Ludwig Wittgenstein on Mathematical Truth

 

“A mathematician is bound to be horrified by my mathematical comments. [] He has learned to regard them as something contemptible []."

— Wittgenstein (in his Philosophical Grammar, 1932)

Much of what Ludwig Wittgenstein (1889–1951) wrote is hard to decipher. And that’s the primary reason why there’s what can (sarcastically) be called a Wittgenstein Interpretation Industry. This also explains why many loyal Wittgensteinians get so hot under the collar when other commentators “get Wittgenstein wrong!”. Indeed, unlike many other philosophers, much of the debate around Wittgenstein’s work isn’t about whether or not what he wrote is true or false, well argued or badly argued, worthwhile or worthless, etc. — but about what he actually meant.

Lee Braver (in his Groundless Grounds: A Study of Wittgenstein and Heidegger) puts all this better when he wrote the following words:

“[Wittgenstein’s] writing style is perhaps the most obscure of all the great analytic figures, leading to an unusual state of affairs: ‘one of the most striking characteristics of the secondary literature on Wittgenstein is the overwhelming lack of agreement about what he believed and why.’ Already in 1961, the literature on the Tractatus was compared to literary scholarship in dissension and sheer mass. His opaque prose and sparse argumentation have given rise to a cottage industry of exegetical work and scholarly contention [].”

Thus all that is but a preamble to the essay which follows. It can also be said that I’m getting my excuses out of the way before I begin.

Mathematical Truth and Mathematical Correctness

“The terms ‘sense’ and ‘nonsense’, rather than the terms ‘true’ and ‘false’, bring out the relation of mathematical to nonmathematical propositions.”

— Wittgenstein (Lectures, Cambridge 1932–35)

The “late Wittgenstein” argued (at least to paraphrase or even to interpret) that if the operations on numbers result in truths, then shouldn’t it also be the case that the numbers themselves (in whichever order) have truth-conditions or references? (Perhaps the term reference is better suited here.) In basic terms, shouldn’t each number correspond or refer to something? But if the numbers themselves have no truth-conditions or references, then how can the concept of truth be carried over to the operations on numbers? Surely you can’t have one without the other.

And all that is largely why Wittgenstein emphasised what he called “correctness” (as well as mathematical “grammar”) rather than truth.

The operations on numbers also fall under Wittgenstein’s meaning is use theory.

So does the correct use of numbers also imply truth?

There may be a correct and incorrect way to operate on numbers; though is there a true way to operate on numbers? The words “truth” and “correctness” aren’t, after all, synonyms.

Wittgenstein believed that correctness is determined by rules; which are themselves a product of persons, conventions and and/or language games. Truth, on the other hand, has been deemed by many philosophers, mathematicians and laypeople to be separable from minds, conventions, etc. (i.e., as in the various philosophical realisms).

Wittgenstein himself wrote the following on rules and their role in mathematics:

“Because they all agree in what they do, we lay it down as a rule, and put it in the archives. Not until we do that have we got to mathematics. One of the main reasons for adopting this as a standard, is that it’s the natural way to do it, the natural way to go — for all these people.”

Thus, according to Wittgenstein, we can count in a correct way; though not in a true way. Truth could only enter the equation if numbers themselves were true of something else or if they referred to something else. In other words, the inscriptions or symbols must have entities to which they can correspond or refer. Only then, on a Platonist picture at least, could we talk of truth in mathematics.

Of course many people intuitively feel that there must be more to mathematics than mere inscriptions/symbols on the page and the correct rules (or correct mathematical “grammar”) for using those inscriptions/symbols. (This position is usually called formalism; though Wittgenstein went way beyond, say, David Hilbert’s formalism.) But do we think in the same way when we play a game of chess? Do we expect the pieces and the moves to somehow correspond or refer to things (whether people or events) external to the actual game of chess? It can be granted that if someone takes chess literally, then he may well think in terms of the pieces and moves corresponding — or referring - to real historical battles, political situations and well-known historical persons. (This may well be the case for certain individuals.) However, such correspondence-relations aren’t in fact needed when one plays chess. Indeed chess can be seen in purely abstract terms despite the fact that we play the game with castles, pawns, bishops, etc. More abstract forms (which have no correspondents or referents in — or to — the external world) could easily become the substitutes of castles, pawns, etc. And such substitutions would have no important impact on the nature of the game itself.

