Reality, metaphysics, infinity

 This post arose from 3 articles I read in as many days: 2 on the same specific topic; and 1 on an apparently unrelated topic. I’ll start with the last one first.
 
I’m a regular reader of Raymond Tallis’s column in Philosophy Now, called Tallis in Wonderland, and I even had correspondence with him on one occasion, where he was very generous and friendly, despite disagreements. In the latest issue of Philosophy Now (No 169, Aug/Sep 2025), the title of his 2-page essay is Pharmaco-Metaphysics? Under which it’s stated that he ‘argues against acidic assertions, and doubts DMT assertions.’ Regarding the last point, it should be pointed out that Tallis’s background is in neuroscience.
 
By way of introduction, he points out that he’s never had firsthand experience of psychedelic drugs, but admits to his drug-of-choice being Pino Grigio. He references a quote by William Blake in The Marriage of Heaven and Hell: “If the doors of perception were cleaned, then everything would appear to man as it is, Infinite.” I include this reference, albeit out-of-context, because it has an indirect connection to the other topic I alluded to earlier.
 
Just on the subject of drugs creating alternate realities, which Tallis goes into in more detail than I want to discuss here, he makes the point that the participant knows that there is a reality from which they’ve become adrift; as if they’re in a boat that has slipped its moorings, and has neither a rudder nor oars (my analogy, not Tallis’s). I immediately thought that this is exactly what happens when I dream, which is literally every night, and usually multiple times.
 
Tallis is very good at skewering arguments by extremely bright people by making a direct reference to an ordinary everyday activity that they, and the rest of us, would partake in. I will illustrate with examples, starting with the psychedelic ‘trip’ apparently creating a reality that is more ‘real’ than the one inhabited without the drug.
 
The trip takes place in an unchanged reality. Moreover, the drug has been synthesised, tested, quality-controlled, packaged, and transported in that world, and the facts about its properties have been discovered and broadcast by individuals in the grip of everyday life. It is ordinary people usually in ordinary states of mind in the ordinary world who experiment with the psychedelics that target 5HT2A receptors.
 
He's pointing out an inherent inconsistency, if not outright contradiction (contradictoriness is the term he uses), that the production and delivery of the drug takes place in a world that the recipient’s mind wants to escape from.
 
And the point relevant to the topic of this essay: It does not seem justified, therefore, to blithely regard mind-altering drugs as opening metaphysical peepholes on to fundamental reality; as heuristic devices enabling us to discover the true nature of the world. (my emphasis)
 
To give another example of philosophical contradictoriness (I’m starting to like this term), he references Berkeley:
 
Think, for instance of those who, holding a seemingly solid copy of A Treatise Concerning the Principle of Human Knowledge (1710), accept George Berkeley’s claim [made in the book] that entities exist only insofar as they are perceived. They nevertheless expect the book to be still there when they enter a room where it is stored.
 
This, of course, is similar to Donald Hoffman’s thesis, but that’s too much of a detour.
 
My favourite example that he gives, is based on a problem that I’ve had with Kant ever since I first encountered Kant.
 
[To hold] Immanuel Kant’s view that ‘material objects’ located in space and time in the way we perceive them to be, are in fact constructs of the mind – then travel by train to give a lecture on this topic at an agreed place and time. Or yet others who (to take a well-worn example) deny the reality of time, but are still confident that they had their breakfast before their lunch.
 
He then makes a point I’ve made myself, albeit in a different context.
 
More importantly, could you co-habit in the transformed reality with those to whom you are closest – those who accept without question as central to your everyday life, and who return the compliment of taking you for granted?
 
To me, all these examples differentiate a dreaming state from our real-life state, and his last point is the criterion I’ve always given that determines the difference. Even though we often meet people in our dreams with whom we have close relationships, those encounters are never shared.
 
Tallis makes a similar point:
 
Radically revisionary views, if they are to be embraced sincerely, have to be shared with others in something that goes deeper than a report from (someone else’s) experience or a philosophical text.
 
This is why I claim that God can only ever be a subjective experience that can’t be shared, because it too fits into this category.
 
