Sunday 21 August 2022

Professor Donald Hoffman’s Idealist Take on Brains and Volleyballs

Donald Hoffman states that when it comes to a brain or a volleyball, “if you don’t look, it’s not there”. He also believes that “a volleyball no more has a position or momentum when it’s not observed than does an electron”. All this is basically a 21st-century update of Bishop Berkeley’s 18th-century idealism (as Hoffman more or less admits in various places).

[P]articles are vibrations not of strings but of interacting conscious agents.”

Professor Donald Hoffman

It’s worth putting Professor Donald Hoffman’s position on volleyballs and brains in its larger context.

Firstly, Hoffman isn’t modest about his “interface theory of perception” (more broadly and philosophically, his idealism). For example, he states that

[i]t consumes decrepit ontology, preserves methodological naturalism, and inspires exploration for a new ontology”.

Hoffman also compares what he’s doing to what Alan Turing did (see here). What’s more, Hoffman believes that his idealism (or what he calls conscious realism) is a

“vehicle sufficiently robust to sustain the next leg of our search for a theory of everything”.

Now it may not be altogether clear to all readers (from that short quote alone) whether or not Hoffman actually believes that his own idealist philosophy will be that “theory of everything”. Alternatively, is Hoffman simply (or only) claiming that his idealism could be (or actually is) a “vehicle” of such a grand enterprise?

That said, it can easily be shown that the former option is far more likely.

That’s the case because in Hoffman’s philosophy, consciousness must ground any theory of everything. (That will include any theory which will be offered in the future by high-ranking theoretical physicists and/or cosmologists.) After all, Hoffman has explicitly argued that his idealism will “boot up space, time and matter” as well as literally everything else.

The clincher, however, can be found in Hoffman’s following words:

“Spacetime is doomed. It, and its particles, cannot be fundamental in physical theory, but must emerge from a more fundamental theory.”

Hoffman believes that this “more fundamental theory” is, of course, his very own conscious realism — aka, his “scientific” idealism.

Hoffman on Brains

Donald Hoffman is an idealist (or conscious realist) who’s stated that “brains and neurons do not exist unperceived”. That isn’t a claim that our perceptions don’t (as Hoffman puts it elsewhere) “resemble” whatever it is that gives rise to them. It’s a straight claim that brains and neurons don’t exist when unperceived.

Hoffman was at his most Berkeleyan when he wrote this simple line about a brain:

“If you don’t look, it’s not there.”

Yet if you don’t look at what is defined as (to use Hoffman’s word) “phenomenal”, then of course it’s not there when no one is looking at it. That’s true by definition.

Here’s a definition of the word “phenomenon” (i.e., if only as used in philosophy and science):

“A phenomenon is an observable event. [] In modern philosophical use, the term phenomena has come to mean things as they are experienced through the senses and processed by the mind as distinct from things in and of themselves (noumena) [].”

In addition:

“In scientific usage, a phenomenon is any event that is observable, including the use of instrumentation to observe, record, or compile data.”

Hoffman doesn’t have much time for physicalism (or materialism), yet a physicalist and even a naïve realist can accept most — or even all — of the definitions above. (They may even accept Hoffman’s use of the word “phenomenal”.) That is, they will accept that a phenomenal brain is only there when someone is looking.

[Naive realism has just been mentioned. Hoffman seems to believe that all positions on “reality” which aren’t his own — or which aren’t idealist — are examples of naïve realism.]

However, such people will not also accept that that the physical brain is only there when someone is looking.

Of course Hoffman collapses this distinction — but at least it should be made clear.

Hoffman on Volleyballs

Hoffman makes his Berkeleyan position even clearer in the following passage:

“The phenomenal volleyball isn’t there when you don’t look, so it isn’t off-white or any other color. Nor is it round or soft or leathery.”

Then he immediately adds the following contemporary scientific gloss on his idealist position:

“The relational volleyball is circuits and software, and it isn’t literally off-white either. There may be portions of the software whose intent is to spray photons on your eyes such that you will construct an off-white phenomenal volleyball. But this software isn’t any color at all. And the color of the circuits is irrelevant to the color of the phenomenal volleyball[].”

Again, if even a physicalist can accept Hoffman’s term “phenomenal volleyball”, then what he wrote will be true by definition.

The reader will have noted Hoffman’s use of the words “circuits” and “software” in the passage above.

Hoffman often — very often — uses technical terms taken from the world of computers or from computer science. (One can even say that Hoffman is hooked on such technical terms.) So perhaps it’s the case that these technical terms from computer science tie Hoffman up in various philosophical knots.

Firstly, does Hoffman use such terms as “circuits”, “software”, “icons” and “interface” analogically or metaphorically?…

No; he doesn’t.

After all, when Hoffman writes “[t]he relational volleyball is [my italic] circuits and software”, that statement isn’t meant to be an analogy or a metaphor. Hoffman is arguing that the relational volleyball literally is circuits and software. (Note that Hoffman isn’t referring to a computer-generated image of a volleyball on a computer screen. He’s referring to a real volleyball which one can literally kick.)

So let’s take a specific example of Hoffman’s fixation on terms from computer science.

Hoffman often refers to the “icon interface on your computer” as a means to get his idealist point across about the icons in human consciousnesses.

Yet the icon interfaces of computers have all been designed by human persons to “guide” human users. No one has ever claimed — or even believed — that an icon of a trashcan is identical to — or even resembles — the “unseen circuits and software” found inside a computer.

So Hoffman’s position basically amounts to arguing that only x is x. (Or: Only x can be x.)