Thus — on this Wittgensteinian reading — there are correct moves in chess; though there are no such things as true moves… Of course that’s unless we’re using the word “correct” as a literal synonym for the word “true”!

[Note: Although no one expects the individual words in a natural-language statement to have their own truth conditions — the names within such statements do have their own references and other words may have their extension. Few people have demanded that connectives, prepositions, etc. have any of these things.]

Mathematical Grammar

“Consider Professor Hardy’s article (‘Mathematical Proof’) and his remark that ‘to mathematical propositions there corresponds — in some sense, however sophisticated — a reality.’ [] We think of ‘reality’ as something we can point to. It is this, that. Professor Hardy is comparing mathematical propositions to the propositions of physics. This comparison is extremely misleading.”

— Wittgenstein (Lectures on the Foundations of Mathematics)

Wittgenstein believed that mathematical statements are grammatical in nature. Thus if the grammar is in order, then the mathematics is correct. So he elaborated on the quote above with the following few words about Blaise Pascal:

“The mathematician Pascal admires the beauty of a theorem in number theory; it’s as though he were admiring a beautiful natural phenomenon. Its marvellous, he says, what wonderful properties numbers have. It’s as though he were admiring the regularities in a kind of crystal.”

So what about the following statement? -

Mathematical statements are correct because such statements are true.

That’s a possible riposte.

Wittgenstein might have simply turned that statement on its head and claimed the following:

Mathematical statements are true precisely because they’re grammatically correct.

That could be to concede that mathematical grammar is parasitical on mathematical truth. Alternatively, it might be to concede that mathematical truth is parasitical on mathematical grammar. In addition, if Wittgenstein dispensed with mathematical truth, then perhaps we can also dispense with mathematical grammar… Or at least it can be said that you can’t have one without the other.

Wittgenstein might also have accepted mathematical truth; though only when it isn’t conceived as some kind of correspondence with (or reference/relation to) abstract entities in a Platonic world.

So is it possible to make sense of mathematical truth when it’s is cashed out exclusively in terms of abiding by grammatical rules?

For a long time truth itself (regardless of mathematics) has been cashed out in many ways other than in terms of correspondence (i.e., as in the correspondence theory of truth). Thus why should mathematical truth be any different?

The question therefore is this:

Can mathematical truth be cashed out solely in terms of following grammatical rules?

What is it, then, to follow a rule?

Is it to conform to a norm and/or to a practice?

Use and Mention: “2 + 2 = 4” ≠ 2 + 2 = 4

In what follows the philosophical and/or semantic distinction between use and mention needs to be highlighted. In this case, the distinction is between the linguistic expression “2 + 2 = 4” and 2 + 2 = 4. Admittedly, sometimes it’s hard to distinguish the two (I had problems in the last section) — at least in the following context and if one takes a broadly Wittgensteinian position.

In very simple terms, the distinction can be shown when it comes to the word “cat”:

Use: “This cat is very aloof.”

Mention: “The word ‘cat’ is derived from...”

The first sentence refers to the animal called a “cat”: it uses the word “cat” to refer to that animal. The second statement is about the word “cat”.

More relevantly:

Mention: “2 = 2 = 4” — a linguistic expression

Use: 2 + 2 = 4 — an (abstract) equation

(Note that the mention example above uses numbers within a linguistic expression. To be careful, some philosophers would advise using numerals or number-words like “two” and “four” instead of the symbols “2” and “4”.)

So now take this statement (a mention):

“The statement ‘2 + 2 equals 4’ is true.”

Isn’t there a rule which tells us that if we add 2 and 2, then the result will be the number 4? That said, there could be a rule which tells us this:

“The statement ‘2 + 2 equals 5’ is true and is perfectly in order.”

That is, when 2 is doubled, an additional number must be added. However, this new rule would simply be parasitical on the rule that 2 + 2 must equal 4 because it does, after all, talk of the addition of a number to the result of doubling the number 2. The rule doesn’t, on the other hand, state “2 + 2” does equal 5: it says that a number needs to be added to the sum of 4 and 4.

So let’s try a purer formulation.

