To clarify, there are formal truths: widely-accepted hard science, e.g. “2 + 2 = 4”. Technically, there’s a point where we can’t fundamentally prove anything (“if a tree falls and nobody hears it, does it make a sound?”), and rarely we get things wrong (e.g. classical physics)….but in practice, these are true, end of discussion.

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).

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ahepp a day ago | parent | next [-]

> rarely we get things wrong (e.g. classical physics)

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

	▲	armchairhacker a day ago \| parent [-]
		I think you’re right and quantum physics is false in some subtle way. We already found experiments that contradict existing theories in quantum physics, e.g. https://en.wikipedia.org/wiki/Cosmological_constant_problem But it’s true enough to detect subtle gravitational waves, build clocks accurate to the nanosecond, and other amazing things.

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ksec a day ago | parent | prev | next [-]

>widely-accepted hard science, e.g. “2 + 2 = 4”.

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.

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d4ng a day ago | parent | prev [-]

2+2=4 is only a formal truth up to the axioms of arithmetic and how we denote numbers. The statement is not statement with regards to objective reality.

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tremon 15 hours ago | parent | next [-]

The statement is a formal truth exactly because it only exists inside the symbolic universe constructed by humans, not despite.

	▲	d4ng 6 hours ago \| parent [-]
		You are right.

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fooqux a day ago | parent | prev [-]

You're being pendantic. Choose whatever symbol you want for "2" and "4". The point is that if you have symbol apples and someone gives you symbol more, than you have an agreed-upon number in total.

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AlotOfReading 18 hours ago | parent | next [-]

It's not being pedantic. With different assumptions you can make a system where 2 + 2 = 0 and it turns out to be extremely useful. You can also build a system where 2 + 2 = 22 like the other commenter lampoons and the free monoid that corresponds to is again useful.

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.

	▲	armchairhacker 17 hours ago \| parent [-]
		But “2+2=4”, in the specific formal system that is common arithmetic, is true. 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.

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d4ng 18 hours ago | parent | prev [-]

Agreed-upon, as in subjective.

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armchairhacker 15 hours ago | parent [-]

The objectivity is in the relations.

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.

	▲	d4ng 7 hours ago \| parent [-]
		You are not objectively wrong. You have simply defined an incoherent abstract system in language. The claim you have made simply does not compute in the system in question. Regardless, that claim is not a claim about the objective world, however that may be defined.