What Do the Words “Ultimate Reality” Mean?

Professor Peter van Inwagen

 

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Aren’t the words “ultimate reality” somewhat poetic and highfalutin? What do they mean?

Just a word of warning here. Some readers may be disappointed by this piece because the title may be somewhat misleading. Rather than the following being my own personal position on the nature of “ultimate reality” (or even a piece which argues that such a thing can’t be discovered), it’s actually about a particular philosopher’s stance on ultimate reality. That philosopher is Professor Peter van Inwagen.

The words “ultimate reality” aren’t often used by professional philosophers. On the other hand, they are often used by well-known writers of “spiritual” bestsellers and by popular-science writers. 

Van Inwagen himself is keen on the words “ultimate reality”. Or, more correctly, he’s keen to tell us that there is such a “thing” as ultimate reality. This immediately raises the question as to whether van Inwagen makes a distinction between (mere) reality and ultimate reality. If there is such a distinction, then is ultimate reality something over and above — something more than — (basic) reality?

But firstly, here are a few biographical words on Peter van Inwagen himself.

Van Inwagen is an American philosopher and John Cardinal O’Hara Professor of Philosophy at the University of Notre Dame. He was also the president of the Society of Christian Philosophers from 2010 to 2013. Van Inwagen has also been a major player in the debate about free will. Indeed he introduced the term ‘incompatibilism’ to stress the position that free will is not compatible with determinism. Van Inwagen has also taken part in the “afterlife debate”. (He wrote a piece called ‘I Look for the Resurrection of the Dead and the Life of the World to Come’.)

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Ultimate Reality/Context-Independent Reality

If Peter van Inwagen himself hasn’t got access to Ultimate Reality (I’ll be using platonic capitals from now on because they seem very apt), then who has? God? Indeed, even if we assume that God exists, then we’d still have the problem of explaining how he communicates his own view of reality to mere mortal human beings like… Peter van Inwagen.

This is similar to the truths (mathematical and otherwise) which “exist” (or have being) in the Platonic realm. Even if such a “place” exists (or has being), then there would still be a question as to how human beings get hold of its pristine “truths” without polluting them with terrestrial or contingent detritus. That is, even if God’s view or the Platonic Realm exist, we fallible human beings may still not have even the slightest access to such things. And even if we did have access to such things, how would we know that we did? On the other hand, why should we ever accept that other individuals have access to God’s View or the Platonic Realm — even if we don’t?

One may ask if van Inwagen himself has tapped into God’s View of reality. (I’m attempting not to be too ironic here.) Van Inwagen would, I presume, deny that. However, he would still say that such a view of reality is at least possible. That is, the quest for Ultimate Reality is actually a philosophical ideal. It’s something we must strive toward even if we can never get there. In that sense, perhaps van Inwagen is echoing the following often-quoted words (written in 1931) from Albert Einstein:

“To know what is impenetrable to us really exists, manifesting itself as the highest wisdom and the most radiant beauty which our dull faculties can comprehend only in their most primitive forms — this knowledge, this feeling is at the center of true religiousness.”

Like the words “ultimate reality” themselves, the passage can of course be taken as some kind of purely poetic expression — not as philosophy and certainly not as science. So if van Inwagen accepts that the phrase “ultimate reality” is a poeticism, then that’s fine and we can move on from there. In other words, acknowledging the aesthetic (or emotional) power of the phrase “ultimate reality” doesn’t automatically mean that it should be rejected as having no philosophical content whatsoever. Nonetheless, it’s still helpful to lay one’s cards on the table about its poetic nature.

In any case, van Inwagen also uses the term “context-independent reality” as a virtual synonym for “ultimate reality”. Here again, we’d need to know what (alternatively put) reality without any context (or reality which has no context) actually means.