Take the statement (or even rule) that “2 + 2 equals 5” without mentioning any addition of an extra number…

A Dialogue Between a Wittgensteinian and an Opponent

A Wittgensteinian:

“Why can’t 2 plus 2 equal 5? Or, at the least, why can’t I express ‘2 plus 2 equals 5’ as a rule? Indeed you’re simply assuming that the numbers I’m using have the same properties as the numbers that you’re using. Clearly, if I use my numbers in the way that you use your numbers, then evidently my statement ‘2 + 2 = 5’ will be incorrect. However, my numbers aren’t the same as your numbers. Thus in my language game (or system) 2 + 2 does indeed equal 5.”

An anti-Wittgensteinian:

“Then you’re misusing the arithmetical concepts [addition] and [equality].”

A Wittgensteinian:

“Yes, if I use the concepts [equality] and [addition] in the same way in which you use them, then evidently my statement ‘2 + 2 = 5’ will be incorrect. But my concepts [addition] and [equality] aren’t equal to yours. In my language game (or system), they work differently.”

An anti-Wittgensteinian:

“But you’ve just contradicted yourself. You said that your concepts [addition] and [equality] aren’t ‘equal’ to my concepts [addition] and [equality]. But you’ve just used the concept [equality] in the way I use it. You’ve just said that your ‘concepts aren’t equal to’ mine. And with that I agree. Therefore it would follow that the concept [equality] you use in your mathematical system isn’t equal to your use of the concept [equality] when you use it to talk about your own mathematical ‘language game’.”

A Wittgensteinian:

“Yes, you’re right. According to one language game (i.e., mathematics) I use the concept [equality] in one way. And according to another language game (talking about mathematics or metamathematics), I use the concept — or at least the word — in another way.”

An anti-Wittgensteinian:

“If that’s the case, then how the hell can we have a proper conversation if we’re using the same concepts (actually, words) in different ways? If you can arbitrarily stipulate a meaning of a concept in any way you like, then perhaps we’re not having a genuine conversation at all. We’ll simply be talking at cross-purposes.”

A Wittgensteinian:

“No, because I know that the concept [equality] is always relative to a language game. Therefore if I know what language game the concept belongs to, then I also understand the concept. I understand your use of the word ‘equality’ because I know which language games it belongs to. Therefore I can understand you and we aren’t talking at cross-purposes. All I need to determine is the language game to which the concept or word belongs. And even in my own case, I need to be aware of how I’m using a particular concept or word. I need to know which language game I’m using when conversing with other people. And you too need to be aware of which language game the people you talk to are playing — otherwise you’ll be talking at cross purposes. You may of course believe that you don’t belong to any language game or even that your position is beyond language games. However, such a position would be a meta-language game; which would simply be another language game with highfalutin ambitions.”

(*) See my ‘When Alan Turing and Ludwig Wittgenstein Discussed the Liar Paradox’.

[I can be found on Twitter here.]

Is Physicist Roger Penrose a (Tacit) Panpsychist?

 

“But there is one thing that I do believe in relation to this problem [of consciousness], and that is that it is a scientific question that eventually should become answerable, no matter how far from being about to answer it we may be at present.” — Roger Penrose

(i) Introduction

(ii) Is Roger Penrose a Panpsychist?

(iii) What About Organisation and Complexity?

(iv) Physics and Biology

(v) Are Ants Conscious?

(vi) Quantum Stuff (e.g., Coherence)

(vii) Conclusion

The title above asks if the British mathematical physicist and philosopher of science Roger Penrose (1931-) is a (tacit) panpsychist. Well, he’s certainly not an open panpsychist. Added to that is the fact that he’s rarely — if ever — used the word “panpsychism”. And he certainly hasn’t used that word to describe any of his own theories.

Stephen Hawking and Roger Penrose

Just to give a quick hint of the main reason why Penrose can’t really be an out-and-out panpsychist.

It’s basically down to his exclusive focus on biological entities. That is, although Penrose offers us the possibility than a single neuron, liver cell or even a paramecium may instantiate some basic form (or level) of consciousness, he never stretches that possibility beyond the biological realm. Indeed his strong scientific, mathematical and philosophical position against the possibility of artificial intelligence makes that crystal clear.

So this essay will conclude that it’s perhaps a little too strong to claim that Penrose’s theories are panpsychist in nature. That said, this issue is complicated; as will be shown later.

In any case, NBC News did once state the following:

“Three decades ago [this was written in 2017], Penrose introduced a key element of panpsychism with his theory that consciousness is rooted in the statistical rules of quantum physics as they apply in the microscopic spaces between neurons in the brain.”

