathematics”→”programming””

Then I’m afraid the same exact comments I made above applies to you.

Marko,

“In the sentence “I have alerted Prof. Pincock of this”, who is the “I”, why weren’t they acknowledged, where are their credentials, etc? Is it just me, or does this essay appear somewhat half-baked?”

The “notable” articles series is based on editorial picks, I have now made that explicit.

“I don’t get what Plateau’s laws have to do with an “explanation”. It would be more natural to consider them a “description” of soap films, describing certain generic properties”

That is indeed my own problem with the article. I see both laws and mathematical treatments as descriptions, not explanations. I my mind, contra the author, all explanations in science are causal.

“I fail to understand philosophers obsession with causality.”

That may be because you haven’t read enough philosophy. Causality is both a fundamental and a quite mysterious notion in itself, hence the “obsession.”

“whereas in physics it is merely an emergent property of (approximate) deterministic dynamics”

To begin with, you have substituted an enigma (emergence) for a mystery (causality). Second, no, causality is fundamental, not an emergent property. It is causality that, I think, explains deterministic dynamics, not the other way around. (In this I actually agree with brodix!)

“My impression is that people seem to be so stuck on causality because they are used to thinking in terms of Newtonian mechanics”

I guarantee you that philosophers are aware of both general relativity and quantum mechanics.

“But to a physicist, such a view on the world appears too naive”

Sometimes I wish (some) physicists got off their damn high horse and stop telling everyone else just how naive they are. Perhaps engaging actual arguments would be more productive.

“causality is just a mirage, a consequence of thinking in deterministic terms”

I know plenty of serious physicists who couldn’t disagree more.

Robin,

“Mainstream philosophers have regarded ‘causality’ as being nothing more than a manner of speaking since Hume pointed out the problem with the concept.”

I have to dispute that. Some philosophers for sure, but I think Hume’s psychological view of causality is simply no longer tenable, with all due respect to one of my favorite philosophers…

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Hi

schlaflyThis might be a difference in how we conceive of “causation”. I would happily accept “conservation of momentum” as an *explanation*, but not as a “cause”.

To me, “conservation of momentum” is an abstract description about how things work, but “conservation of momentum” is not in itself an agent capable of “causing” anything. Whereas, things like “protons” or “electrons” are capable of “causation”.

Thus, I’d assert that there are low-level entities “causing” what happens, and statements such as “momentum is conserved” are then descriptions of the outcome.

It may be, though, that the difference here is largely semantics.

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Massimo,

“As usual, I find this sort of statement unhelpful. Our “minds”? Built for a purpose?”

I’m certainly willing to be corrected, but I didn’t see it as a controversial point. Our minds, or rather my mind, processes information. For instance, I would describe the words on this screen as information, while my mind isn’t concerned about the energy required to transmit them to me. We tend to describe a wave in terms of frequency and amplitude, rather than project the energy being manifested directly into our thought processes. Colors, textures, sights, sounds, etc. would all seem to be information conveyed by energy. As I look around this room, I see forms being expressed and the information conveyed by energy. Yet my mind seems more focused on these shapes than the processes creating them. It is only when I consider the accumulation of information acquired over my life that I can more deeply analyze these processes.

“I don’t, in fact I find that attitude highly, ahem, uninformative.”

If you could give me some idea why you think this assumption is flawed, I would be grateful.

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What Is Causality?

Advanced mathematics/logic/physics give a different sense of causality.

Minimal surfaces were invented to explain soap films and bubbles. The effort was in full swing in the 18th century already. Recent developments are less important.

Massimo wonders what is causal about Fermat’s Last Theorem. No need to get that complicated. Just look at 101 = 100 + 1. Call it T.

T is a theorem.

T can be demonstrated from a number of axioms. I say that these axioms “cause” T.

Massimo: ”You either don’t understand what causality means or what axioms are. Or both.”

Mathematics explains how axioms “cause” theorems.

Russell and Whitehead, colossal mathematicians and philosophers, decided to demonstrate 1 + 1 = 2. Without making “Cretan Liar” self-contradictions.

They wrote a book to do so. In the second volume, around page 200, they succeeded.

I prefer simpler axioms to get to 1 + 1 =2.

It would be interesting that Massimo define what “causing” means, and what “causality” is, for us. Say with explicit examples.

I want to know what cause causes. It’s a bit like pondering what is is.

As Marko said, all what all many creatures with philosophical pretentions know is 17th century physics, something about billiards balls taught in first year undergraduate physics. (I know it well, I have taught it more than once.) These first year undergraduates when to explain the entire world with the nail and hammer they know well.

They never made it to Statistical Mechanics, Thermodynamics, etc. And the associated “Causality” of these realms of knowledge.

How does “causality” work in the Quantum Mechanics we have?

You consider an experiment, analyze its eigenstates, set-up the corresponding Hilbert space, and then compute.

“Billiard Balls” is what seems to happen when the associated De Broglie wave has such high frequency that the eigenstates seem continuous.

So Classical Mechanical “causality” is an asymptote.

***

Quantum style causality is more environmental. Can nature be a computer? (Answering Philip.)