It’s hard to imagine or even conceive what a context-independent reality could even be — never mind what it would “look like”. Thus such a thing may well fail the test of conceivability. (see David Chalmers here.) That may not matter much. After all, many things could exist (or have being) which we could never conceive of. (Say, in the manner argued by the philosopher Colin McGinn in his philosophy of mind — also see here.) Nonetheless, we may still have grounds for being skeptical about the reality of a context-independent reality (or Ultimate Reality). More prosaically or pragmatically, what point does the idea of (or the thing) Ultimate Reality serve? Where does it take us?

Whichever attitude one has, the words “context-independent reality” themselves almost read like Spinoza’s sub specie aeternitatis or Thomas Nagel’s own “view from nowhere”.

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Appearances

So what does Peter van Inwagen take “ultimate reality” (or Ultimate Reality) to be?

He believes Ultimate Reality is what (to use his own words)

“lies behind all appearances”.

For a start, Inwagen obviously believes that “appearances” aren’t everything. That rules out idealism. However, even if there is something (or some things) “behind appearances”, then does that also mean that appearances aren’t part of reality? So why aren’t appearances part of reality? That is, if appearances aren’t part of reality, then what are they part of? They surely aren’t unreal. And appearances aren’t abstract either. Thus, even if appearances do lie (as it were) in front of Ultimate Reality, then that means that they must still be something. Appearances are still… well, real. And if appearances are real, then they must be part of reality.

But are appearances part of ultimate reality? Van Inwagen clearly believes not. Why is that?

I quoted van Inwagen’s word “behind” (i.e., as in “lies behind all appearances”) a moment ago.

Is that word a metaphor? I can’t see how it can be anything else but a metaphor. This may seem facetious, but if Ultimate Reality lies behind all appearances, then it could (at least in principle or if we take the word literally) lie on top or below appearances too. After all, the word “behind” is usually — though not always — used as a spatial term. Sure, we also have phrases such as “What’s behind your actions?” in which the use of the word “behind” hasn’t a literal spatial meaning. However, in van Inwagen’s case, the word “behind” most certainly does seem to be being used in its spatial sense.

So, again, what is it for Ultimate Reality to lie behind all appearances?

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Objective Truth and Real Metaphysics

Van Inwagen ties what he calls “objective truth” to Ultimate Reality. That is, objective truths are truths about Ultimate Reality. To use van Inwagen’s own words:

“[T]hose statements would be objectively true that correctly described the ultimate or context-independent reality.”

So perhaps the words of the English mathematical physicist and mathematician Roger Penrose will help us here because he too uses the words “objective”, “dependent” and he also hints at Ultimate Reality. Penrose writes:

“Platonic existence, as I see it, refers to the existence of an objective external standard that is not ‘dependent’ upon our individual opinions nor upon our particular culture.”

Thus we must conclude that subjective (or non-objective) truths mustn’t be about Ultimate Reality. But surely that must also mean that they aren’t truths at all. In addition, if subjective (or non-objective) “truths” are not about reality, then what are they about?

Alongside van Inwagen’s commitment to Ultimate Reality is his parallel belief that

“metaphysics is the attempt to discover the nature of ultimate reality”.

At least van Inwagen uses the word “attempt” in the statement above. This must mean that van Inwagen acknowledges that metaphysical realists may not take us — all the way? — to Ultimate Reality; though at least that’s their overall aim. Whichever way, it’s only metaphysics itself that can take us to this destination. According to van Inwagen, anti-realism, on the other hand, is a “denial of [this] possibility”.

Indeed van Inwagen doesn’t even exclude idealism from this metaphysical attempt to discover Ultimate Reality. It’s just that the (lower-case) reality which idealists attempt to discover is (to simplify and generalise) what's contained in the heads of either individual human beings or the collective heads of human beings. So even though van Inwagen rejects idealism and embraces metaphysical realism, he still deigns to see idealism as at least an attempt to discover Ultimate Reality. Anti-realism, on the other hand (as already stated), is not “a metaphysic” at all because van Inwagen believes that it rejects both “the possibility of metaphysics” and therefore the possibility of discovering Ultimate Reality.