Yet this particular journalist continued by saying that Penrose “does not overtly identify himself as a panpsychist”.

And just as Penrose doesn’t use the word “panpsychism”, so he’s never used (as far as I know) the word “cosmopsychism”. Yet here again is Space.com tying Penrose to this philosophical position:

“Importantly, however, ‘Orch OR suggests there is a connection between the brain’s biomolecular processes and the basic structure of the universe’, according to a statement published in the March 2014 paper ‘Consciousness In The Universe: A Review of the Orch OR Theory’, written by Penrose and Hameroff in the journal Physics of Life Reviews.”

So whatever the case is, Penrose is certainly doing panpsychists at least some favours when he shows them (even if that’s not his aim) that panpsychism can be grounded in at least some kind of science (see opening quote). And that’s even though Penrose’s own science of consciousness is hugely controversial!

Is Roger Penrose a Panpsychist?

Roger Penrose most explicit raising of the possibility of panpsychism (though, again, he never actually uses the word “panpsychism”) can be found in the following passage:

“The question is significantly raised, of course, as to whether a paramecium — or, indeed, an individual human liver cell — might actually possess some rudimentary form of consciousness [].”

This question is significantly raised because it’s the logical result of Penrose’s own position on consciousness. This position, in basic terms, has it that cytoskeletons and their microtubules are vital when it comes to the “bringing about” (or instantiation) of consciousness. And a paramecium and a human liver cell contain both of these things! In Penrose’s own words:

“I have been making the case that it is to the microtubules in the cytoskeleton, rather than to neurons, that we must look for the place where collective (coherent) quantum effects are most likely to be found.”

And yet

“cytoskeletons are ubiquitous amongst eukaryiotic cells — the kind of cells that constitutes plants and animals”.

Penrose specifically waxes lyrically about the single-celled paramecium when he writes:

“If we are to believe that neurons are the only things that control the sophisticated actions of animals, then the humble paramecium presents us with a profound problem.”

So what is the nature of that problem? Penrose continues:

“For she [a paramecium] swims about her pod with her numerous tiny hairlike legs — the cilia — darting in the direction of bacterial food which she senses using a variety of mechanisms, or retreating at the prospect of danger, ready to swim off in another direction. She can also negotiate obstructions by swimming around them. Moreover, she can apparently even learn from her past experiences [].”

Finally:

“How is all this achieved by an animal without a single neuron or synapse? Indeed, being but a single cell, and not being a neuron herself, she has no place to accommodate such accessories.”

But forget these other creatures! What about the neurons in human brains?

Penrose writes:

“It is the cytoskeleton's role as the cell’s ‘nervous system’ that will have the main importance for us here. For our own neurons are themselves single cells, and each neuron has its own cytoskeleton!”

More relevantly:

“Does this mean that there is a sense in which each individual neuron might itself have something akin to is own ‘personal nervous system’?”

What About Organisation and Complexity?

It may — at least at first — seem like a bizarre possibility that a paramecium, liver cell or individual neuron may instantiate a “rudimentary form of consciousness”. However, Penrose does go on to qualify his position when he states the following:

“[I]t must also be the case that the detailed neural organization of the brain is fundamentally involved in governing what form that consciousness must take. Moreover, if that organization were not important, then our livers would evoke as much consciousness as do our brains.”

So Penrose’s basic (if implicit) point is that we should firstly establish what “form” (or level) of consciousness any given entity has (i.e., whether that’s a paramecium, a human liver cell, a single neuron, or an entire human brain). And clearly Penrose is raising the possibility of an extremely basic form of consciousness for a paramecium, liver cell and an individual neuron. Indeed one can even use the technical terms of philosophers here and say that a paramecium, liver cell and an individual neuron may instantiate “proto-experience”, “protophenomenal properties” or “panprotophenomenal properties”.

Yet even though Penrose makes it clear that he’s only talking about extremely basic levels of consciousness here — and even then he’s only raising the possibility of such things — he still concludes with the following words:

“Nevertheless [] what the preceding arguments strongly suggest is that it is not just the neuronal organization of our brains that is important. The cytoskeletal underpinnings of those neurons seem to be essential for consciousness to be present.”

The obvious point to make here is that even if (or even though) the “cytoskeletal underpinnings of those neurons seem to be essential for consciousness to be present”, these underpinnings alone may not bring about consciousness.