More accurately, the upshot of Hoffman’s argument is that only experience x can be like (or “resemble”) experience x. (This argument is taken directly from Bishop Berkley.) That is, only that which is phenomenal can also be phenomenal.

But who’s ever argued otherwise?

Another way of putting this is to say that a “phenomenon” is by definition something that only belong to minds or to conscious experiences. That’s essentially how that word was defined by Immanuel Kant some 240 years ago. More clearly, in Kant’s scheme we have phenomena and we also have a noumena. So obviously phenomena aren’t noumena.

But no one has ever claimed otherwise.

[Of course that’s if readers — and others — accept these Kantian terms and philosophical distinctions at all.]

This means that if a volleyball is entirely defined as a phenomenal volleyball, then by definition it can’t exist as a volleyball if no one is looking at it. Unless, here again, Hoffman simply means phenomenal volleyball by the single word “volleyball”. If Hoffman does mean that, then his claim is true by definition.

Hoffman then compares a “phenomenal volleyball” to an electron.

Hoffman Compares a Volleyball To An Electron

To give a flavour of where Hoffman is going with all this, it’s worth noting that Hoffman’s position on a volleyball must be — at least partly — a result of a position he expressed in the following (to be rhetorical for a moment) almost meaningless, jargon-infested passage:

“We show that one particular object, the quantum free particle, has a wave function that is identical in form to the harmonic functions that characterize the asymptotic dynamics of conscious agents; particles are vibrations not of strings but of interacting conscious agents.”

It’s also important to note here that Hoffman began using mathematics — or mathematical technical terms — on a large scale and as an seemingly essential part of his philosophy when he started working with the mathematician Chetan Prakash. And, from then on, Hoffman began using copious mathematical terms (i.e., in his idealist philosophy) as if they were round shapes being pushed into square holes.

In direct relevance to an electron, Hoffman writes:

“A volleyball no more has a position or momentum when it’s not observed than does an electron. Only in the act of observation do you construct a phenomenal volleyball with a position, motion, color, and shape. Similarly, only in the act of observation is an electron constructed with a position, or momentum, or other dynamical properties. All phenomena are constructed by observation, whether quantum phenomena or volleyball phenomena.”

There’s a severe problem with comparing a volleyball to an electron.

Even if we accept that a phenomenal volleyball is, well, a phenomenal volleyball, then Hoffman’s comparison to an electron is not at all accurate.

It’s true that a phenomenal volleyball needs to be perceived. However, arguably it still exists as a physical object when not perceived. Yet when it comes to an electron, the situation is very different indeed.

According to the Copenhagen interpretation (as well as most other interpretations) of quantum mechanics, nothing (much?) can be said about an electron when it’s not being indirectly observed or when it’s not part of an experimental setup. Indeed the experimental setup largely determines what the electron is taken to be (or what is said about it). This essentially mean that if an electron isn’t part of any experimental setup, then it isn’t really anything at all. (What is this electron that exists apart from an experimental setup and all indirect observations? Tell me something about it.)

On the other hand, much can be said about any given volleyball even when it isn’t being observed.

For a start, one can still know (or have a good guess) where it still is. One can also know that it must have the same shape, size and weight as it did when observed.

Of course all these properties can also be deemed to be phenomenal — at least on Hoffman’s Berkeleyan reading.

[Hoffman mentions and quotes Berkley’s idealist position favourably — see here and here. For example, he writes: “Resemblance between the phenomenal and relational realms: I argue that there need be no resemblance. But Berkeley has an ingenious argument that goes much further, and is probably valid.”]

But isn’t there still some x which is in a place and which has a given weight, shape and size?

In terms of the “off-white” colour mentioned by Hoffman, however, the volleyball may not have that colour when not observed. (Some will say that it does. Others will say that it doesn’t. Yet virtually no one offers idealist reasons for either position.) But should we go as far as Bishop Berkeley (1685–1753) and say the same things about location, weight, shape and size (see here)?

Hoffman does.

Now in order to make more sense of Hoffman’s position on brains and volleyballs, it will help to tackle his notion of an “arbitrary representation”.

Hoffman on Arbitrary Representations

One central point which Hoffman advances is that even though he accepts that we have (what he calls) “representations” of this volleyball, those representations need not — and indeed do not — resemble anything in the “objective world”. Or, more accurately, they don’t resemble whatever it is that (as it were) underpins this volleyball in what Hoffman calls “the relational realm”.

Hoffman himself writes:

“If ‘well adapted’ doesn’t mean ‘resembles,’ then what does it mean? It means a systematic but arbitrary relation. Our perceptual experiences are well adapted to the relational realm because they provide a systematic but arbitrary guide to those aspects of the relational realm that are critical to our needs and our survival — just as the icon interface on your computer is well adapted because it provides a systematic but arbitrary guide to the computer’s unseen circuits and software.”

Sense now has to be made of Hoffman’s word “arbitrary”.

[“Arbitrary” = df. “existing or coming about seemingly at random or by chance or as a capricious and unreasonable act of will”. Or: “arbitrary” = df. “not fixed by rules, but left to one’s judgment or choice; discretionary”.]

Even if the word “arbitrary” simply means could have been otherwise (or something similar), then it still seems to be too strong. That is, if the relational realm might have been represented (or whichever the correct word is) differently, then does that still automatically mean that all representations are arbitrary?

If Hoffman simply means (as discussed above) that that what is phenomenal can’t also be relational (by definition and an idea Hoffman takes from both Bishop Berkeley and Immanuel Kant), then, in that strict sense, x can’t be y. But simply because x can’t actually be y, then why does it follow that this relation (whatever it is) between x and y should also be arbitrary?