I recently got involved in a discussion on Facebook in a philosophical group, about Wittgenstein’s claim that language determines the limits of what we can know, which I argue is back-to-front. We are forever creating new language for new experiences and discoveries, which is why experts develop their own lexicons, not because they want to isolate other people (though some may), but because they deal with subject-matter the rest of us don’t encounter.
 
I still haven’t mentioned the other 2 articles I read – one in New Scientist and one in Scientific American – and they both deal with infinity. Specifically, they deal with a ‘movement’ (for want of a better term) within the mathematical community to effectively get rid of infinity. I’ve discussed this before with specific reference to UNSW mathematician, Norman Wildberger. Wildberger recently gained attention by making an important breakthrough (jointly with Dean Rubine using Catalan numbers). However, for reasons given below, I have issues with his position on infinity.
 
The thing is that infinity doesn’t exist in the physical world, or if it does, it’s impossible for us to observe, virtually by definition. However, in mathematics, I’d contend that it’s impossible to avoid. Primes are called the atoms of mathematics and going back to Euclid (325-265BC), he proved that there are an infinite number of primes. The thing is that there are 3 outstanding conjectures involving primes: the Goldbach conjecture; the twin prime conjecture; and the Riemann Hypothesis (which is the most famous unsolved problem in mathematics at the time of writing). And they all involve infinities. If infinities are no longer ‘allowed’, does that mean that all these conjectures are ‘solved’ or does it mean, they will ‘never be solved’?
                                                                                                                    
One of the contentions raised (including by Wildberger) is that infinity has no place in computations – specifically, computations by computers. Wildberger effectively argues that mathematics that can’t be computed is not mathematics (which rules out a lot of mathematics). On the other hand, you have Gregory Chaitin who points out that there are infinitely more incomputable Real numbers than computable Real numbers. I would have thought that this had been settled, since Cantor discovered that you can have countable infinite numbers and uncountable infinite numbers; the latter being infinitely larger than the former.
 
Just today I watched a video by Curt Jaimungal interviewing Chiara Marletto on ‘Constructor Theory’, which to my limited understanding based on this extract from a larger conversation, seems to be premised on the idea that everything in the Universe can be understood if it’s run on a quantum computer. As far as I can tell, she’s not saying it is a computer simulation, but she seems to emulate Stephen Wolfram’s philosophical position that it’s ‘computation all the way down’. Both of these people know a great deal more than me, but I wonder how they deal with chaos theory, which seems to drive the entire universe at multiple levels and can’t be computed due to a dependency on infinitesimal initial conditions. It’s why the weather can’t be forecast accurately beyond 10 days (because it can’t be calculated, no matter how complex the computer modelling) and why every coin-toss is independent of its predecessor (unless you rig it).
 
Note the use of the word, ‘infinitesimal’. I argue that chaos theory is the one phenomenon where infinity meets the real world. I agree with John Polkinghorne that it allows the perfect mechanism for God to intervene in the physical world, even though I don’t believe in an interventionist God (refer Marcus du Sautoy, What We Cannot Know).
 
I think the desire to get rid of infinity is rooted in an unstated philosophical position that the only things that can exist are the things we can know. This doesn’t mean that we currently know everything – I don’t think any mathematician or physicist believes that – but that everything is potentially knowable; I have long disagreed. And this is arguably the distinction between physics and metaphysics. I will take the definition attributed to Plato: ‘That which holds that what exists lies beyond experience.’ In modern science, if not modern philosophy, there is a tendency to discount metaphysics, because, by definition, it exists beyond what we experience in the real world. You can see an allusion here to my earlier discussion on Tallis’s essay, where he juxtaposes reality as we experience it with psychedelic experiences that purportedly provide a window into an alternate reality, where ‘everything would appear to man as it is, Infinite’. Where infinity represents everything we can’t know in the world we inhabit.
 
The thing is that I see mathematics as the only evidence of metaphysics; the only connection our minds have between a metaphysical world that transcends the Universe, and the physical universe we inhabit and share with innumerable other sentient creatures, albeit on a grain of sand on an endless beach, the horizon of which we’re yet to discern.
 
So I see this transcendental, metaphysical world of endless possible dimensions as the perfect home for infinity. And without mathematics, we would have no evidence, let alone a proof, that infinity even exists.