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Conclusion

One may also ask exactly how we can “discover [the] nature of ultimate reality”. What philosophical (or otherwise) tools must we use to do so? It’s not enough to say that we must — or can — do so through metaphysics. And neither is it enough simply to say that metaphysical realism is the best shot at discovering Ultimate Reality. We’d also need to know why metaphysical realism is the best shot.

That is, simply because a metaphysical realist (or Peter van Inwagen) is committed to the existence (or being) of Ultimate Reality (and also believes that metaphysical realism is the means to discover Ultimate Reality), that doesn’t necessarily mean that metaphysical realism is the means to discover Ultimate Reality.

So which philosophical and logical tools, concepts, emotional or personal standpoints, ways of thinking (other than thinking that metaphysical realism is the way), etc. are used by metaphysical realists? And why do they — or why can they (at least in principle) — take us to Ultimate Reality? Again, it’s no use ostentatiously proclaiming that metaphysical realism is the means to discover what lies behind all appearances if that claim isn’t backed up with results that other philosophers, scientists, and laypeople can agree upon. In other words, we’d need to know how such philosophical and logical tools do lead us to something as grand as Ultimate Reality.

Empty “Analytic Metaphysics”: Michael Loux’s Vicious Circle of Modal Properties

 

The American philosopher Michael J. Loux seems to be a master of playing games with modal terms — at least within this particular 2002 discussion of bare objects (i.e., within ontology).

Now it’s often been said that modal terms form a “closed circle” in that the definition of one term must include reference to all, some or at least one other modal terms (i.e., they’re necessarily interdefinable). And since I’m going to be sceptical about the use of modal terms (if only within the context of what Michael Loux has to say), here’s the English philosopher Bob Hale on the sceptic’s position on necessity and how it must bring in (at least part of) the aforesaid closed circle of modal terms or properties:

“It is difficult to see how his scepticism about necessity could be so much as expressed without employing the notion of possibility. And once a notion of possibility has been granted houseroom, the intelligibility of a correlative notion of necessity can hardly be denied.”

More particularly, Loux (as it were) fuses different modal terms (or properties) in that he believes that the acceptance (or use) of one must bring on board at least one other modal term (or property).

Just to cite another example of this modal (as it were) fusion, take Loux’s fellow American philosopher Alvin Plantinga. He also goes in for using modal terms together when he tells us that “some properties” are “necessarily essential to all objects”. (He offers us the examples of the properties self-identity and existence.) Plantinga also makes the statement that “a necessary proposition is just a proposition that has truth essentially”.

In the specific case Michael Loux tackles here, the terms “essentially”, “necessarily” and “contingently” are played around with. And these terms are played around with in the specific context of the ontology of bare objects (or bare particulars).

The words “essentially” has just been mentioned. It’s worth saying here that there is some dispute as to whether the word “essence” (or “essentially”) is a modal term and what its precise status is. (For example, E.J. Lowe argues that “rather than attempt to explain essence in term of necessity, we need to explain necessity in terms of essence”.) Some modal theorists claim that “essence” (or “essentially”) isn’t actually a modal term and therefore that it isn’t a modal property. However, Michael Loux himself strongly connects essential properties to the other modal properties. Yet, in terms of the passage above, one may have no problems with what Bob Hale says about necessity and possibility and still have problems with Loux’s shoehorning of essential properties into these modal domains.

Loux is committed to essential properties. And he — at least partly — arrives at this commitment via necessity. For example, Loux writes:

“[N]ecessarily everything has some properties essentially.”

Loux believes that this metaphysical fact (if we can use the word “fact” in this ontological context) is a way of “refuting” what he calls “anti-essentialism”. Here again Loux displays his closed circle of his modal terms. That is, according to Loux it is a necessary metaphysical fact that all things have at least “some” essential properties. (We also have some kind of non-Quinian modal universal existential quantification in the quote above. See here.)