Take this loose comparison.

When I put a sandwich in the freezer, it freezes. The sandwich and the freezing process aren’t the same thing . However, the relation between the sandwich and the freezing process (in the freezer) certainly isn’t arbitrary.

Similarly, a phenomenal representation of something that isn’t itself a phenomenal representation needn’t be arbitrary simply because the representation and the represented aren’t one and the same thing.

In addition, there may be many reasons as to why the represented x is represented (in the way it is actually represented) by y. Those good reasons would still hold even though representation y isn’t the same thing as the represented x.

In terms of Hoffman’s example of a volleyball. There may be other reasons (other than what is conducive to survival) as to why members of the species homo sapiens represent this volleyball the way they do.

So Hoffman really gives the game away when he uses the word “resembles”. He writes:

“If ‘well adapted’ doesn’t mean ‘resembles,’ then what does it mean? It means a systematic but arbitrary relation.”

The words “systematic but arbitrary relation” can’t possibly mean well adapted. If a systematic but arbitrary relation is anything, then it’s a single characterisation of something that’s merely connected to being well adapted — it isn’t its meaning.

So we still need to why this supposedly arbitrary relation also leads to being well adapted (more of which later).

In addition, of course the word “resembles” doesn’t mean identical to. That is, if y resembles x, then that doesn’t also mean that y is identical to x.

However, Hoffman may be right to argue that the idea of resemblance doesn’t work at all in his case of some given x in the relational realm and its representation in the phenomenal realm. Indeed Kant and Kantians — long before Hoffman — have deemed the notion of any resemblance between anything noumenal and anything phenomenal to be confused.

Hoffman also makes much of successful adaptation not (always?) coming alongside what he calls “truthful perceptions”.

Perceptual Adaptation and Truth?

Hoffman writes:

“Our perceptual experiences are well adapted to the relational realm because they provide a systematic but arbitrary guide to those aspects of the relational realm that are critical to our needs and our survival.”

This question now needs to asked:

How are our perceptual experiences “well adapted” to the world at all?

How does that adaptation work without what Hoffman calls resemblance? It’s certainly the case that resemblance may not be required. However, we need to know how our perceptual experiences are well-adapted in ways which don’t involve “reality”, “truth”, “resemblance”, accuracy, etc. In other words, what is the precise relation between our perceptual experiences and Hoffman’s relational realm?

Hoffman only seems to answer that question negatively.

The argument is that the relation between our perceptual experiences and “reality” needn’t be — or actually isn’t — one of resemblance, truth, correspondence, accuracy, etc. Instead, Hoffman focusses on filtering out superfluous data in order to survive. Yet this hints at the idea that the perceptions or representations which are left (i.e., after the filterings) may still be of a non-idealist reality. Indeed doesn’t the very idea of filtering assume a non-idealist reality?

But, again, what is the precise relation?

Even if perceptual experience x doesn’t resemble y, then why does it have the character that it does have? Indeed what evolutionary role does perception x not resembling y have? (Again, Hoffman explains all this is terms of the evolutionary disadvantage of, basically, sensory overload.) And why does perception x have the character it does have in the first place?

Another way of putting all this is to argue that if our perceptual experiences are only (as Hoffman puts it) “critical to our needs and our survival”, then how and why are they so? That is, how is such survival brought about without any resemblance, correspondence, truth. accuracy or whatever?

So Hoffman tells us that all species don’t need truth when it comes to perception. But we are left in the dark as to what species do need. We can’t simply be happy with phrases like

“[p]erception guides adaptive behavior; it does not estimate a preexisting physical truth”

without also being informed as to why we have given perceptions and what their precise relation is to… what? Reality? The physical world. Hoffman’s (non-physical) relational realm?

Hoffman then writes:

“More information requires, in general, more time to obtain and process. But in the real world where predators are on the prowl and prey must be wary, the race is often to the swift. [] So natural selection tends to favor perceptual systems that, ceteris paribus, take less time. One way to take less time is, again, to see less truth, especially truth that is not informative about fitness.”

Interestingly, there’s an (implicit) acknowledgement of the (for want of better words) external world (i.e., something outside consciousness) in that passage. Indeed Hoffman’s phrase “less truth” implies some truth. That is, the truth that is left may well be conducive to survival — even if the complete truth isn’t. And surely that works against Hoffman’s idealism (or his conscious realism).

[See my ‘A Contradiction in Donald Hoffman’s (Idealist) Fitness-Beats-Truth Theorem’. This essay tackles Hoffman’ implicit acceptance of a non-idealist physical world.]

Hoffman seems to be aware of this counterargument when he quotes the psychologist James J. Gibson in the following manner (as expressed in Gibson’s ‘The Ecological Approach to Visual Perception’):

[I]n Gibson’s ecological theory of perception, our perceptions primarily resonate to ‘affordances,’ those aspects of the objective world that have important consequences for fitness [].”

Yet Hoffman believes that there are no affordances — at least not if they’re based on any “resemblances” to, truths about, accuracies in relation to, etc. what Hoffman calls the “objective world”. Alternatively put: perceptions can “resonate to affordances” without any need for resemblance, truth, accuracy, etc. In the idealist picture, then, affordances need have no relation at all to anything outside consciousness.

Yet despite his book title, rhetorical statements about “reality”, etc., Hoffman actually does believe in the objective world. It’s just that Hoffman’s objective world isn’t what he believes most people take it to be. (Hoffman nearly always takes his opponents to be naïve realists.) To Hoffman, objective reality is, in fact, an idealist reality.