So, in basic terms, the following is a simplification of Penrose’s position:

the cytoskeletal underpinnings of neurons + neuronal organisation = consciousness

Indeed we can invert Penrose’s earlier words

“it is not just the neuronal organization of our brains that is important”

with the following statement:

It is not just the cytoskeletal underpinnings of neurons that are important when it comes to consciousness.

Physics and Biology

It will be seen that all Penrose’s examples of the possibility of consciousness (i.e., other than human beings and higher animals) are biological in nature. So that, in itself, won’t be of much help to those panpsychists who believe that consciousness exists all the way down the line from human beings to apes to mice to ants to rocks to particles… and even to spacetime itself. That said and despite the tenor of this essay, Penrose doesn’t see any “essential” reason why non-biological entities can’t be conscious too— at least in principle. Indeed he even argues that

“such (putative) non-computational processes [i.e., in the brain and which Penrose believes are vital for both consciousness and what he calls 'understanding'] would also have to be inherent in the action of inanimate matter, since living human brains are ultimately composed of the same material, satisfying the same physical laws, as are the inanimate objects of the universe”.

Penrose also tells us that he doesn’t “perceive any necessity that such a device [one that instantiates or merely simulates consciousness] be biological in nature”. He goes on:

“I perceive no essential dividing line between biology and physics (or between biology, chemistry, and physics).”

Yet it doesn’t follow that because Penrose doesn’t perceive an “essential” distinction, difference or “dividing line” between biology and physics that he that doesn’t perceive any dividing line at all. And that’s precisely why Penrose immediately carries on with the following words:

“Biological systems indeed tend to have a subtlety of organization that far outstrips even the most sophisticated of our (often very sophisticated) physical creations.”

It must now be stated that Penrose stated all the above in reference to his earlier discussions of artificial intelligence. Yet his words equally apply to the issue of panpsychism too.

Now strictly in terms of AI.

Are Ants Conscious?

Roger Penrose believes that ants are one step ahead of all AI entities. And here again his stress on biology inevitably enters the picture. Penrose claims that the

“actual capabilities of an ant seem to outstrip by far, anything that has been achieved by the standard procedures of AI”.

It’s not clear if Penrose was being careful or if I’m being pedantic here. That is, when Penrose stated the above did he ignore (or dismiss) the ability of AI entities (or even basic computers) to do advanced mathematical calculations, win people at chess, read fingerprints, etc? As far as I know, there aren’t many ants that are good at chess, mathematical calculations, etc. It can be supposed, then, that this may boil down to what Penrose means firstly by the the words “actual capabilities” (i.e., of an ant) and by the the words “standard procedures” (i.e., of AI).

In any case, many AI theorists and champions of AI have pointed out that most of the critics of AI tend to artfully select those things which humans and other animals can do and which AI entities or computers can’t do. Yet of course this approach can be turned on its head by stressing the things that AI entities can do but which humans and other animals can’t do. So, in both these cases, this approach may not be very helpful and may simply amount to mindless point-scoring.

But let’s move on.

Penrose also implicitly ties his ants-vs-AI argument to panpsychism — at least via the issue (again) of microtubules. Penrose continues:

“One might well wonder how much an ant gains from its enormous array of nano-level ‘microtubular information processors’, as opposed to what it could do if it had only ‘neuron-type switches’. As for a paramecium, there is no case to answer.”

So, on a (partly) sarcastic note, this question can now be asked:

How much microtubular quantum stuff must an ant — or anything else — have (or instantiate) in order to actually be conscious?

Now it can be wondered if the supposed “measure” of consciousness (i.e., phi or Φ) in integrated information theory (IIT) may be of help here. Indeed, as Penrose himself hints, even a humble single-celled paramecium may have enough microtubular quantum stuff to bring about — or instantiate — its own consciousness.

Having said all that, Penrose then deflates his tacit panpsychism when he says that he has “always had difficulties in believing that insects have much or any of this quality [of consciousness]”.

To complicate matters even more, Penrose goes straight ahead and qualifies these “difficulties” by tying ants yet closer to a possible panpsychist position — at least at it must be tied to microtubules, etc. Penrose writes:

“Nevertheless [] the behaviour pattern of an ant is enormously complex and subtle. Need we believe that their wonderfully effective control systems are unaided by whatever principle it is that give us our own qualities of understanding?”