What are Properties?

Michael Loux assumes (at least within the passages quoted) the existence of essential properties. And, from that assumption, almost everything else in his general argument follows.

For a start, if there are essential properties, then there must also be contingent properties. After all, the postulation of essential properties literally makes no sense without also postulating contingent properties. So, to paraphrase a well-known statement (usually about an entirely different subject), take the following:

If all properties were essential (or contingent), then no properties would be essential (or contingent).

(It must be said here that in the Leibnizean position on objects and their essences it is argued — at least by some — that all an object’s properties must be taken as being essential to it. See here.)

And in which way do such properties “belong” to objects? Do they “inhere” in objects? How, exactly, do these specific properties belong or inhere in objects? Within this context, what do those words actually mean?

Trivial Properties?

Michael Loux argues that “everything” has essential properties. (This isn’t the Leibnizean position that all an object’s properties are essential to it.) So which kind of properties must everything have? Loux firstly cites “trivially essential properties”. They’re

“properties like being self identical, being red or not red, being coloured if green and being either identical with or distinct from the shape of triangularity”.

Now I don’t mind saying here that I have a very strong aversion to these ostensible properties. Or, more correctly, I have a very strong aversion to them being used in philosophical arguments. Having said that, I don’t want to be a philosophical philistine about them. So perhaps there are profound logical and philosophical consequences to be had from accepting these properties. Then again, Loux may simply accept them because he believes that they are real (or that they have being)— full stop.

So what if the property having no properties (cited by Loux later) is not actually a property at all? Similarly, what if properties like being self-identical or being red or not red (two more examples from Loux) are not properties at all? This must depend on what properties are actually taken to be. In this sense, then, they’re surely abstract if they’re anything. That is, one can’t observe, touch, kick, smell, experiment upon, etc. the property being self-identical or being red or not red.

As stated, all this may entirely depend on what a property actually is. Or, more accurately, all this may entirely depend on what properties are taken to be in these very specific modal and ontological contexts.

From a cursory point of view, it can quickly be seen that trivial properties (of the kind that Loux accepts) must be infinite in number. After all, if there is the property being red or not red, then there must also be the property being blue or not blue. Similarly, if there is the property being either identical with or distinct from the shape of triangularity (an example from Loux himself), then there must also be the property being either identical with or distinct from the shape of a banana. Finally, if there’s a property being colored if green, then there must also be the property being an animal if a human being… and so on ad infinitum.

And then we also have weirder properties such as not being self-identical. And what about the conjunctive property being self-identical and being an apple?

Impure Properties

The American philosopher Albert Casullo refers to what he calls “impure” properties. These are similar — though not identical — to Loux’s trivial properties. He cites “being identical with individual A” as an example.

Now the property being identical with individual A (as well as other impure properties) is different to the trivial properties which Loux argues all objects must have; as well as being different to the properties that just some objects must have (such as being coloured if green). That’s the case because only one object can “have” the property being identical with individual A (at least according to the identity of indiscernibles thesis). Thus the property being the number 4 also fits into this category. Indeed Casullo states that “such properties are obviously unshareable”. Of course a property being unshareable doesn’t automatically make that property suspect. However, it may be suspect anyway.

Casullo himself uses the words “[i]mpure properties, if such there be”. That at the least hints at a degree of scepticism on Casullo’s part.

In any case, Casullo seems to countenance impure properties because he uses them as a means to another philosophical end. (In his case, it’s to show that “individuals [] are ontologically derivative from properties” — see note at the end of this piece.) So perhaps Loux himself is countenancing his own trivial properties for other philosophical ends too. In other words, fake, silly, trivial or impure properties are smuggled into these arguments in order to advance various philosophical arguments which are independent of these supposed properties. Clearly, Loux uses these properties to reject bare objects and to advance his own essentialism. (In Casullo’s case, he uses his impure properties to advance an argument against the bundle theory.)