In fact Hoffman repeatedly uses the term “objective reality” (which few contemporary philosophers and scientists use — at least not in their technical work) without ever really telling us what he means by that term. Here’s another example:

[T]he idea is that natural selection has not shaped our perceptions to be insights into the true structure and causal nature of objective reality, but has instead shaped our perceptions to be a species-specific user interface, fashioned to guide the behaviors that we need to survive and reproduce.”

This, again, is Hoffman acknowledging objective reality without telling us what he takes it to be. Perhaps that’s because if he did so, then his idealism would have to embrace something outside consciousness (or consciousnesses) and thus render it contradictory.

So how can an a idealist (or conscious realist) accept any objective reality at all? That is, how can any idealist accept an objective reality if that reality is meant to be something outside consciousness or consciousnesses?

Of course it may be that to Hoffman objective reality is his “relational reality” (which is very similar to Kant’s noumenal realm). But Hoffman hardly ever explicitly states that. And even if he did, then he would be using the term “objective reality” in a way that hardly any scientist, philosopher or layperson uses it. Hoffman may be very happy with that fact. And of course he’s free to use an old term in his own new way. Indeed since Objective Idealists and other idealists have used the term “objective reality” to refer to something that is an exclusive matter of consciousness, consciousnesses, Cosmic Consciousness, Geist or whatever, then that may actually be what Hoffman is doing.

Hoffman also tells us that the cognisance — or experience — of the (to use a philosophical phrase) Kantian manifold (or Hoffman’s “every bit of information”) has led to species-death. (How could this be known anyway?) Yet we aren’t told about the truth-remainder (which Hoffman implicitly accepts) and its relation to… what?

So here again it can be said that even though perceptual experiences can’t be identical to what they are experiences of, then that doesn’t also mean that they are arbitrary.

Hoffman goes into more detail when he writes that

[e]xperiences need not resemble the relational realm to be well adapted, they need only be a useful guide for behaviour”.

Why are such experiences “useful”? And useful in which respects?

One obvious riposte to Hoffman’s statement above is to argue that experiences of volleyballs, brains or anything else are a “useful guide for behaviour” precisely because they do “resemble”… something outside consciousness.

[The existence of a relational realm needn’t be accepted here. Bear in mind that the term “relational realm” is Hoffman’s own.]

So all anyone needs to argue is that his/her perceptions (or experiences) of a volleyball, a brain or anything else must have strong connections to things (whatever they are) outside consciousness — or things outside a collective of what Hoffman calls conscious agents.

Of course Hoffman, as an idealist, must reject that claim.

****************************

Note: See also my ‘A Contradiction in Donald Hoffman’s (Idealist) Fitness-Beats-Truth Theorem’, ‘Donald Hoffman’s Philosophy of Consciousness and Reality: Conscious Realism’ and ‘Donald Hoffman’s Long Jump From Evolutionary Biology/Theory to Highly-Speculative Philosophy’.




Monday 15 August 2022

A Platonist Take on the A Priori and the Analytic?

The philosopher Anthony Quinton expressed an “anti-conventionalist” (or Platonist) position on the analytic when he wrote: “There is a non-conventional identity of concepts which would still exist even if no means of expressing the concepts had ever been devised.”

Anthony Quinton (1925 — 2010) was a British philosopher. He was educated at Christ Church, Oxford University, where he obtained a first-class honours in Philosophy, Politics and Economics. He was President of Trinity College, Oxford from 1978 to 1987; and a chairman of the board of the British Library from 1985 to 1990. Quinton was also the president of the Aristotelian Society from 1975 to 1976.

Quinton once presented the BBC Radio programme, Round Britain Quiz.

Axioms

It’s often argued that axioms don’t need to be true. That is, axioms can — and do — have a purely formal or syntactic role. What follows from axioms, however, must do so according to strict logical rules. This basically means that different geometrical and mathematical systems can be — and are — constructed on axioms which needn’t be taken as being true. ( As a result of various findings in geometry, this largely came to be seen to be the case in the late 19th century.)

Of course all this depends on how the word “true” is taken.

Anthony Quinton (in his 1963 paper ‘The A Priori and the Analytic’) saw axioms very differently. He argued that

“axioms only confer truth on theorems if they are true themselves”.

So how is the truth of axioms established?

Generally speaking, axioms are seen as “assumptions”. Alternatively, it has been argued that axioms can be “taken to be true” — but only in order to (as it were) get the ball rolling. (Axioms have also been seen as being evident or even self-evident.)

It’s worth stressing here that the term “axiom” is defined differently when used in mathematics, logic, and, indeed, philosophy. In philosophy, an axiom has traditionally been seen to be a statement that’s evident or simply well-established. In modern logic, axioms aren’t treated this grandly. They’re simply seen as being the starting points for reasoning. In mathematics, axioms are often taken to be statements which are often taken to be true — but only within the logical systems they define or generate.

So the word “axiom”, in this case at least, needs to be seen within the context of Anthony Quinton’s discussion of the a priori and the analytic — both terms hardly used outside philosophy. Indeed the term “analytic” only became widely discussed in analytic philosophy in the1930s. (For example, with the logical positivists and others; though such philosophers did work on Gottlob Frege’s ideas — see here.)

According to Quinton, a “formally sufficient axiom will be materially adequate only if it is intuitive”. This means that an axiom’s truth is discovered (or seen) intuitively.

This reliance on intuition (see also here) here must also mean that there’s no other way to see (or discover) the truth of axioms precisely because they’re so basic. In other words, they can’t be shown to be true by other axioms, the world, evidence, data and certainly not by theorems.