Computers can present imaginative solutions, just by serendipity: trying a lot of things, and then proposing for human inspection.

A program is a finite set of instruction. Say F.

Is the universe a finite set of instruction, U? There are technical issues. Clearly only particular universes could be generated from F. Another difficulty is that, due to Quantum Entanglement, any finite piece of the universe can be influenced from beyond the event horizon.

Another problem with the present computer programs is that they are non-Quantum. Quantum programs have been written extensively in the last 20 year (say Shor’s work). However, Quantum computers (the day they really work) will change the way computers are looked at. It is clear that full Quantum computers (there are degrees of Quantum-ness) will not be fully explainable.

So nature is probably a computer. Mostly a local computer, somewhat entangled beyond the horizon.

And a non-programmable, not fully knowable, Quantum computer. Something not causal in the 17th century sense.

Mathematical explanations can be so vast, they make worlds. Provisonally.

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Dissagreable Me,

You said:

I personally would not say so. I would say there is a logical relation. The physical events of the world are sufficient to give a causal explanation for the mathematician’s actions, but there is a certain logical or structural similarity between the world and the Form. I don’t think most modern Platonists conceive of themselves as directly perceiving Forms with some kind of mathematical sense.

> I heard a podcast with Cedric Vilani who said he believes that he is discovering what is there, not inventing.

Sounds about right to me.

My question was not the causation of the mathematician’s actions but the relation between the mathematician and the Form. How is the mathematical Form discovered, per Vilani, if there is no causal connection? If the Forms are really there, as the mathematical Platonists claim, and they are discovering them or in some way ascertaining “a certain logical or structural similarity between the world and the Form” as you claim, how is this similarity percieved?

Roger Penrose, Cedric Vilani and Kurt Godel are all on record saying that their job is in some way capturing what is already there and expressing it. I have read that the majority of mathematicians are Platonists, though they only admit that reluctantly. Hence my interest in the question.

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it seems that can view things differently on these issues depending on which “type” of mathematics one holds to be the case. (I think of the three,

mathematical materialismis the best approach.)On mathematical platonism, intuitionism, materialism:

Platonism and intuitionism are allied in the respect that both views are implicitly opposed to thematerialistic accounts of mathematics which take the subject matter of mathematics to consist (in a direct way) of material objects.Perhaps it is for this reason that platonism is sometimes called “objective idealism” and intuitionism is sometimes called “subjective idealism”. Both views hold that mathematical objects are “ideal” at least in the sense that they are not material. The platonist holds that the mathematical “ideals” do not depend on a mind for their existence, the intuitionist that they do.(pg. 1)

Intensional Mathematics

– http://books.google.com/books?id=-53qNDMcz9UC

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It is the philosophers who have a problem with causality and mathematical abstraction, not the physicists. Physics built the $10B LHC to prove that the Higgs boson causes electrons to have mass. They also wanted to show that supersymmetry causes various other things, but there the conclusion seems to be that it is not the cause. (Maybe Coel would rather use the word “explanation”.)

Just look at our moderator. Someone mentions something having a purpose, and Massimo recoils in horror, as if a demon had just been summoned from the underworld.

Sure, Fermat’s Last Theorem is not causal. But the mathematics under discussion is the solving of differential equations modeling physical phenomena, and that is directly causal. The equations are not time-dependent, as equilibrium solutions are being sought, but you could phrase it as the long-time solutions of a time-dependent explicitly-causal system of equations. It answers the question of what is caused to happen if a wire-frame is dipped in liquid soap.

Pincock defines an abstract explanation as one using an “abstract entity that is appropriately linked to the phenomenon being explained.” Really? That would cover every explanation in physics, and in most other sciences as well. Then he says “the best, recent work on causal explanation is not able to naturally accommodate these abstract explanations.” So what can it accommodate? Is the best recent philosophy stuck on the level of Aristotle’s science?

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Massimo: {Tienzen, … I wonder if you could come down to earth a bit and speak in language that we mortals can actually understand.}

Thanks for the comment, as it help me a great deal.

Yes, the key is for mortals to understand, but the way of achieving this by removing all mortals out of the picture, let the Nature doing its DANCING, with its own CHOREOGRAPHY.

So, what is empirical to Nature? What is abstraction to Nature? What is a priori to Nature? Let’s get rid of all those nonsensical terms {empirical, abstraction, a priori, …, epistemology, methodology, understanding, …} from Nature’s choreography. So, if we mortals understand that choreography, it is great; if not, so what (Nature’s dancing continues). I do SEE Nature’s choreography as follow:

Nature has at least four dancing floors (domains): Physics, math, life, spiritual (intelligence and consciousness).

These four domains are SEPARATED with domain walls, and there is no reduction among domains as they are all arisen from the same source. Items in each domain are chain-linked (reduced), but these linkages stop at the domain wall (see https://scientiasalon.wordpress.com/2015/03/05/science-vs-scientism/comment-page-1/#comment-12621 and

https://scientiasalon.wordpress.com/2015/03/05/science-vs-scientism/comment-page-2/#comment-12648 ).