Quantum Stuff (e.g., Coherence)

Penrose expresses his prime motivation for stressing the importance of cytoskeletons and microtubules when he states that

“without such quantum coherence we shall not find a sufficient role for the new OR [Orchestrated objective reduction] physics that must provide the noncomputational prerequisite for the encompassing of the phenomenon of consciousness within scientific terms”.

Penrose then cites the biological and technical reasons why he takes this position. He continues:

“Their controlling neuronal cells have their own cytoskeletons, and if these cytoskeletons contain microtubules that are capable of sustaining the quantum-coherent states that I am suggesting are, at root, necessary for our own awareness, then might they not also be beneficiaries of this elusive quality?”

Moreover:

“If the microtubules in our brains do posses the enormous sophistication needed for the maintaining of collective quantum-coherent activity, then it is difficult to see how natural selection could have evolved this facility just for us and (some of) our multicellular cousins.”

Then, almost like a good panpsychist, Penrose goes all the way down the line by finishing off with the claim that these

“quantum-coherent states must also have been valuable structures to the early eukaryotic one-celled animals, although it is quite possible that the value to them may have been very different from what it is to us”.

Conclusion

The new interest in panpsychism as produced a lot of cheap and easy “New Age” crap.

In the end, then, it may be unclear if Penrose is a panpsychist — even a tacit panpsychist. His stress on biology certainly puts him at odds with most — or even all — panpsychists. Indeed one can argue that the whole point of panpsychism is that it downplays biology; and, in the process, seemingly gets rid of such problems as strong emergence.

The other thing is that Penrose only discusses the possibility of consciousness in these rudimentary biological entities. This isn’t odd because, as a theoretical physicist, he’s always discussing all sorts of other possibilities too. (Usually possibilities which are worlds away from the issue of panpsychism.) In fact he’s doing what all good philosophers should do — give (most/some of!) these possibilities the benefit of the doubt… at least at first.

On the other hand, it seems that most panpsychists have somewhat smoothly and easily moved from the possibility of consciousness in rudimentary entities to their actually being conscious. (There are various philosophers — such as David Lewis, David Chalmers, Philip Goff, etc. — whose entire philosophies seem to be based on the reality of possibilities.) And most panpsychists have found it easy to move from possibility to actuality because they’ve almost completely divorced their panpsychism from science. (Scientific terms and issues are — of course — brought up by panpsychists; though often in a very superficial way and usually to give panpsychism a little scientific kudos.) Thus the move from the possibility to the actual truth of panpsychism has been easy for such panpsychists.

All this (as it were) turning-the-(merely)possible-concrete is something Penrose himself would have a serious problem with.

And that’s why I believe he probably isn’t a panpsychist.

[I can be found on Twitter here.]

Bertrand Russell (1927) on the Particles of Quantum Mechanics

 

Way back in 1927, English philosopher Bertrand Russell (1872–1970) fused philosophical and psychological (i.e., Humean ) insight with physics when he discussed whether or not quantum particles are things. Indeed Russel wrote his An Outline of Philosophy during the height of the (first) “revolution” of quantum mechanics.

Particles aren’t Things

Russell believed that particles aren’t things (or objects). He wrote the following words:

“The idea that there is a little hard lump there, which is the electron or proton, is an illegitimate intrusion of common-sense notions derived from touch.”

It was then that Russell offered us both a empiricist and psychological account of how most laypersons and even some scientists interpret the quantum realm.

Firstly, the following passage highlights the observational or experimental reality:

“The events that take the place of matter in the old sense are inferred from their effect on eyes, photographic plates, and other instruments.”

As for the specifics of the rejection of a (as it were) thing-ontology, Russell went on to say that “[t]here is no reason to suppose that there is a ‘thing’ at the place where the ‘crinkle’ is most crinkly”. In parallel, Russell also stated that “matter has ceased to be a ‘thing’”. Yet doesn’t the layperson believe that there is matter and that there are also things? Indeed aren’t things (or at least objects) made up of matter? That is, matter (what philosophers call a “mass term”) itself is rarely deemed to be a specific thing. That said, an ontologist can just as easily say (via stipulation and ontological analysis) that a mere random or arbitrary lump of matter can indeed be deemed to be a thing too. (Think here on the lump-of-clay-to-statue disputes in contemporary “analytic” metaphysics.)

So what did Russell believe to be the scientific reality of particles?