Remember also that axioms are used as the starting-points of systems or chains of reasoning. This means that axioms can’t rely on anything else. And that must explain why Quinton believed that their truth is seen intuitively. His position has the consequence that there’s no alternative to that position.

Still, what is meant by truth here? How are axioms true at all?

Philosophers of mathematics have often asked if it’s even meaningful to state (or believe) that axioms are true. (See Penelope Maddy’s paper ‘Believing the Axioms’.)

For example, the French mathematician Henri Poincaré expressed what has been called a conventionalist view. Poincaré’s use of non-Euclidean geometries showed him that the axioms used in geometry should be chosen not for their truth, but for what they can produce. What’s more, axioms shouldn’t be chosen (at least not exclusively) for their (supposed) coherence with human intuitions about the world.

Does all this mean that axioms aren’t about — or derived from — the world at all? And, presumably, do this also means that axioms aren’t about — or derived from — other axioms or theorems either?

So, again, why are axioms deemed to be true? Why can’t they simply be taken syntactically or even as simple scribbles on a page?

Analytic Statements

Anthony Quinton tied the intuitive truth of axioms to the intuitive truth of analytic statements. He wrote:

According to the analytic thesis, an a priori truth is intuitive if its acceptance as true is a condition of understanding the terms it contains.”

To state the obvious: analytic statements are very unlike (simple) axioms. Most of the oft-quoted analytic statements (such as “All bachelors are unmarried”) contain predicates about — and references to — worldly items. Axioms are usually nothing like that. (Quinton himself gave no examples in his paper.)

It can of course be argued that we (as it were) see the truth of the statement “All bachelors are unmarried” intuitively. However, that only means that we understand the concepts or words involved and see that they are synonyms. Surely that can’t be said of individual axioms.

Indeed it’s tempting to think that analytic truths — along with tautologies — are pretty pointless if they really are only about words (or symbols) and their synonymy. Moreover, if they’re all about conventionality, synonymity or analyticity (see W.V.O Quine’s own ‘Two Dogmas of Empiricism’), then the world (or reality) seems to completely drop out of the picture. (Of course analytic truths — as written down, spoken or even thought about — must still be part of the physical world.)

All that said, Quinton did make a distinction between analytic sentences and the (as he put it) “propositions they express”.

Propositions

Quinton argued that

“the conventionality principle fails to distinguish sentences from the propositions they express”.

This is a clear commitment to abstract propositions. Or, at least for now, a commitment to propositions.

In other words, Quinton must have believed that it’s the words (or sentences) used in analytic statements which abide by the rules of convention. However, the “propositions they express have nothing at all to do with such rules.

So take the following sentence:

“All bachelors are unmarried men.”

Clearly, that’s a sentence because it occurs within quotation marks (among other things).

But we also have this:

All bachelors are unmarried men.

Is that a proposition?

It’s of course the case that the the (?) about bachelors directly above is again expressed by a sentence. However, when we take away the inverted commas, it (to put it ironically) suddenly becomes a proposition… Or does it? Isn’t proposition still expressed by a sentence even if the quotation marks have been taken away! And, without sentences (as well as minds), what purchase can we have on these supposedly abstract propositions?

Moreover, even if I write

The state of affairs of bachelors being unmarried men.

or more simply

Bachelors being unmarried.

they are still two sentences.

In any case, these linguistic expressions simply seem to be about facts or states of affairs (or the philosophers’ truth conditions). Yet propositions aren’t deemed to be worldly or concrete things. That is, propositions have often been seen (from Frege to Quinton) as being abstract entities which don’t belong to time and space and which have no causal relations with the world.

So how do human minds gain access to these abstract propositions?

Concepts

Quinton moved on from using propositions as an argument against mere conventionality (or mere analyticity) to arguing exactly the same thing about concepts.

(Wikipedia defines concepts as “abstract ideas”. Yet an abstract idea is an abstraction that needn’t itself be taken to be an abstract object.)

So now it’s concepts which are seen as being non-conventional and, therefore, abstract entities. (To be more accurate, Quinton was putting the position of what he called the “anti-conventionalist”.) Quinton wrote:

[T]he anti-conventionalist maintains that there is a non-conventional identity of concepts, lying behind the conventional synonymy of terms, which would still exist even if no means of expressing the concepts had ever been devised.”

It’s not really a surprise that anti-conventionalists (or Platonists) should move from propositions to concepts because, on Frege’s picture, senses are the non-spatial and non-temporal parts of non-spatial and non-temporal propositions. In Frege’s own words:

[T]houghts are neither things of the outer world nor ideas. A third realm must be recognized.”

To use Frege’s own terms, senses are (non-spatial) parts of what he called Thoughts. And both senses and Thoughts are “eternal” (see here). In that case, again, a sense (though not identical to a concept in Frege’s philosophy) is simply an abstract part of a larger abstract entity — a proposition.

[See Frege’s own ‘The Thought: A Logical Inquiry’, from 1918. Also bear in mind here that propositions and Thoughts aren’t deemed to be identical in Frege’s philosophy.]

Yet problems remain.

If we can’t make sense of abstract propositions, then perhaps we can’t make sense of abstract concepts (or even senses) either.

For one, it seems utterly bizarre that Quinton should have argued that the concepts (to use Quinton’s spatial metaphor) “behind” the terms “bachelor” and “unmarried man” are actually “timeless and objective”. Really? Perhaps it can provisionally be accepted that an abstract, timeless and objective number lies behind the symbol, say, “2”. However, can we really say the same about the concepts behind the words “bachelor” and “unmarried man”? Surely not.