Physics domain (choreography):

C1, source of domain: initial condition (timelessness and immutability)

C2, step one, giving rise to arrow-of-time {with EQUATION consists of (64, 48)}

C3, step two, giving rise to nature constants (the Cabibbo and Weinberg angles, Alpha equation (locking three measuring rulers; e (electric charge), c (light speed), ħ (Planck constant), etc.} with EQUATIONS (not talking talks).

C4, step three, constructing quark/lepton structure, with LANGUAGE: in terms of space-time sheet}

C5, step four, giving rise to {spin (1/2)}

C6, step five, giving rise to {Force (dark energy) to derive (delta P x delta S > =ħ)} and {Planck data (dark energy = 69.2; dark matter = 25.8; and visible matter = 4.82)}

All those choreography steps are expressed with EQUATIONS (not talking talks).

I (one of the mortals) do understand these steps as:

{the Cabibbo and Weinberg angles, Alpha equation (locking three measuring rulers; e (electric charge), c (light speed), ħ (Planck constant)}

{quark/lepton structure}

{spin (1/2)}

{(delta P x delta S > =ħ)}

{Planck data (dark energy = 69.2; dark matter = 25.8; and visible matter = 4.82)}

are mortal physics, all empirically known. The equations which derive them are not talking talks and can be evaluated precisely with human (Earthly) mathematics. No, no heavenly language nor mystical math is used in those calculations.

The above is the choreography steps (a chain-linked steps) of Nature, no epistemology involved. Now, we can do our epistemological dance on them with (empirical, abstraction, a priori, …).

By understanding one domain, we can understand all domains.

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Hi

Occam’s beardI count myself a Platonist, and as far as I know my views are not that different from those of Villani et al, but I can speak only for myself.

Mathematical forms are perceived just as nominalists or other non-realists would say they are perceived. We observe structures in the world and we extrapolate and extrapolate on the extrapolations to discover a vast landscape of possibilities, but only an infinitesimal fraction of those which exist.

Everything mathematicians do (which includes announcing new discoveries) can be explained in terms of physical events and interactions in the physical world. The actual existence of the mathematical objects has no causal effects. We say they exist not because this resolves some empirical puzzle (such as the “unreasonable effectiveness of mathematics” in physics) but because it feels intuitively right for a number of reasons and because it solves a number of philosophical problems:

1) We are not really free to invent mathematical objects without constraint. There are only 5 possible Platonic solids and nobody is free to create a 6th. Psychologically it feels like we are dealing with matters of fact rather than fiction.

2) If the verb “to be” is interpreted as interpreted as somewhat synonymous with “to exist”, it’s clear that we find it intuitive to talk of mathematical objects as if they exist. “There are two solutions to this equation”. “There is no greatest prime number”, etc. Platonism takes this intuition and this language at face value without the need for a more complex account of what is actually being said.

3) An intuitive tenet of mathematical Platonism is that any two abstract structures which are identical are the same structure. So, if I conceive of an abstraction and you independently conceive of an identical abstraction, we are both thinking of the same object. There is some sense in which the object I am thinking of is not simply identical with the state of my particular brain.

4) To continue, since we operated independently with similar psychological experiences, and since the same object cannot be created for the first time twice, it feels wrong to say that one of us was the creator and the other merely discovered the other’s creation. If mathematical objects exist, they must do so independently of mathematicians.

Platonism is not in any way mystical or mysterious. It is just an attitude with respect to what we should deem to exist, and so can be regarded as a particular way of defining the concept of “existence”. When I say “there are 5 platonic solids”, I am saying quite the same kind of thing as “There are 2 surviving members of the Beatles”. The latter is a statement about the physical state of our world, the former is not, nor is it a statement about the physical state of some other world. Mathematical objects don’t exist in a world, they just exist, outside of space and time (for certain values of “exist”, anyway!).

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Correction,In the above, I meant to say ” I am

NOTsaying quite the same kind of thing as “There are 2 surviving members of the Beatles”.LikeLike

Tienzen, seriously, and this goes for others as well. While I usually filter comments only based on rudeness, I am seriously considering beginning to filter them for opaqueness and/or downright lack of sense. Too many people here seems to think that it is okay to just write stuff that either is incomprehensible (assuming that it actually would make sense otherwise) or has nothing whatsoever to do withe topic under discussion.

You are certainly not the only culprit, but I am taking this opportunity to issue a general warning: I’m investing far too much time and energy into this site to see the quality of the discussion dragged down by crank, irrelevant or meandering and repetitive comments. If this keeps going unchecked, it will turn off both academics potentially interested in contributing to Scientia Salon and serious readers.

So, everyone, please consider this your warning shot…

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HI Massimo,

You are in a better position to know than I am, so I accept that.

In any case I seem to detect a contradiction in Marko’s statement. On the one hand he is saying that philosophers are obsessed with causality and on the other hand he is saying that they are tied to a naive view of the concept, which would imply an unexamined view.

I also note that he and Coel seem to have diametrically opposite about how physicists view causality.

