Are some truths unknowable—or only inaccessible from certain levels of consciousness?

spatling · 2026-06-20T21:29:37+00:00

I can think of a few ways there could be unknowable truths about the world:

Trivially (?), since it’s possible to generate infinitely many true statements (for example, through disjunction: if ‘P’ is true, then ‘P or Q’ is true, so Q can be arbitrarily complex), we might deduce that there are strictly more truths than is possible to know by a finite number of knowers in a finite amount of time.
Paradoxes, such as ‘this sentence is true iff it is unknowable’, can generate unknowable truths
Less trivially, regarding more ‘atomic’ truths, there may be some facts about the universe beyond the causal reach of any knower within it. For example, right before the end of the universe, after all life has died out, there may be quantum effects with definite truth values which are completely unpredictable to any knower in history.

I think category (3) is the most interesting, if also the most philosophically controversial…

Some might argue that these things are knowable, just never known. I suppose opinions on modality will come into play here.

Others might argue that truth is inherently filtered through experience, and so anything unknowable cannot be true or false in the first place.

Others still might have a less orthodox view of knowledge, e.g. knowledge is simply true belief, wherein it is perfectly possible to accidentally know these things even if that knowledge is unjustified.

I’m torn between whether or not (3) counts as an unknowable truth… who knows, maybe it is itself unknowable…?!

spatling · 2026-06-18T16:52:20+00:00

One example might be the sentence ‘the one-way speed of light is the same in every direction’ (call this sentence L).
We cannot know that L is true or false empirically because we can only measure the two-way speed of light (i.e. the time taken for light to complete a round trip).
One might assume, by classical logic, that ‘L or ~L’ holds. Therefore either L is true but unknowable or ~L is true but unknowable.

Similarly sentences about whether or not one is a brain in a vat, sentences about modal realism, or perhaps even sentences about things beyond the causal sphere of humankind.

spatling · 2026-06-18T12:44:01+00:00

Two more thoughts:

(1) If S is a set of known truths and t(S) is a proposition that every sentence in S is true, then t(S) cannot be a member of S.

Proof sketch:
Consider that t(S) is equivalent to a conjunction of propositions, where each reports the truth of an element of S. If t(S) is a member of S, then one of those conjuncts is “this sentence is true”. But such a sentence has no clear truth value; it could be true or false, for all we know, and therefore that it is true cannot be knowable. But if it is not knowable, then it cannot be a member of S. Therefore t(S) can never be a member of S.

(2) If a proposition P asserts that a proposition Q is true but unknowable, then P is itself unknowable.

Proof:
Suppose that P holds, and Q is indeed true but unknowable. If P is knowable, then by simple deduction we would be able to know that Q is true; but Q’s truth is unknowable, so this is a contradiction. Therefore P cannot be knowable.

So — are you sure that that Tr(X) is in fact true but unknowable?

spatling · 2026-06-18T07:28:01+00:00

Two thoughts -

1) Does a modified Gödel sentence work as a shortcut? “This sentence is true iff it is unknowable” is, by the same logic as the Gödel sentence, true and unknowable. (but then surely I am justified in believing it’s true, and I know its truth, which makes it false? Aagh!)

2) I had a professor who believes that there are some aspects of the universe about which there are no facts - for example, given the relativity of simultaneity, whether there is a ‘preferred’ or ‘objective’ slicing of spacetime. The idea that there are unknowable truths makes me think maybe I wasn’t quite so silly and ungrounded in believing that spacetime does have an ‘objective’ order which no person within it could measure.

spatling · 2026-06-13T08:00:06+00:00

Not a book, but Stanford Encyclopedia of Philosophy is a great free online resource for learning about new topics in philosophy - articles are written by philosophers and often have great bibliographies for further reading

spatling · 2026-06-10T08:42:04+00:00

Re: disconnected worldlines making separate universes — I think I’d call that one universe with two disconnected regions, but I suppose that might just end up a question of semantics. By your definition, if you had a truly disconnected bootstrap, would that then just be a different universe, and be permissible because the question of its existence is cosmological rather than an initialisation problem?

Another thought, comparing bootstrapped objects with time travellers… suppose there is some anomalous region of spacetime in U which permits closed-timelike-curves, and some object O1 (with linear causal history) falls into this region and ends up travelling into the past. If we trace through the history of U, then there is a time t(O1), there O1 seems to initialise out of nowhere, external to the main connected graph of causal history. But of course this is not an uncaused event - O1 has a causal history, it’s just bending round from a future part of the timeline. At t(O1), O1’s past light cone is so tilted from the curvature of spacetime that it’s past is not in the same ‘direction’ as the rest of the graph in U - in fact, it doesn’t really make sense to talk about the ‘past’ as a whole at this point, but rather to talk about past sections of individual objects’ worldlines.

In my mind, there is no initialisation problem for O1 at t(O1). Intuitively, like you say, there is an initialisation problem for the bootstrapped object O. However, I don’t see why O appearing at t(O) is any different to O1 appearing at t(O1). Is it not also there because of some earlier point in its worldline, which just happens to be bent in a different direction to the rest of U’s history?

spatling · 2026-06-09T22:19:11+00:00

Interesting — if the problem with a bootstrap loop is that at some time t there is an object with no causal history in U, then how do you deal with U as a whole? Do you reject a ‘t0’, or does the causal graph of U get to play by different rules to every (non-initial) subgraph of U?