For one, the words “bachelor” and “unmarried man” have only existed since the institution of marriage began. And therefore the concepts themselves (if expressed by different words in different languages) must have only begun to exist when the first words about (or even institutions of) marriage existed. So surely none of these things are timeless, atemporal or objective.

[It must be assumed here that Quinton used the word “objective” to refer to those words which had abstract objects — in this case, abstract concepts — as their referents.)

Perhaps it can be accepted that the concept [bachelor] is both objective and abstract. However, is it also timeless? That’s unless it’s believed — and it often is — that timelessness must necessarily always come along with being abstract and also with being objective. Yet if abstractness and objectivity do come along with timelessness, then the concept [bachelor] may not be abstract or objective either…

Conventionalism

In the philosophy of mathematics, and even in mathematics itself, a link was made — roughly from the 17th century to the 19th century — between the conventionality of mathematics and the fact that mathematical statements are true simply because they assert identities. (See here for the basic mathematical position on identities or equalities.) In other words, the identities of mathematical statements (according to Quinton’s conventionalists) follow from the fact that mathematics is about symbolic conventions — not truth. This was — very broadly speaking — the position advanced by David Hume (see here), Henri Poincaré (see here) and then Ludwig Wittgenstein in his Tractatus (see here). (See also ‘Tautology’.)

However, perhaps mathematical conventionality and identities don’t go together. Alternatively, perhaps conventionality and the importance of identities can both be rejected.

According to Quinton:

“Leibniz knew to much about mathematics to regard it as conventional.”

However, it seems that

“he did not know enough about it to realise that its propositions were not identities”.

So, according to Quinton, Leibniz believed that mathematical statements — indeed truths — were (mere?) identities. That is, he believed that both sides of the equality sign state the same thing — though in different ways.

This can be seen as a deflationary view of mathematics and it has been almost universally rejected. (The rejection largely set in the early 20th century; though perhaps before.)

Quinton even touches on Kant’s “synthetic a priori truths”.

If mathematical statements aren’t identities, then does that mean that they’re synthetic a priori truths? That is, truths that are neither mere identities nor determined by the meanings of the symbols on both sides of the equality symbol.

It is still argued that such truths too can be known a priori. However, that’s not because they’re identities or simply because both sides of the equation state the same thing. Yet such truths can still be known — according to Kant — without (further) experience.


Friday 12 August 2022

Physics is Pythagorean: A Case For Ontic Structural Realism

One Pythagorean position on physics is summed up by the ontic structural realists James Ladyman and Don Ross: “Mathematical entities such as sets and other structures are part of the physical world and not therefore mysterious abstract objects.”

This essay is primarily a commentary on the ‘Ontic Structural Realism and the Philosophy of Physics’ chapter of James Ladyman and Don Ross’s book Every Thing Must Go: Metaphysics Naturalized.

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The ontic structural realist philosophers James Ladyman and Don Ross have been classed — variously — as “neo-Pythagoreans” and “Platonists”.

If a philosopher were a neo-Pythagorean (i.e., rather than a Platonist), then such a philosopher may think that (to use Ladyman and Ross’s words)

“mathematical entities such as sets and other structures are part of the physical world and not therefore mysterious abstract objects”.

At least this position “suggest[s] a kind of Pythagoreanism” to Ladyman and Ross.

It must be said here that — on my reading at least — the fusing of mathematical entities with the physical world isn’t really Platonist. It’s not Platonist because Plato’s prime concern was the abstract and atemporal realm of numbers and other abstract objects (such as Forms, Ideas or universals); not abstract objects as they’re instantiated in the physical world.

What does sound very much like Ladyman and Ross’s position (as well as being partially Pythagorean) is the suggestion of

“abandoning the distinction between the abstract structures employed in models and the concrete structures that are the objects of physics”.

Ladyman and Ross go on to say that such “abstract structures employed in models” actually are the “objects of physics” (i.e., if such a distinction is indeed abandoned). In Ladyman and Ross’s case, we can say that abstract structures are the things of physics. In other words, the argument is that if we erase abstract structures from the picture of physics, then we have nothing left

However, does it follow that abstract structures are literally everything in physics?

Ladyman and Ross quote the Dutch philosopher Bas van Fraassen who stated that

“it is often not at all obvious whether a theoretical term refers to a concrete entity or a mathematical entity”.

Bas van Fraassen’s position would be agreed upon by many actual physicists — or at least by many quantum physicists. (One can read many physicists stating more or less the same thing as Bas van Fraassen.)

Ladyman and Ross then express a position which one would imagine critics have aimed at their own position. They argue that

“the fact that we only know the entities of physics in mathematical terms need not mean that they are actually mathematical entities”.

Now are Ladyman and Ross endorsing that position or simply stating that, as a matter of logic, the following argument is invalid? -

i) If we only know the entities of physics in mathematical terms,
ii) then the entities of physics must themselves be mathematical entities.

Ladyman and Ross go on to explain their position in terms of rejecting what they call the “abstract/concrete distinction”. They argue that

“the dependence of physics on ideal entities (such as point masses and frictionless planes) and models also offers another argument against attaching any significance to the abstract/concrete distinction”.

We still need an answer to whether or not (in Ladyman and Ross’s words) “the fact that we only know the entities of physics in mathematical terms” leads to the conclusion that such entities “actually [are] mathematical entities”. Yes, it needn’t lead to that conclusion. However, to Ladyman and Ross, it does lead to that conclusion.