Marko:

Coel:

Sounds like a job for a philosopher 🙂

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I should also note that I am being somewhat unfair to

Coelin quoting the above while leaving off his next paragraph where he says it may be a matter of semantics.But then again if it is just a matter of semantics whether or not something is causal, and if causality is to be used as a criterion for existence then it may also be a matter of semantics whether or not abstract objects (like mathematical objects) exist or not.

My thinking has always been coloured by Carnap’s essay on the subject Empiricism, Semantics, and Ontology

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I’m curious. In physics there’s a “principle of least action” that allows one to derive equations of motion (Lagrangian and Hamiltonian formulations of classical mechanics) and the laws of (classical) optics. How would Pincock classify a principle of least action? Abstract, casual, empirical?

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DM rolls out the distinction between mathematics (5 Platonic Solids) and physics (number of Beatles).

The idea is one is demonstrated, the second is observed. However, more refined… observations show this to be rather a matter of semantics.

Indeed the proofs of the 5 Platonic solids depend upon the space in which the demonstration is made to be flat. Thus an axiom is crucial. Some will say: oh, it is just one axiom. Yet, if one digs further, one finds more crucial axioms.

When I pointed out in the past that Euclid depended upon axioms he had not made explicit (such as circles intersecting), Massimo was amused. I was glad to lift the mood.

But it goes beyond amusement. Much mathematics is just based upon observations, like physics (see the Platonic Solids).

So what is the difference between mathematics and physics? Well, mathematics makes up some of its “observations”. Call them axioms.

It turned out that often, later, or simultaneously, mathematics, or physics, fed on the other (see for example Connection Theory by the geometer Levi-Civitta and al., while Einstein, Hilbert and others were trying to write down General Relativity).

This is where the “unreasonable efficiency of mathematics” (Wigner) comes from. Elie Cartan, who invented (or discovered, take your pick) Spinor Theory was extremely aware of the attempt (launched in 1866 by Riemann) of using spaces to explain forces. Cartan developed it before WWI, and collaborated with Einstein afterwards. Dirac made the physical breakthrough with his electron theory (QED).

This is why I do not swallow that Minimal Surface theory is an “abstract explanation. Abstract explanations involve an appeal to a more abstract entity than the state of affairs being explained.”

Suppose a puma bites a neck, causing death. Simple enough. Suppose a medical examiner explains the carnivore’s canines went between some the 2th and 3rd vertebrae. Is that more abstract?

The point is that, to understand Plateau’s observations one needs the math of minimal surfaces. And no less than that.

Pincock: “it remains unclear how to unify abstract and causal explanations as instances of a single sort of thing…”

Unify abstract and causal explanations? It is extremely simple: just go back to Euclid. The model there is axioms, and then demonstrations. Same as physics. OK, biology does not work that way, and is closer to cooking. With tasty recipes.

I do not seem why this would be controversial. Observations that are crucial are axioms one needs.

The demonstrations are the causal chains.

Although I approved of Schlafy’s second comment, I grievously fail to see the difference of nature between (101 = 100 + 1) and Fermat’s Theorem. Such a difference could only happen if the latter was false! In my unifying SEMANTICS, both statements are “causal”.

Tu quoque? Why not?

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Massimo,Right, I was confused, sorry for the noise. 🙂

I seem to have a systematic problem with that, since I remember you already telling me this once before. If it isn’t too big of a problem, would you invite some philosopher to write an essay about why causality is fundamental in philosophy, and have them promise to participate in the subsequent discussion? I’d really like to have some questions answered regarding this.

I am sorry if my words came across that way. I certainly did not mean to sound condescending or such. Rather, I am genuinely puzzled by philosophers perception of causality. I really fail to see any other explanation, aside from imagining that philosopers think solely in terms of Newtonian mechanics.

Ok, this can be tested. Pick your favourite physicist, and ask them the following two questions: what is the cause of the spontaneous emission of a photon by an atom? Moreover, what are the causes for the values of phase and direction of the outgoing photon, once it has been emitted?

The relevant background about this is nicely summarized here and here.

I’d like to know what they will answer. Note, this is not an example of radioactive decay (contentious because we don’t really know all of QCD), is not an example of double slit experiment (contentious because of various interpretations of QM), or otherwise. This is just quantum electrodynamics of an atom, something that everyone should agree is very well understood by physicists and completely uncontroversial (story of QED agreeing with experiments to 10 decimal places, etc…). I am honestly curious — how would any physicist (embracing causality as fundamental) answer the above questions?

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Schlafly,

“Is the best recent philosophy stuck on the level of Aristotle’s science?”

It’s funny, perhaps you think this is because you, as a scientist, are stuck on the level of Aristotle’s philosophy.

I think you are a scientist, but even if not, my point applies.

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Joe,The stuff about controlling the variables in experiment measures the correlation between those variables. And as you and everyone else already know all too well, correlation does not imply causation.

At the fundamental level, determinism of *anything* is plain false. As a consequence, at the same fundamental level, causality (of anything) is really a mirage. That said, for a large number of physical systems, the lack of determinism may take a long time to manifest itself. In a way, due to our short-term timeframes of looking at Nature, we are fooled into thinking that determinism may hold for some systems. But it really holds only *approximately*. Ditto for causality — approximately, one can assign causes to effects in any system that appears deterministic. But such causality is not an intrinsic feature of Nature, it is an artefact of our approximation.