To give one more example.

I mentioned Alvin Plantinga earlier and he too offers his own seemingly genuine property: existence. This subject has been well-debated in philosophy and Plantinga is fully aware of that fact. So he tells us that “[s]ome philosophers have argued that existence is not a property”. However, Plantinga himself believes that “every object has existence in each world in which it exists”. Here again I’ll only mention Plantinga’s philosophical position on the property existence in passing because it seems similar to Loux’s own positions.

Examples

Example 1

The following is a perfect example of Michael Loux seemingly fusing properties which are contingent with properties which are essential. He writes:

“[T]here is another property they [bare objects] have essentially — the property of having merely contingently the property of having no properties essentially.”

Apart from that passage being hard to understand and it being very strange (at least intuitively), here the terms (or properties) “contingently” and “essentially” are intimately linked to one another.

Loux is arguing here that a contingent property is “essential” to (in this case) a bare object. That is, the contingent property having no properties essentially is essential to the bare object which has that property. What’s more, that essential property is the very property having no properties essentially. Thus a property which is — at least initially — deemed to be contingent is shown to be an essential property. In other words, when an ontologist commits himself to an object which is bare, he’s also committing himself to an object which has no properties. However, Loux argues that this commitment to an object with no properties is an implicit and necessary commitment to that bareness itself being an essential property. It is essential because it’s deemed necessary (if implicitly) that a bare object be bare. And if a bare object is deemed to have no properties necessarily, then it must also have at least one property essentially: the property having no properties essentially.

Of course this may simply be Loux showing us that this position (on bare objects) leads to absurdity (or to a contradiction). That’s unless he’s actually arguing that a bare object has a property that is both contingent and essential. (His other conclusion is that there is no such thing as a genuinely bare object — and that’s precisely because it must have at least one property.)

As hinted at earlier, what if the believer in such a bare object doesn’t see having no properties as being a property at all? What’s more, if he doesn’t believe having no properties is a property, then (by definition) he won’t accept the modal having no properties essentially is a property either.

To go into more detail. Why does Loux stick the word “essentially” on the end of “having no properties”? If the ostensible property having no properties can — at least initially — be seen as being suspect, then the property having no properties essentially is surely an even more suspect property. Yet, of course, Loux is attempting to show us that the commitment to the idea that a bare object must have no properties is also to be commitment to accepting that such a bare object must have no properties essentially.

Thus, is the property having no properties essentially what Loux calls a “trivial essential property”?

Example 2

Michael Loux also asks this question:

“Does a thing with no essence have the property of being essenceless essentially?”

Here again it’s assumed that being essenceless is a property. And because Loux sees it as being a property, then it follows (as least in Loux’s own scheme) that the property being essenceless must be a property of some particular kind. That is, it must either be an essential or a contingent property.

Loux’s first question generates his next statement:

“If not, then apparently it [a bare object] could have had an essence [].”

Loux is arguing that if a bare object having no essential properties is a contingent metaphysical fact, then it’s also possible that this very same bare object could possibly have had an essential property. Thus it’s not necessary that this bare object is without essential properties. Indeed, as we’ve already seen, according to Loux’s scheme this bare object must have at least one property. Indeed that one property turns out to be an essential property!

Loux’s argument (at least here) is specifically about bare objects. However, it still shows us Loux’s fusion of modal terms; as well as his assumption that essential properties are real (or have being). Thus, from seemingly showing that bare objects must have at least one property, Loux then concludes that that at least one property could be an essential property. Taken together, then, Loux offers an argument against the bareness of bare objects; as well as an argument which supports (some kind of) essentialism.

Loux then goes one step further in his fusion of modal terms by bringing in necessity and possibility. He writes:

“[B]ut, then, on any plausible understanding of the notions of necessity and possibility, there is another property that is essential to [this bare object]— that of being possibly essenceless.”