Isn’t it the case that if there were only mathematical models or mathematical structures, then we couldn’t call them “mathematical models” or “mathematical structures” in the first place? Surely such words exist precisely because of the abstract/concrete distinction. This isn’t necessarily to say that we should attach too much significance to that distinction; or even that we can know the entities of physics without abstract mathematical structures and models. Nonetheless, none of this (in itself) is a reason to reject the abstract/concrete distinction or even to refuse to (in Ladyman and Ross’s words) “attach any significance to” it.

Take the case of a very-explicit Pythagorean: Max Tegmark.

Max Tegmark

To sum up Max Tegmark's position:

i) Because the models of causal processes are identical to those processes,
ii) then they must be one and the same thing.

More precisely, Tegmark’s argument is as follows:

i) If a mathematical structure is identical (or “equivalent”) to the physical structure it “models”,
ii) then the mathematical structure and the physical structure must be one and the same thing.

So, if that’s the case (i.e., that structure x and structure y are identical), then it makes little sense to say that x “models” (or is “isomorphic with”) y. That is, x can’t model y if x and y are one and the same thing in the first place.

Tegmark also applies what he deems to be true about the identity of two mathematical structures to the identity of a mathematical structure and a physical structure. He offers us an explicit example of this:

electric-field strength = a mathematical structure

In Tegmark’s own words:

“‘ [If] [t]his electricity-field strength here in physical space corresponds to this number in the mathematical structure for example, then our external physical reality meets the definition of being a mathematical structure — indeed, that same mathematical structure.”

But here’s an argument and a question:

i) If x (a mathematical structure) and y (a physical structure) are one and the same thing,
ii) then one needs to know how they can have any kind of relation at all to one another. [Gottlob Frege’s “Evening Star” and “Morning Star” story may work here.]

In terms of Leibniz’s law, everything true of x must also be true of y.

But can we observe, taste, kick, etc. mathematical structures?…

Yes we can! But only if we deem physical things to be identical to mathematical structures!

In addition, can’t two structures be identical and yet somehow separate (i.e., not numerically identical)? Well, not according to Leibniz.

All this is perhaps easier to accept when it comes to mathematical structures being compared to other mathematical structures (rather than to something physical): not when it comes to mathematical structures being compared to things. Yet if things are mathematical structures, then even that qualification won’t be accepted by either Pythagoreans or by ontic structural realists.

All this is also expressed (at least as it is applicable at the quantum scale) in the following passage written by the science writer John Horgan (1953-):

[M]athematics helps physicists define what is otherwise undefinable. A quark is a purely mathematical construct. It has no meaning apart from its mathematical definition. The properties of quarks — charm, colour, strangeness — are mathematical properties that have no analogue in the macroscopic world we inhabit.”

This means that if mathematics is all we’ve got, then it’s not really a surprise that many physicists (i.e., the more philosophical ones) argue that everything important — or even relevant — that’s said about the quantum world is said by the maths.

Structures: Relations and Relata

A realist about things can happily accept that mathematical structures are

“used for the representation of physical structure and relations, and this kind of representation is ineliminable and irreducible in science”

and still be a realist about things (or events/conditions/states/etc.). However, it’s precisely because of the ineliminable nature of mathematical structures in physics that has led ontic structural realists to become eliminativists about things (i.e., they see things as structures too — see here); just as it led Plato and Pythagoras to similar conclusions.

Indeed we can even accept that it’s an important fact that the (as mathematical structuralists put it) “world instantiat[es] mathematical structure” and still believe that the abstract/concrete distinction is important.

For example, the coffee cup and carrot in front of me instantiate mathematical structure. However, they also exist qua coffee cup and qua carrot. There’s also the fact that all objects, events — all things! — exhibit (or instantiate) mathematical structure. That, however, is (in a strong sense) a banal fact because all it amounts to is the fact that every thing can be given a mathematical description and also be mathematically — or otherwise — modelled (i.e., even a coffee cup or a carrot).

Ladyman and Ross also provide a useful set of four positions which focuses on the nature of relations and relata (or things). Thus:

(1) There are only relations and no relata.
(2) There are structures in which things are primary, and relations are secondary.
(3) There are structures in which relations are primary, while things are secondary.
(4) There are things such that any relations between them are only apparent.

At first glance one would take ontic structural realism to endorse (1) or (3). However, since things are themselves structures (according to Ladyman and Ross), then we must settle for (1) above (i.e., “There are only relations and no relata”).

Looking at (1) to (4) again, can’t it be said that (2) and (3) amount to the same thing? In other words, can we distinguish

(2) There are structures in which the things are primary, and relations are secondary.

from

(3) There are structures in which relations are primary, while things are secondary.

at all? Isn’t that a difference which doesn’t make a difference?

So one can still ask — in the metaphysical pictures of (2) and (3) — the following question:

Can things exist without relations and can relations exist without things?

That’s a question of existence.

Now what about natures?

One can now ask:

Can things have their natures without their relations and can relations have their natures without things?

As already stated, Ladyman and Ross adopt option (1) above: There are only relations and no relata.

Universals

Ladyman and Ross give a very interesting Platonist reason as to why they adopt (1) above. They cite as an example this assertion:

“The Earth is bigger than the moon.”

In terms of relata, it’s certainly true that the Earth and the moon exist. It’s also true that the Earth is bigger than the moon.

So what about the relation bigger than?

Here (just as in Bertrand Russell’s ‘The World of Universals’) the metaphysical (well) things called universals come to the rescue. Ladyman and Ross state that the

“best sense that can be made of the idea of a relation without relata is the idea of a universal”.

Thus the relation BIGGER THAN is a universal. (Ladyman and Ross also see it as being “formal”.) That is,

“when we refer to the relation referred to by ‘larger than’, it is because we have an interest in its formal properties that are independent of the contingencies of their instantiation”.