Brodix,Actually, of all people on the planet, the folks working on LHC are perhaps the most vividly aware of the lack of causality in Nature. Really, take a 10bn state-of-the-art piece of equipment, use it to do the same thing (smash two protons) every single time, and observe something *different* happen, every single time. And all they essentially do is to count the number of appearances of this or that outcome. And the only thing they can talk about is the *probability* that a collision of two protons would “cause” one outcome or another.

When it comes to observing lack of causality in Nature, really, it’s hard to get any more hands-on than that.

DM,Just a note — there are only 5 possible Platonic solids, but only

given certain assumptions(axioms of Euclidean geometry, axioms of set theory, axioms of predicate calculus). If we choose not to uphold some of these assumptions, all bets are off. Maybe there can be 8 Platonic solids, maybe none. So the existence of exactly 5 solids is not that much a matter of fact, but rather a matter of agreement about underlying assumptions. Btw, this is the reason why I’m not a Platonist. 🙂Robin,Umm, so where is the contradiction in there?

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schlafly

I wouldn’t assume philosophers distrust math. I wouldn’t assume anything about philosophers in general from a single paper.

There are old debates between rationalism and empiricism.

http://plato.stanford.edu/entries/rationalism-empiricism/

And see the current debate outlined in the last couple of articles as going along a similar line. Not the same line but similar.

When you look at what you are doing and what assumptions you make when doing science you are doing philosophy. You shouldn’t be hard on philosophy or philosophers. It’s unnecessary. They are just interested in your reasons for or against their views.

Marko:

“And as you and everyone else already know all too well, correlation does not imply causation.”

Sure but it might *suggest* causation. I am not sure why we would deny causation is possible. I think we may be thinking on different terms. I agree with Massimo that causation is an interesting topic, in law, philosophy and science. But I am not convinced it’s wrong to say the car hitting my mother’s leg caused it to break. Perhaps I am not familiar with the issues you have with causation.

Robin:

“Mainstream philosophers have regarded ‘causality’ as being nothing more than a manner of speaking since Hume pointed out the problem with the concept.”

I am not sure which problem you are referring to – there are a few. But on the whole I can say that although his arguments undermined my confidence in my beliefs about causation and science, I do not think he made a convincing proof causation can not possibly exist.

BTW when I say causation or morality exists I don’t mean it exists as a physical object. Just like I don’t think think “tallness” is a physical object yet i think some people really are taller than others. I just mean it’s a real feature of the world.

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The essay, although I think well written, is actually rather difficult, because it presumes familiarity with both the topic and the literature, and I am still groping my way through it.

I’m a little surprised, and a little annoyed, that many commenters here have pretty much missed the yin to the yang of the essay, so to speak. The essay’s primary concern is with *explanation*. So why does it wrestle with ‘causation’? Because unfortunately, one cannot engage in explanation without deploying causal language – as I have just done. Description: “An essay about explanation concerns itself with causation.” Cause: “Discussing explanation requires causal language” – together these form an explanation of why the essay discusses explanation and concerns itself with the issue of causation. QED.

‘The cue-ball rolls until it apparently touches the 8-ball. The 8-ball then begins to roll.’ That is merely description of a witnessed event. ‘The roll of the cue ball conveys force to the 8-ball; the 8-ball begins rolling;’ is a higher level description assuming the unseen (but possibly measurable). ‘The 8-ball begins rolling *because* the cue ball conveyed force to it on impact’ is an explanation. And possibly useful if one is going to teach elementary physics, or debate with some mystic who argues its all done by magic.

In the previous discussion on the Unger/Smolin review, pete1187 wrote a sentence, I so objected to, I cut it down mid-way:

“’If there is a mathematical Lie Group(s) that is/are found to govern the interactions of fundamental particles (…).’”

“No. Mathematical formulas only govern the human practice of mathematics (…).”

– That’s because, if the conditional clause were allowed to stand, it could be asserted positively as a causal explanation: ‘Fundamental particles interact as they do *because* they are governed by Lie Group relationships,’ – which couldn’t possibly be right, IMHO, since fundamental particles are oblivious to our mathematical descriptions of their behavior.

Richard Feynman, in a lecture, noted that Newton’s theory of gravity actually reduces to a formula describing the behavior of masses in interaction; the ‘why’ of the matter is inconsequential. True enough; but it is really the ‘why’ of the matter that people expect from science. That ‘masses tend to attract’ forms part of the explanation of (for instance) ‘why the earth revolves around the sun’ – this is what people accept as the scientific explanation of macro-level astronomy.

That is the clue to the stakes here – *it is explanation, not description, that constitutes (what most people understand as) knowledge*.

As a Pragmatist, if scientific theory works, then it doesn’t matter if the objects are real; the relationships are probably more important anyway, since these tend to be dynamic and produce results. My suspicion is that all explanations are fictive. But the reason I am not an extreme relativist is because I think it absolutely necessary that we accept the truth of our (best) explanations; if they have fictive natures, this will be revealed as we develop stronger explanations.