The Science of Particles

Bertrand Russell offered us a hypothesis on the matter. He stated that

“[f]or aught we know, the atom may consist entirely of the radiations which come out of it”.

Russell then predicted the obvious response when he continued by stating that it’s “useless to argue that radiation cannot come out of nothing”. Yet surely that response is understandable and it is Russell’s own position that’s a little counterintuitive.

In any case, Russell stated that the something-from-nothing scenario is no less (or no more) “intelligible” than thinking that radiation “comes out of a little lump”. However, surely it can be said that the idea that radiation comes out of lumps is more (not less) intelligible than saying that it comes from nothing. So no matter how inaccurate the idea that protons and electrons are things is, it was still a more believable position than stating that radiation can come out of nothing.

Russell also expressed more of the basic science of electrons and protons (at least in the 1920s) and why it is that laypersons took them to be things. Thus, in point of fact,

“the modern physicist faces cheerfully the possibility than an electron and a proton may mutually annihilate each other, and even suggests that this may be the main source of the radiant energy of the stars, because when it happens it makes an explosion”.

Thus firstly we conjecture that the electron and proton have some kind of mutual relation with one another. That alone will raise questions as to their ontological reality as separate entities (or what philosophers call individuals or particulars). In other words, if two things — a and b — always have a necessary and “mutual” relation to one another, then what right have we to see them as distinct entities in the first place?

[Note that all this isn’t directly connected to the notion of entanglement. It also turned out that it is electrons and positrons which “annihilate each other”, not protons and electrons. (Paul Dirac theoretically hinted at the positron in 1928 and Carl David Anderson discovered it in 1932. Russell was writing in 1927!)]

That later possibility is scientifically elaborated upon when Russell told us “[w]hat can be asserted” about these matters (i.e., the electron and the proton). He wrote:

“When energy radiates from a center, we can describe the laws of its radiation conveniently by imagining something in the centre, which we will call an electron or a proton according to circumstances, and for certain purposes it is convenient to regard this centre as persisting, i.e. as not a single point is spacetime but a series of such points, separated from each other by time-like intervals. All this, however, is only a convenient way of describing what happens elsewhere, namely the radiation of energy away from the centre. As to what goes on in the centre itself, if anything, physics is silent.”

Whereas earlier it was said that the word “centre” was being used as a substitute for the word “thing”, now Russell speaks of ‘“spacetime points” instead. Thus even though Russell stated that “what goes on in the centre itself, if anything, physics is silent”, he still felt comfortable talking about “spacetime points”.

Events and Substances

Bertrand Russell also offered us a physicist’s overview of events within the quantum realm. He stated that

“[m]odern physics, therefore, reduces matter to a set of events which proceed outward from a centre”.

Since Russell believed that the idea that radiation comes from lumps is unintelligible, then why is it any more intelligible to say that events (or radiation) “proceed outward from a centre”? Is a physical centre more intelligible than a lump? Despite that, Russell backs himself up by making the Kantian (as in his reference to a noumenon) point that “[i]f there is something further in the center itself, we cannot know about it”. Indeed such a thing is “irrelevant to physics”.

To put it simply: Russell believed that there are only events. The layperson — and indeed some/many physicists — mistakenly believe, however, that there are also things.

Russell went on to argue that “[w]e must think of a string of events [as a] thing”. Psychologically this is accounted for by the fact that different events are seen to be “connected together by certain causal connections”. One (Humean) conclusion to this is that we deem such events to have “enough unity to deserve a single name”.

This ostensible movement of things is also accounted for when Russell stated that when “the events are not all in the same place”, we then “say the ‘thing’ has ‘moved’”. However, such a belief is “only convenient shorthand”.

Russell scientifically and metaphysically concluded that “it can be no part of legitimate science to assert or deny the persistent entity”. To assume a persistent thing is to “go beyond the warrant of experience”.

Russell carried on with his theme of Humean constant conjunction by speaking of a light waves. He stated that these too are a “connected group of rhythmical events”. And, as before, Russell rejected the idea that a light wave is a thing. It is, instead, a “connected group of rhythmical events”. One thing that can be said here is that it can be doubted that even scientifically (or philosophically) illiterate people deem light waves to be things in any strict (or literal) sense of that word. Indeed all this depends on how closely we tie the word “thing” to the word “individual” or “particular”.