Loux believes that he’s just established that this bare object could possibly have an essential property. Now he simply makes the obvious conclusion that this same bare object could possibly be essenceless. Here we have another property — being possibly essenceless. But what kind of property is that? It seems to be (to use Loux’s own word) trivial.

So Loux is attempting to show that it’s impossible for an object (even an ostensibly bare object) to be essenceless. Yet here he’s discussing the property being possibly essenceless. And of course the property being possibly essenceless can itself be seen as being an essential property!

As earlier, I would question the reality of the property being essenceless. What’s more, being possibly essenceless seems to be an even more suspect property.

Example 3

Michael Loux concludes by saying that

“[n]ecessarily every object has every one of these properties essentially”.

In this particular example of the vicious circle of modal terms we have Loux tying necessity to essence

Loux also tells us that that

“it is a necessary truth that every object has many such properties essentially”.

In other words, Loux has chosen properties that every object must “have”. Specifically, Loux says that every object must be self-identical, red or not red, etc. However, that doesn’t apply to his other example of “being coloured if green”. (Obviously, that property only applies to objects which are green.)

Having said that, Loux does provide us with essential properties which don’t belong to “every object”. He gives the examples of the properties being distinct from the number nine and being non-human. Clearly, the number nine isn’t distinct from the number nine. And humans can’t have the property being non-human.

Finally, Loux arguments are all designed to lead to the following conclusion:

“So it is impossible that there be any entities with no properties essentially.”

Loux’s position that bare objects must have at least one property arises because each bare object must have the property not having any properties. More relevantly, Loux is specifically advancing the position that the property having no properties is an essential property. That is, being committed to an object having no properties is, by default, also a commitment to it having at least one property: having no properties. This leads to contradiction and/or absurdity. Thus Loux concludes that bare objects — and all objects — must have at least one property. Not only that: all objects must have at least one essential property.

To sum up. Loux argues against the position that bare objects have no properties as a means to advance his essentialist position on all objects. That is, Loux believes that all objects must have at least one essential property. Thus Loux is advancing ontological essentialism.

Note:

Casullo’s argument is that the property being identical with individual A incorporates a reference to an individual — individual A. Thus individuals — not properties — seem to be primary.

Things Themselves are Numbers: Contemporary Pythagoreanism

 

In a simple sense, mathematics may be viewed as an extremely useful tool. The English cosmologist, theoretical physicist and mathematician John D. Barrow, however, holds a slightly different view. That is, he posits the view known as Pythagoreanism, summing up the relationship between mathematics and physics in the following way:

“By translating the actual into the numerical we have found the secret to the structure and workings of the Universe.”

So the Universe and its parts are assigned numbers… Or are described by numbers… Or are captured by numbers… Or are explained by numbers… Or are (to use Barrow’s own words) translated into numbers.

But what does all that actually mean?

Sure, if Pythagoreanism holds at least some water, then it’s no wonder that so many people have also believed that through maths (as Barrow puts it) “we have found the secret to the structure and workings of the Universe”. But even here there’s a non-Pythagorean (as it were) remainder. After all, maths finds the secret of things which already exist — i.e., the “structure and workings” of the world. It isn’t actually being argued that these structures and workings are literally maths. The world is not itself maths.

… Or is it?

To the Pythagorean, the world and its parts are actually mathematical. This means that it isn’t that maths is simply helpful for describing the world — the world itself is mathematical. Indeed one must take this literally. Here’s Barrow again on the Pythagorean position:

“[The Pythagoreans] maintained ‘that things themselves are numbers’ and these numbers were the most basic constituents of reality.”

And Barrow then becomes ever clearer when he continues in the following manner:

“What is peculiar about this view is that it regards numbers as being an immanent property of things; that is, number are ‘in’ things and cannot be separated or distinguished from them in any way.”

Moreover:

“It is not that objects merely posses certain properties which can be described by mathematical formulae. Everything, from the Universe as a whole, to each and every one of its parts, was number through and through.”

