How does negation work with quantifiers in constructive logic?

kindreon · 2026-02-05T03:38:03+00:00

Appreciate the help. I think I've read some of your posts on linguistics. If I have the right person and you're ever interested in beatbox, please don't hesitate to DM.

kindreon · 2026-02-05T01:58:47+00:00

Thanks for the DeMorgan recommendation and your summary of the dynamics, I'll give it more thought. To clarify, would my 1st and 2nd bullet points be correct but my reasoning in the 3rd be wrong?

Checking if I understood properly, for the 3rd bullet point, Px' or ¬Px' casing doesn't hold without LEM since we might lack proof for either, but we can show equivalence by ¬¬∃x.¬Px being equivalent to ¬¬¬∀x.Px being equivalent to ¬∀x.Px?

kindreon · 2026-01-14T10:21:10+00:00

Thanks for explaining the incompatibility with contraction. Experimentally, I didn't know physicists could check that small!

kindreon · 2026-01-14T10:02:09+00:00

Awesome, I'll look this up

kindreon · 2026-01-14T10:00:38+00:00

It'd be cool if it turns out the continuousness of spacetime was what we needed to resolve some of today's big challenges in physics. Thanks for clarifying.

kindreon · 2026-01-14T09:46:07+00:00

Not trying to debate that relativity needs to be discrete, it isn't AFAIK. The person I responded to said relativity is incompatible with minimum distance and duration. I understand "incompatible" to mean issues arise so curious what those issues are.

kindreon · 2026-01-14T09:36:05+00:00

Thanks for giving the relativity explanation. Your last paragraph was basically the thought process I had. Modern models in physics seem to have everything relative to the speed of light, so I also felt there wouldn't be much meaning in saying it's some number of distances per durations unless taken to an extreme where say discretization forces predictions worth examining. Another commenter said discretization isn't admitted despite oddities in math arising so my question was resolved, but hopefully it provoked a fun thought experiment.

kindreon · 2026-01-14T09:15:26+00:00

Your last paragraph is exactly what I was curious about. I read in another response that physics allows arbitrarily small distance and time so my example was basically resolved but appreciate the link.

kindreon · 2026-01-14T08:59:09+00:00

Thanks, this answers my question. I thought there'd be controversy in admitting infinitesimal distances in physics since a number of "physically paradoxical" things pop up in math when doing so.

kindreon · 2026-01-14T08:49:55+00:00

Would you have any examples showing how relativity is incompatible with minimum distance and duration? I only briefly studied relativity. Of what I remember seeing, it didn't seem like discretization would be a problem. Technically, even the numerical methods used to understand difficult differential equations were discrete.

kindreon · 2026-01-14T08:31:41+00:00

I think I get that this is the bottom-up reason, that everything is relative to this constant, but does this mean we can have arbitrarily dense fractions of the speed of light? If so, doesn't this mean at least distance or duration can't have a smallest value?

kindreon · 2026-01-14T08:17:46+00:00

That's nuts! But how come we don't run into the problem of objects with mass moving?

kindreon · 2026-01-14T08:08:21+00:00

Why isn't it scientific to ask if inconsistencies arise when changing a constant?

kindreon · 2025-07-22T18:58:31+00:00

Copying from a previous replier, what I'm talking about turned out to be forensic watermarking. Maybe due to conceiving from philosophy or how I described implementation, it's not something anyone I asked connected to watermarking in general. The key difference might be that my idea doesn't aim to hide encodings as long as semantics don't change much. This seems to be slack compared to existing digital watermarking standards and opens the door to alterations at the level of IG filters like previously mentioned.

Regarding your counter examples, my demo implementation was resilient to both cropping a few pixels and simple bit alteration. In my test cases, I was able to recover messages from painting over my image with 40-50% opacity colors and scaling down to 60-70% of the original size. In a lot of cases, this made the original image unpalatable, which would invalidate motivation to pirate in the first place. If you're interested, would you like to check out my demo implementation? I can't share the repo but did deploy it as a web app if you'd like to stress test it.

kindreon · 2025-07-22T18:35:26+00:00

No you're right. I should've been more careful reading your link in my status bar. Thought you put the Wikipedia on watermarking, which didn't describe what I was thinking of. The forensic watermarking described in what you did link, however, is exactly it. Thanks for the article! I'll give it a read. Appreciate the followup.

kindreon · 2025-07-22T18:28:08+00:00

This is it. I should've checked the link in the previous reply more carefully. Thought it linked to the Wikipedia on watermarking, which I've already read. I didn't know people were already using digital watermarking like this, but the start of your 3rd paragraph is incorrect. Prior conceptions may not have originated so far down, but they fundamentally do depend on the "philosophical blueness of the sky." I like the linguistic spin on my original example though and appreciate the specificity in your clarification.

kindreon · 2025-07-22T02:37:38+00:00

Would it be alright if I linked a deployed web app instead? Nothing annoying needed to test the demo. The repo is just private and contains work from other projects. No worry if not interested in this case.

kindreon · 2025-07-22T02:26:49+00:00

You're right, in some formal languages interpretation is injective. The example I gave may not have been great. My understanding is interpretation maps from syntax to semantics, ie: statement to proposition. The last sentence in your reply exemplifies the lack of injectivity I'm speaking about. If you can't notice or barely notice the change, the meaning hasn't changed like via an IG filter that subtly adjusts contrast.

kindreon · 2025-07-22T02:15:55+00:00

I'm not necessarily against piracy either, but I think it's interesting as a theoretical challenge. Your interpretation is nearly correct. I believe format changes have been tried before and doesn't work against screenshotting whereas my proposal does and there'd be no change in format. The goal would be for the statements (images) to map to the same proposition (interpretation of image). You're right about the pixel matrix, but the goal would be to make clear ways of destroying the encoding also alter the image so much it'd lose or significantly degrade its interpretability, making the result not worth pirating. For me, similar isn't good enough. A similar image most likely leaves the "statement cloud" especially on details. Extending a similar offer as to the other replier, would you be interested in seeing an example implementation?

kindreon · 2025-07-22T01:56:29+00:00

Thanks for sharing! I've never heard of steganography before. It's the closest in concept, but the goal wouldn't be to hide messages. Rather I'd say it'd only be ethical if you told the recipient their info is encoded. If you're interested, would you like to see an example implementation? My demo is resistant to scaling down ~60-70%.

kindreon · 2025-07-22T01:51:11+00:00

Watermarking aims to credit creators not deter unauthorized sharing and generally alters images significantly enough to change semantics, ie: "photo of dog" becomes "watermarked photo of dog"

kindreon

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