Then there are informal truths: e.g. “the Earth is round”, “the sky is blue”, “Gala apples are red”. You can nitpick them (the Earth isn’t a perfect sphere, the sky is only blue during the day in areas without high pollution, Gala apples may be pinkish or have yellow blotches, or exceptional discoloration), endlessly or until they become formal (possibly by becoming self-referential). But in practice, these are also true (like formal truths; although it’s important to know the difference because…)
The problem is, there’s no line between an informal truth and uncertainty/opinion that isn’t true. Like you know ##FF0000 is red and ##00FF00 is not, but there’s no exact color that separates “red” and “not red” (it depends on person, mood, surroundings…) Consequently, unlike formal truths, informal truths have false implications (“fuzzy logic”). An informal truth can be phrased in a “misleading way”, priming the reader for a false implication (a formal truth can be phrased in a convoluted or unintuitive way, but interpreted formally, never leads to a false implication).
The vast majority of discussion is not formal. Even the smartest people constantly fall for false implications. And this isn’t completely solvable, because we fundamentally can’t formally define everything (too much detail): we tried with GOFAI, it failed and its successor, neural networks, informally defines things like us (by forming a lossy model of the world, then generalizing it).
Except we live in a world where people do argue 2+2 could also be 22 ( Because they use Javascript /s ) Which is basically people believe what they want to believe in. Rationale rarely works.
If we had a radically different perspective (like Borges' Funes the memorious), you can imagine how adding wholly distinct objects might seem ridiculous and derive some other wacky system of arithmetic instead.
Of course, you could alternatively derive it from set theory, but you might also end up with something fundamentally different than what the grandparent intended like presburger or skolem arithmetic.
Furthermore, you can translate “2+2=4” to any other formal system (your examples, “2+2=10 (base 4)”, “2+2=1 (mod 3)”, etc.), and it’s still true.
“2+2=4” is a universal truth, just expressible in different ways.
If you define a system where “2 + 2 = 5”, but also “a square has 5 corners”, “carbon has 5 covalent bonding positions”, etc. your system is coherent, but you actually are stating the abstract property “2 + 2 = 4” in common math, just using the symbol “5” to represent what’s commonly represented as “4”. A bit confusing, a less confusing example is common math, substituting “2” with “B” and “4” with “D”, so “B + B = D, a square has D corners, …”
If you define a system where “2 + 2 = 5, a line segment has 2 ends, a square has 4 corners, 4 < 5”, you’re objectively wrong (unless you’re taking common math and substituting more than digits)…if you extend this system you’ll find contradictions (what happens if you combine 2 parallel line segments of the same length at that length distance?), especially if you try to apply it to the real world.
Curious, do you think quantum physics is the end of the line? I wouldn't claim to have a good understanding of anything beyond classical physics, but I've just assumed it's turtles all the way down and at some point we'll find serious issues with the quantum model
But it’s true enough to detect subtle gravitational waves, build clocks accurate to the nanosecond, and other amazing things.
Especially in tech, for which there are basically only tradeoffs.
I use Zig in most things lately, and I use AI. I have a high quality standard (that AI honestly sometimes makes difficult to meet), but my github has never been more active:
I have a really good code-review skill (which I'm actually in the middle of updating, but it's here): https://github.com/pmarreck/llm_skills/blob/yolo/deep-code-r...
I also have a pretty neat (although arguably janky) way for LLM agents in different tmux terminals to talk to each other: https://github.com/pmarreck/llmsend
My own addendum: the atoms are stories, too.
“There is only a perspectival seeing, only a perspectival ‘knowing’; and the more affects we allow to speak about one thing, the more eyes, different eyes, we can use to observe one thing, the more complete will our ‘concept’ of this thing, our ‘objectivity,’ be.” — Nietzsche:On the Genealogy of Morals III
It's a target. Objectivity does not appear in nature in a stable form. Nothing is fixed and certain. Some things just appear that way from our point of view.
These aren’t truths. It’s cases like “is the earth flat?” that have an answer in objective reality and people still argue about it where some people are simply wrong.
It's what people consider and call a truth. Language terms are defined by use.
And people absolutely argue, fight, unite, or even go to war, for the version of those that they'll consider and call the truth of such matters.
“sincerity in action, character, and utterance” is different than “the body of real things, events, and facts”
This distinction very much exists in how people talk about such things. You don’t need to “have faith” that something like gravity exists such that when you trip you can fall down. “We hold these truths to be self evident” isn’t how you talk about the distance between NYC and Boston.
So? I didn't refer to truth in the former sense.
I said there are several kinds of meanings of the term "truth", and that the one that's about mere facts about things that can be measured objectively (the stricter version of your second definition) is the least interesting one.
The truths of the "We hold these truths to be self evident” variety, the truths of "this proposal is really bad", "this behavior is wrong", "this person is guilty", and many others even more nuanced varieties, are the ones that matter, and for those objective reality is nowhere near the "single source of truth", if it even applies at all.
By acknowledging that nobody considers these objective truths, there’s nothing interesting to say on the topic.
You were playing around with the linguistic ambiguity for whatever reason using a different definition than was used by “There is only a single source of truth and that is objective reality.” and I called you out on it. Thus the subject dies.
On the contrary, that's where most interesting things to say happen in the real social world. From relationships all the way to wars.
>You were playing around with the linguistic ambiguity for whatever reason using a different definition than was used by “There is only a single source of truth and that is objective reality.” and I called you out on it.
Nope, you were limited by the one definition you had in mind, unable to understand that real world, real people, don't constraint themselves to it, and argue regarding the truth or falsehood in all kinds of things that are not bound to "objective reality".
In other words, you pedantically erased most of human life and discource on the truth (not to mention the incovenient other philosophical and dictionary definitions of it) with "well, ahchtually".
Intentionally misunderstanding what someone said is at best wordplay, and wordplay is fucking boring.
Stop being boring.