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Marko, you seem to think that a physical event is not causal if there is a mathematical formulation using probabilities. I assure you that if you shoot someone with a gun, and get charged with causing his death, it will do you no good to argue that the bullet only had a probability of hitting him.

You also deny the 5 Platonic solids. A proper statement of the 5 Platonic solids involves Euclidean space, but there are no dubious assumption. You are just denying mathematics, as well as physics.

The QED explanation of spontaneous emission is as causal as a bat hitting a baseball. The cause is the initial state (wavefunction of election, electric field) and the dynamics (time evolution equations). What’s the problem? It is true that there is some uncertainty about the wave function for a particular atom, and you could say that we only have a probabilistic explanation. But you could say that about the baseball batter, who might have a probability of hitting the ball of only .300.

You say “whereas in physics it [causality] is merely an emergent property of (approximate) deterministic dynamics”. This is not true. I doubt that you can find one physics textbook saying this.

I also doubt that you will find many LHC workers declaring a “lack of causality in Nature”. When it smashes protons, they aren’t necessarily in the same state, so it is not doing the exact same thing over and over. When I use my gun to shoot 6 shots at a target, I get 6 different holes. Would you use that to deny that the gun can be used for causal purposes? I doubt it.

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Hi

Marko,I agree with you that at the low level there seems to be non-determinism and non-caused events. Bell’s inequality even rules out full local causation.

But, I’m puzzled, since this is the same Marko who wants to explain the second law of thermodynamics, as it operates in the universe today, in terms of the tightly specified microstate of the Big Bang 14 billion years ago, and hence make it a big mystery.

And yet, all this ongoing probabilistic non-deterministic dice throwing will, over time, completely scramble the microstate and make it irrelevant. The probabilistic dice-throwing is in itself entirely adequate to explain the 2nd law (= things head towards more probable states), and so explain the arrow of time in the mid-level laws.

Anyway, that was a previous thread. But I’ll make a request to

Massimofor an article that deals with both determinism/causality and arrow-of-time in the same article, to see if it produces a quantum superposition of both Markos! 🙂While I fully agree about the role of non-deterministic non-causality, I think you’re going way too far in throwing it out entirely and making it purely an artifact. There is no way we could predict a solar eclipse twenty years in advance to one-second accuracy, except in a world with a very high degree of causality and determinism.

The lesson surely has to be that both causality/determinism and non-causality/non-determinism are fundamental features of our world. “What happens next” seems to result from deterministic dynamical laws and probabilistic non-determinacy entwined together.

For example:

Yes, there is probabilistic non-determinacy there. But there is also causation. Why bother spending 10 billion on the smashing together of the two protons if that had no effect on the outcome? Why not just watch the same events happening uncaused in your own lab? (Answer: because they don’t, because causation is also part of it.)

Hi

Massimo,As I noted to

schlafly, we may be differing only in semantics. A high-level description such as “momentum is conserved” is indeed the product of causal events, and so it is indeed “about” causality, but it is not stated in terms of causality if the explanation is in terms of a high-level abstraction (“conservation of momentum”) that is not in itself a causal entity.It is surely for nature to tell us (science) how things are. If it is indeed the case that some low-level quantum events have no cause (= are not determined by the prior state of the system) then it is science’s job to report that.

We shouldn’t impose our preconceptions on this. Thus, adopting a Humean hat and a radical scientismistic hat, absolutely everything in the Quinean-web is up for revision. Even notions such as “events have causes” and modus ponens are tested by, and adopted to, the extent that they model the world, and thus are ultimately empirical.

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I note this: ‘Disagreements arise concerning what a cause is and how the explanatorily relevant causes are to be identified.’

If disagreements arise concerning what a cause is, then you are just playing with words.

‘If this claim is accepted, then we can have as many kinds of explanation as there are dependence relations.’

How many kinds of dependence relations are there? Actually, scratch that. How many kinds of ‘relation’ are there, if one of them is taken to be ’cause’.

This is quoted with approval, as ‘how Koslicki concludes her recent paper “Varieties of Ontological Dependence”’:

an explanation, when successful, captures or represents (. . . ) an

underlying real-world relation of dependence of some sort which

obtains among the phenomena cited in the explanation in question

. . . If this connection between explanation and dependence

generalizes, then we would expect relations of ontological dependence

to give rise to explanations within the realm of ontology,

in the sense that a successful ontological explanation captures or

gives expression to an underlying real-world relation of ontological

dependence of some sort.

Now, if we take a step back, here, and reflect on what we supposedly think we are doing, coming up w/a cure for cancer? I think the answer to that question is ‘playing with words’.

I don’t think there is any such thing as an ‘underlying real-world relation of ontological dependence of some sort’. Is it bigger than a bread box? I can allow that there is any such thing as a ‘relation’, but, where, exactly, is it that we find relations? Heck, A is A is a relation. Not, you may say, a ‘real world relation’, but there is no such thing as a ‘real world relation’. Now, maybe ’cause’ seems like a ‘real world relation’, but I say that ’cause’ is only as real as ‘substance’. Think, here, of the ink that has been spilled on substance, Aristotle and Descartes & etc. Substance, just for starters, is something permanent. Does something permanent actually exist? If you can say ‘yes’ to this, then we may return to the matter of how it is that ’cause’ exists (‘something not permanent’).