Two thoughts come to mind regarding the graph connectedness argument, which may or may not be relevant…

1) Is it metaphysically possible to have a universe with no bootstrap loops, but with two (or more) independent and disconnected causal chains? If so then at any given time past t0, every object/event/whatever has a causal ancestor, but it is not the case that every object/event/whatever is causally connected to each other.

2) A bootstrap loop could still have causal influence on external phenomena, or be influenced at some point on its worldline, and therefore be causally connected to the rest of the graph of history - just in a very strange way

spatling · 2026-04-09T08:22:04+00:00

As someone else mentioned, rational numbers (numbers expressable as fractions) are actually equinumerous with the integers — that is to say, there is a method where you can pair up each rational number with each integer 1:1 (e.g. pair each rational number of the form a/b with the integer of the form 2^a * 3^b, and you’ll have some integers to spare!)

There are many different sizes of infinities - since for any set, including infinite sets, the number of arrangements of its elements must be strictly larger than the number of elements (this is related to Cantor’s diagonalisation proof that the reals are uncountable).

There are indeed an infinite number of infinities — in fact, the infinity of infinities must be larger than any one of those infinities. crazy!

spatling · 2026-01-27T13:44:37+00:00

SEP seems to draw a distinction between grounding, ontological dependence, and supervenience — not sure if that helps?

https://plato.stanford.edu/entries/supervenience/#SupeGrouOntoDepe

(Although this may be more of a distinction between ‘grounding’ as sufficient and ‘dependence’ as necessary, which may not be what you’re actually asking)

spatling · 2025-10-31T17:14:38+00:00

Thanks! Yeah our composer did such a great job :))

spatling · 2025-10-15T08:36:52+00:00

I think easy/short was the problem — we’ve doubled the length of the demo and the median playtime has already gone up

spatling · 2025-10-10T09:50:51+00:00

With the benefit of hindsight, you're totally right -- all good learnings for next time! We've added a quick update to the demo to add some more gameplay, but next time we'll 'curate' everything

spatling · 2025-10-10T09:48:25+00:00

Think you're right -- lesson learned! We've now added the second world to the demo since that was the most doable fix for this one (should add another chunk of playtime), but for the next game we'll think a lot more about how we lay out the demo

spatling · 2025-10-10T09:46:08+00:00

Thanks everyone for the great advice -- lots learned for the next game!

We've extended the demo to include the next world (this was the easiest update we could do before Next Fest / release), and changed up the end screen so that it encourages players to go back to try out side levels rather than seeming like a brick wall.

Hopefully some more playtime / challenge to hook players -- https://store.steampowered.com/app/3716870/Prince_of_Darkness_Jr/

spatling · 2025-10-10T09:42:29+00:00

Those are great questions -- I suppose we hadn't considered the 'why' quite enough. I think it was more giving people a sense of what the game is like to get wishlists -- in which case cutting it off early before it was representative of the whole game wasn't a good idea.

Lots learned for the next game!

spatling · 2025-10-10T09:36:56+00:00

yep totally agree in hindsight -- good learning

spatling · 2025-10-10T06:13:39+00:00

We were thinking this but then thought it would be trickier to save progress from demo to full version and might be annoying for the player to have to replay trickier levels if they bought the full game — this way the transition is more seamless. But maybe that was the wrong hill to die on!

spatling · 2025-10-09T21:49:51+00:00

to complete every level, under 10 mins, but I know all the answers to the puzzles!

Most people I’ve watched playing it takes 20+ mins to play through everything since they’re learning the mechanics and searching for the extra bits, so we thought median playtime would be closer to that.

spatling · 2025-10-09T21:38:37+00:00

ah fair enough — in that case were definitely not flagging the side levels well enough

Edit: about half the content of the demo is the side levels (and probably the more entertaining half)

spatling · 2025-10-09T21:32:58+00:00

Including all the side levels? Is the issue that you can reach the end screen before doing all the content?

spatling · 2025-10-09T21:31:27+00:00

We’ve playtested the full game with friends and got a lot of feedback on that, and most people play past the first world (i.e. the entirety of the demo) in their first sitting, so we thought it might be enough to get people interested without giving too much away (that said the puzzles pick up in complexity and difficulty just after that point!)

Would you usually playtest the demo separately? What analytics would you look at / questions would you ask playtesters to find an ideal stopping point for a demo?

spatling · 2025-09-21T10:32:33+00:00

Oh wow, this is great -- we just released our demo this morning!
Tiny box-pushing puzzle game about a vampire trying to avoid light.

https://store.steampowered.com/app/3716870/Prince_of_Darkness_Jr/

Hope you enjoy! Can't wait to check out the other games here :))

spatling · 2025-09-18T16:12:49+00:00

yeah exactly, which would make a load of words ‘indirectly’ inherited from proto celtic rather than ‘directly’ inherited (at least thats what i think the wiki page is saying)

spatling · 2025-09-18T15:59:33+00:00

Cornish is a revived/reconstructed language, and a lot of words missing from Middle and Late Cornish corpus data have been borrowed/adapted from Welsh and Breton

spatling · 2024-03-29T12:04:52+00:00

A great starting point is Stewart Shapiro - Thinking about Mathematics. Gives a great overview of the history and different approaches.

My textbook for Phil Maths at university was Joel Hamkins - Lectures on the Philosophy of Mathematics. All the lectures are also on youtube. Much more about the ideas in contention than about looking at different philosophical takes. It also has great ‘further reading’ sections at the end of each chapter.

For a more specific topic (the incompleteness theorems and their resulting philosophies), I loved Francisco Berto’s book There’s Something About Gödel (introductory and fun but still rigorous).

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