In much traditional philosophy, things (or particulars/individuals) were required to have substances to be the things that they are. In addition, all things (or substances) were deemed to be impenetrable. (Is this true? Particles were indeed deemed to be impenetrable; though not necessarily all things and certainly not substances.) As Russell put it, “[i]mpenetrability used to be a noble property of matter”. However,

“[t]he events which are the real stuff of the world are not impenetrable, since they can overlap in space-time”.

To offer more on his position on ontological substances, Russell wrote:

“It was traditionally a property of substance to be permanent, and to a considerable extent matter has retained this property in spite of its loss of substantiality. But its permanence now is only approximate, not absolute. It is thought that an electron and a proton can meet and annihilate each other; in the stars this is supposed to be happening on a large scale. And even while and electron or a proton lasts, it has a different kind of persistence from that formerly attributed to matter.”

Thus, just as it can be said that the word “centre” has become a substitute for the word “thing” in this ontology; so Russell also seems to believe that events are (in a strong sense) things too. This is shown in Russell’s articulation of the meaning of the philosophical theory of neutral monism.

Firstly, Russell stated that neutral monism is monism

“in the sense that it regards the world as composed of only one kind of stuff, namely events”.

What about Russell’s “pluralism” of entities? He then told us that “it is pluralism in the sense that it admits the existence of a great multiplicity of events”. It’s here that the notion of a thing (or an entity) is resurrected. Russell went on to state that “each minimal event” is seen as “being a logically self-subsistent entity”.

So does that all this mean that we’re left with a simple transitive statement of identity? Namely:

an event = “a self-subsistent entity” = a thing

Intrinsic and Extrinsic Properties

Bertrand Russell also asked this question:

“What do we mean by ‘piece of matter’?”

He answers his own question by telling us that “[w]e do not mean something that preserves a simple identity throughout its history”. Now that statement is partly correct and partly incorrect. It’s true that any particular thing (or “piece of matter”) won’t be have precisely the same properties over any given period of time. (That statement may not be true of particles, depending on how we see them.) So object O at time t¹ will be different in some — or in many — ways to O taken at t². In everyday terms, there are things about Paul Murphy which are true in December 2021; though which won’t be true of Paul Murphy in February 2022. And, of course, the same can be said of any given oak tree or a crab.

In other words, an object (or entity) needn’t ( as Russell puts it) “exist complete at every moment”. So it depends on what’s meant by the word “complete”. If it means that everything that “belongs” to object O at time t¹ will not do so at t², then that’s correct. Though an entity doesn’t need to be the sum of literally all its properties at every single point and place in time in its entire existence. (This was Leibniz’s position, at least according to Robert Stalnaker!) It’s only the case that certain (essential) properties are passed on from t¹ to t² to tⁿ. Of course if there aren’t any essential or intrinsic properties in the first place, then this scenario can’t work and we must take Russell literally.

So it doesn’t follow that because any object (or thing) x doesn’t remain identically the same in all respects over time that it doesn’t remain the same in at least some respects.

In metaphysical terms, we call those unchanging aspects intrinsic or essential properties. (Although the terms “essential” and “intrinsic” are related; they aren’t synonyms.) However, we may not like such a reference to essential properties and want to to use the words, instead, “important” or “enduring” properties (see Quine 1960). Thus I will loose millions of neurons (or cells) over time; just as an oak tree will loose many of its leaves. Nonetheless, both persons and trees do have important characteristics — functional, formal and physical — which last over time. Indeed if that weren’t the case, then indeed we wouldn’t have any right to keep on referring to a particular thing (or even a particular person) with the same name over time. It can be said here that Russell did believe that we have no (philosophical) right to use the same name over time because he rejected intrinsic properties. Either that or he didn’t deem the enduring and/or important properties of an x to also be intrinsic properties.

The upshot of Russell’s position (if only in 1927) is that there are no intrinsic properties and, consequently, there aren’t really any things (or objects). That is, all x’s properties are extrinsic. (Semantically, surely if there are no intrinsic properties, then there are no extrinsic properties either.)

Russell’s (partly Kantian) bottom line is that we have no access — either observationally or otherwise — to the intrinsic characteristics of such things. Instead “[w]hat we know about them” is simply “their structure and their mathematical laws”. That is, all we’ve got is mathematical structure.

This basically means that it’s mathematical structure “all the way down” — at least in the case of quantum mechanics.

[I can be found on Twitter here.]