Indeed I’m perturbed to the point of distraction that this connection between cause and substance (as opposites) that is so clear in early modern philosophy has been lost. Talk about reinventing the wheel.

‘One variety of ontological dependence that Koslicki isolates is what she calls

constituent dependence (Koslicki [2012], p. 205). For example, for lightning

to occur is just for energy to be discharged by some electrons in a certain way,

and when lightning occurs, these electrons are constituents of the lightning.’

Is this really saying something? Let me rephrase: ‘for energy to be discharged by some electrons in a certain way’ is just for lightning to occur. Oh, that’s what he meant? Then I suppose, that the lightning is a constituent of these electrons? You’re welcome.

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Patrice Ayme: “So nature is probably a computer. Mostly a local computer, somewhat entangled beyond the horizon. And a non-programmable, not fully knowable, Quantum computer. Something not causal in the 17th century sense.”

Programming languages (domain-specific) for natural systems is one of my interests. There are a bunch of them for quantum systems (of different types) now. There are some languages now for biological systems [1,2]. Here programs ultimately would be compiled to actual molecular assemblies that go out and actually live and interact with other molecules and living things in the world and not just run as animations changing pixel colors and making heat inside my MacBook.

(Those who say programs aren’t “causal” are just wrong.)

[1] BioCoder

– http://oreilly.com/biocoder/

[2] Biological Computation

– http://research.microsoft.com/en-us/groups/biology/

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Hi

Patrice Ayme,Marko,You point out that changing the axioms might lead us to different numbers of Platonic solids, and imply that this undermines Platonism. According to you, t’s not a fact that there are 5 Platonic solids after all.

However, from a Platonist perspective, “Platonic solid” is usually taken to mean a Platonic solid in the context of Euclidean geometry with the usual axioms. Pseudoplatonic solids in other geometries also exist and there are facts about them too, but these are not true Platonic solids. The fact remains that there are only 5 Platonic solids in Euclidean geometry.

To be clear, Platonic solids are no more real or important than these other solids. They are only distinguished by being more familiar to us.

> So the existence of exactly 5 solids is not that much a matter of fact, but rather a matter of agreement about underlying assumptions.

My view is that axioms are not so much assumptions as stipulations — they are neither objectively true nor false but form part of the definition of a mathematical object. Any mathematical system which changes the axioms is equally valid from my point of view (although not necessarily equally useful or interesting), with the caveat that changing the axioms changes the topic of our discussion. For example, if we change the axioms concerning logical AND so that “A AND NOT A” is true, we are in fact no longer talking about AND but about something else (and if we change the axioms concerning Platonic solids we are no longer talking about Platonic solids).

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Marko,

“take a 10bn state-of-the-art piece of equipment, use it to do the same thing (smash two protons) every single time, and observe something *different* happen, every single time. And all they essentially do is to count the number of appearances of this or that outcome. And the only thing they can talk about is the *probability* that a collision of two protons would “cause” one outcome or another.

When it comes to observing lack of causality in Nature, really, it’s hard to get any more hands-on than that.”

This illustrates the point I keep trying to make, that when we think of time as that narrative vector from past to future, with the present as some dimensionless point seeming to move along it, then the issue of moving from a determined state to an indeterminate state is an issue of probabilities. Now what does determine a particular outcome, if not the very physical action of smashing those protons together? It is not what the operators “talk about,” but what they are physically doing. It is the protons smashing together which is the physical cause of the outcome. Causality yields determination. Future becomes past.

We have to learn to distinguish our perceptions, what we count and talk about, from what is happening.

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There’s been quite a bit of to-ing and fro-ing regarding causality in this and other threads. I’m reminded of a comment attributed to Carl Sagan along the lines of “to bake an apple pie, you first create your universe…”. This example of the universal connectedness of things has obvious implications for our understanding of causality. The existence of any entity is dependent upon the state of the entire universe, its past, and for completeness, its future too. We are usually satisfied, for all practical purposes, with identifying more proximate (and more approximate) causes. But all “causes”, even the apparently cut-and-dried Newtonian variety, are therefore the necessary, but not necessarily sufficient (or, given indeterminism, never sufficient), antecedents of their effects. Or so it seems to me, but obviously not to others.

I would find it very useful if Massimo or another professional could find the time to do a series of short “basics of…” pieces aimed at clarifying or at least concisely exploring the usage of such terms as “causality”. Any attempt to do so might end up as an effort to find out how many definitions can be inscribed on the head of a pin, but it might be worth it.

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Marko, DM, Philip, etc: It seems that an agreement is actually surfacing that axioms are “causative”. Causes, after all, are in the head, just as axioms. Both materialize neurologically.

Axioms are how human beings explain and describe the world. That the “son of god” made it so that the world is supported by turtles all the way down, and all other religious inventions out there, are axioms.