It’s hard to grasp what the phrase “things themselves are numbers” even means. Can we say that reality and its parts are mathematics (as in the “is of identity”)? That reality and its parts are literally made up of numbers or equations? That reality and its parts somehow instantiate maths, numbers or equations?

And what does it mean to say that “numbers are in things”? Indeed there’s a problem here. If things are literally numbers, then how can numbers also be “in” things? In other words, how can numbers be in themselves? That would be like saying that cats “are in” cats; or that a dog is in the very same dog.

The Unreasonable Effectiveness of Mathematics

The important distinction here is that this isn’t about the “unreasonable effectiveness of mathematics in the natural sciences”. (In which we note the miraculous fact that maths is often a perfect tool for describing the world and then wonder why that is the case.) This is about (to use Barrow’s words again) “the Universe as a whole, [and]each and every one of its parts [being] number through and through”.

Thus description and being are two very different things.

Another way to describe the maths-world relation is to say that (as Barrow again does) that

“mathematics has proved itself a reliable guide to the world in which we live and of which we are a part”.

Yet here again, saying that mathematics is “ reliable guide to the world” is no more of a Pythagorean statement than saying that maths describes the world.

To be clear. A map of Essex is not actually Essex. The set of rules for chess is not an actual game of chess. (Though each game of chess is always — as it were — a variation on the rules of chess.) So it may well be the case that if we didn’t have a map of Essex, then we’d get lost in that county. Similarly, if we didn’t have maths, then we wouldn’t have a reliable guide to the world.

But what of that “miracle” that is math and its relation to the world?

The Hungarian-American theoretical physicist Eugene Wigner (famously) put it this way:

“The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. It is difficult to avoid the impression that a miracle confronts us here, quite comparable… to the two miracles of laws of nature and of the human mind’s capacity to divine them. The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and… there is no rational explanation for it.”

Albert Einstein was similarly perturbed when he wrote:

“How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?”

However, Einstein’s own conclusion appears to be radically at odds with Wigner’s when he continues with the following words:

“In my opinion the answer to this question is, briefly, this: As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”

Despite those sceptical remarks from Einstein, let’s get back to the being I mentioned a while back.

The physicist and cosmologist Max Tegmark puts the contemporary case for (Pythagorean) being in the following very concrete example:

“[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.”

To spell out the above.

Max Tegmark isn’t saying that maths is perfect for describing the “electricity-field strength” in a particular “physical space”. He’s saying that the electricity-field strength is a “mathematical structure”. That is, the maths we use to describe the electricity field is one and the same thing as the electricity field. Thus, if that’s the case, the “miracle of mathematics” is hardly a surprise! That’s because it’s essentially a situation in which that maths is describing maths. And if maths is describing maths, then the word “describing” is surely not apt word to use in the first place.

In any case, Tegmark gives us more detail on his position when he tells us that

“there’s a bunch of numbers at each point in spacetime is quite deep, and I think it’s telling us something not merely about our description of reality, but about reality itself”.

Yet Tegmark appears to contradict himself in the above. At one point he says that a field “is just [ ] something represented by numbers at each point in spacetime”. So here we have the two words “something represented”. Yet elsewhere Tegmark says that the field “is just” (or just is) a mathematical structure — the latter two words implying that all we have is number. To repeat: Tegmark says that the field is “represented” by “three numbers at each point in spacetime”. Yet he doesn’t (in this passage at least) say that the field is a set of numbers (or even a “structure” which includes numbers).

So perhaps there’s a difference between saying that “things themselves are numbers” (as the Pythagoreans did) and saying that the world is mathematical. (I may be drowning in a sea of grammar here.) The latter may simply state that the world exhibits features which are best expressed (or described) by mathematics. The former, on the other hand, says that the world literally is mathematics. But (as already stated) it’s hard to grasp what that even means.