In other words, the universal BIGGER THAN doesn’t need the moon, Earth or anything else concrete to have being. Indeed the universal BIGGER THAN need never be instantiated between any two concrete objects.

This is the classic position of Plato.

Aristotle, on the other hand, believed that universals must be instantiated.

Ladyman and Ross round this off by making their Platonist position (at least in this specific respect) explicit. They write:

“To say that all that there is are relations and no relata, is therefore to follow Plato and say that the world of appearances is illusory.”

Let’s be explicit here.

The “world of appearances” includes carrots, cups and other human persons. (It certainly doesn’t include subatomic particles.) Yet in order to get to the Platonic truth, we must cut through such appearances (which are “illusory”) and discover the mathematical structures of what it is we’re examining. Alternatively, we must discover the universals and mathematical structures which underpin appearances.

Sunday 7 August 2022

Scientific Theories Don’t Need To Be True

The philosopher Ernan McMullin didn’t believe that the “acceptance of a scientific theory [also] involves the belief that it is true”. Moreover, “to suppose that a theory is literally true would imply that no further anomaly could arise”. And surely such a stance on truth is counterproductive in science.

The Irish philosopher Ernan McMullin (1924 — 2011) was the O’Hara Professor of Philosophy Emeritus at the University of Notre Dame. He was a philosopher of science who wrote on theology, cosmology, values in science, Darwinism, etc. McMullin was also a Catholic priest and an expert on Galileo.

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Karl Popper (1902–1994) once argued that the notion of truth is counter-productive in science because the attainment of complete truth (even if possible in principle) would bring the (or a) scientific story to an end. Instead, Popper argued for what he called verisimilitude.

[As one source defines verisimilitude: “In philosophy, verisimilitude (or truthlikeness) is the notion that some propositions are closer to being true than other propositions.”)

The main problem here is that it can be argued that the notion of complete truth is actually contained (or embedded) within the notion of verisimilitude. Ernan McMullin (in his ‘A Case for Scientific Realism’) made this point when he wrote that the

term ‘approximate truth’ [] is risky because it immediately invites questions such as: how approximate, and how is the degree of approximation to be measured?”.

In order to know that a theory is approximately true, wouldn’t we also need to know what would make it completely true and/or what makes it partly false? And in order to know both those things, wouldn’t we also need to know what the complete truth of that theory is? Moreover, what is a theory’s approximate truth measured against?

On this critical reading, then, there is no approximate truth or verisimilitude at all.

The Canadian philosopher Ian Hacking (in his book The Social Construction of What?) hints at a similar point when he mentions the positions of Thomas Kuhn and the physicist Steven Weinberg. He writes:

“In Structure Kuhn rejected the idea of scientific progress towards some one final vision of the world. What we see in the history of science is progress away from previous beliefs. Weinberg (1996b, 56) quotes some of Kuhn’s later writing, where Kuhn had said ‘it’s hard to imagine… what the phrase ‘closer to the truth’ can mean.’ [].”

One doesn’t need to be be a Kuhnian to agree that the phrase “closer to the truth” is both problematic and odd. So perhaps it should never be taken literally (i.e., it should be taken poetically or even rhetorically). But, of course, in the cases mentioned in this essay at least, the phrase is taken literally.

Ernan McMullin added to all this when he wrote the following:

I do not think that acceptance of a scientific theory involves the belief that it is true. Science aims at fruitful metaphor and at ever more detailed structure. To suppose that a theory is literally true would imply, among other things, that no further anomaly could, in principle, arise from any quarter in regard to it.”

It can be doubted that McMullin actually knew that no scientist believes that his own and other scientific scientific theories are true. That’s because there are many scientists who have used the word “truth” — if perhaps sometimes loosely — about their own and other scientists’ theories.

So perhaps McMullin’s position was both philosophical and normative. Indeed the normative and logical elements of his position are encapsulated in his final words:

“To suppose that a theory is literally true would imply, among other things, that no further anomaly could, in principle, arise from any quarter in regard to it.”

On another tact. Strictly speaking, only statements can be true or false. Nonetheless, if a theory is simply seen as a collection of true statements, then its entirety can also be seen as being true due to the fact that all the statements it contains are also true…

Yet scientific theories don’t really work like that.

Even though theories do contain statements, not all its statements are either true or false. (Strictly speaking, then, perhaps they aren’t statements at all.) Some statements involve predictions, probabilities, conjectures (or speculations), reference to “unobservables” and whatnot. Only few of the statements (or expressions) which make up most theories will have a purely (as analytic philosophers put it) truth-conditional content.

In addition, it’s also clear that what McMullin referred to as “fruitful metaphor[s]” can’t be true or false either.

What McMullin also seems to have argued is that a “worldly structure” shows itself only slowly — over time. Each successive theory about the (same?) structure comes… well, closer to the truth. (This is the position of scientific structuralism.) However, since this is ongoing process concerning theories about structure x, then no single theory of x can ever be said to be conclusively true.

McMullin then gave an example of a worldly structure.

He stated that “[s]cientists in general accept the quantum theory of radiation”. He then asked: “Do they believe it to be true?” McMullin concludes:

“Scientists are very uncomfortable at this use of the word ‘true’ because it suggests that the theory is definitive in its formulation.”

In other words, scientists don’t need to classify (or even see) their theories as being true. Indeed it can even be said — and it has been said — that scientists don’t need truth at all. Instead, a scientist can “accept an explanation as the best available”. Moreover, “one accepts a theory as a good basis for further research”.

All that said, some readers may detect truth — even complete truth — lurking underneath all these words, arguments and positions.