Mathematical axioms have been changed, as needed. Say to invent algebra, algebraic geometry, calculus, complex numbers, analysis, differential geometry.

This happened all the way to the Twentieth Century: the Axiom of Choice allows to construct most of modern mathematical objects (I am against AC, BTW)

Axioms correspond to the simplest neurological structures, centered on axons: if such a neuron fires, other down the axonal chain, in turn react. Local linear logic, in other words.

By the way, Plato blossomed nearly a century before Euclid. We know, from the six passages in Aristotle (in Ethics…) that, at the time, NON-Euclidean geometry was fully considered (the sum of the angles of a triangle could be 180 degrees, or more, or less, Aristotle expressly points out). So indeed, Plato and company knew very well that “Platonic Solids” were implicitly found only in a particular geometry, the flat one.

Whenever, wherever we try to explain, or even describe, anything, there are axioms. They are more or less explicit. Archimedes’ axiom, an axiom in Model Theory, was ignored for 23 centuries, until it dawned around 1950, that, by violating it, one made sense of what Leibnitz tried to do with his infinitesimals.

There are even emotional axioms. They have an impact even in science.

An example was the hostility against genetics depending upon the environment, which reached great heights in the 1960s.

Examples? Anything remotely related to Lamarckism was viewed as grossly irrational; the rise of epigenetics is changing the mood completely.

Moods can be axiomatic: for example, viewing “Islamophobia” as racism (whereas Christianophobia has rolled all over Europe for centuries now, thanks god).

Buridan was fully aware that the denial of “Newton’s First Law” by Aristotle was the greatest obstacle to the heliocentric theory. So he corrected that by discovering and stating said law of inertia (three centuries before Newton’s birth). That law was, and is, an axiom.

Mach wanted to explain where that axiom came from. Einstein followed his lead (and also mostly failed).

The little exchange between Marko and Schlafy about the LHC was right on both sides. Sort of. LHC scientists have to sort out among billions of significant events, hence the super-giant teams with 3,000 PhDs working on just one experiment.

More amusingly the very definition of an elementary particle is, basically, a more pronounced hump in some curves depicting energy. Thus many debates about what it all means.

In High Energy Physics all ways to guess evidence and explanation are used.

It is also pretty much the case in modern biology, where new experiments are all too often irreproducible.

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‘We have to learn to distinguish our perceptions, what we count and talk about, from what is happening.’

I’m not sure I grasp the thought. I’m wondering, do we also have to learn to distinguish what is happening in our perceptions of what is happening, from our perceptions, and in turn from what is happining?

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It seems to me that causal explanations are just a special kind of logical explanations; that is physical causality is a special case of logical causality. Just as a logical consequence is derived (deduced) from premises so is a physical consequence derived from premises, which are, in the physical case, some initial conditions (called “causes” or “factors”) and some time-invariant feature of reality (called “laws”), in the context of the arrow of time. The “laws” transcend particular moments of time, so in this sense they are abstract entities and a causal explanation involves appeal to abstract entities.

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Hi DM,

I agree with you that the Euclidean space forms part of the definition of a Platonic solid, so it makes no sense to say that there may be more Platonic solids because analogous constructs in non-Euclidean spaces might number more or less than 5.

On the other hand I would not say that this necessarily leads to a Platonic view about mathematics, (nor does it necessarily lead to a non Platonic view).

Hi Patrice,

Buridan and his pupils were not really moving towards heliocentrism so much as as away from geocentrism. Following Buridan, Albert of Saxony and Oresme, the popular non-Aristotelean view in the Middle Ages seems to have been that the universe was infinite and therefore it had no centre as such, other than the apparent centre to observers on any particular world.

Hi Marko,

A naive view implies, as I said, an unexamined view. A philosophical interest would imply an examined view. So you appear to be saying that they are obsessively examining their unexamined view, which is a contradiction.

In any case, why should you assume that philosophers who wish to examine the idea should do because they have a “naive” view? Didn’t it occur to you to test that assumption? I alluded to Hume before who said:

He goes on to point out that the various versions of the concept of causality are just such cases.

If a naive view of causality survived Hume then I doubt it weathered Russell:

A modern philosopher examining the notion of cause who is worth his or her salt would certainly have the views of Hume, Russell and many more under his or her belt so I am pretty sure that there are no serious philosophers entertaining a naive view of causality.

I think that the discussion in this thread alone shows that it is a notion not entirely unworthy of examination.

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Coel:

“It is surely for nature to tell us (science) how things are. If it is indeed the case that some low-level quantum events have no cause (= are not determined by the prior state of the system) then it is science’s job to report that.

We shouldn’t impose our preconceptions on this. Thus, adopting a Humean hat and a radical scientismistic hat, absolutely everything in the Quinean-web is up for revision. Even notions such as “events have causes” and modus ponens are tested by, and adopted to, the extent that they model the world, and thus are ultimately empirical.”

I go along with this util you start saying modus ponens is tested. I can not imagine any empirical data that would make me reject modus ponens. It seems to me that when people make such claims they are becoming incoherent.

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‘If a naive view of causality survived Hume then I doubt ..’

Well, it didn’t.

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