Re: Log i = 0

On 05/25/2025 10:17 AM, sobriquet wrote:

Op 25/05/2025 om 19:03 schreef efji:

Le 25/05/2025 à 18:17, sobriquet a écrit :

Op 25/05/2025 om 18:03 schreef efji:

Le 25/05/2025 à 17:50, sobriquet a écrit :

Op 25/05/2025 om 16:58 schreef efji:

Le 25/05/2025 à 15:02, sobriquet a écrit :

There is no certainty in math. But when you encounter conflicting
claims

>
Well, that's exactly the opposite :)
There is nothing but certainties in math, since everything is
proved in a non-discutable way.

>
Not really.. for instance, there are people who reject proofs by
contradiction, so some proofs might be acceptable to some while
being rejected by others.
Also, things that used to be considered obviously true, like the
shortest distance between two points being a straight line have
later become uncertain (with the potential curvature of geometry as
opposed to flat geometry).
And there is evidence that we can't even have a completely reliable
system where we can prove everything that is true and nothing that
is false, since Gödel has shown that any formal system that
includes basic arithmetic must necessarily be incomplete.

>
Well, that's true about Gödel's theorem: it says that there exists
some propositions that cannot be proven true or false. It does not
imply that what is proved can be "uncertain"!
>
In practice, what we call "maths" in 2025 is totally proved in a
rigorous way, with the proper hypothesis clearly given. The famous
example of the "straight line" is historical and is related to a
period of time where the logical basis of maths where not strongly
established. We are not in the XIX's century any more!
>
99.9999% of mathematicians accept the proofs by contradiction,
and I really wonder what is the point of the remaining 0.0001% :)
>

>
But the same holds for science. It's reasonable to assume that theories
like evolution are proven beyond reasonable doubt, but
philosophically speaking, there is no certainty in science.

>
Yes, there is no certainty in science, EXCEPT in maths !
Take any maths book or article, take any proposition entitled
"Theorem", you know that it is true forever, without any doubt and
without any chance that somebody in 1000 years in the future could
disprove it, whatever "science" will be at this time.
>
>

>
Humans are fallible creatures. Math communities consist of humans.
Conclusion, there is no certainty in math. Though of course it's
extremely unlikely for something to turn out to be false if its proof
has been verified and accepted by the entire community of mathematicians
and has stood the test of time. But there are also other factors
involved. For instance the proof could consist of terabytes of data, so
in that case we might increase our confidence level if we formalize the
proof so it gets checked independently by a computer.
>
In science things approach certainty as results get independently
replicated and confirmed and we have various strategies to eliminate
errors (like double-blind, randomized, placebo-controlled,
peer-reviewed, independently replicated studies).
>
>

It's like, if you haven't heard of the "Principle of
Sufficient Reason", you might want to look into it,
since it's the sort of modern idea of the classical idea
of first principles and final cause.
Then, as for what makes for a "Principle of
Sufficient, and Thorough, Reason", has that
things like "material implication: the quasi-modal"
have been around since at least 0 AD/CE, with the
old-wrapped-as-new bit, then whether it's Plotinus
or Russell, there's Chrysippus with Chrysippus' "moods"
what make the modal, and today there's a modern sort
of relevance logic, about that the quasi-modal is wrong
and the riddle of induction has a deductive answer,
about why a "Principle of Sufficient, and Thorough, Reason",
helps for things like strong mathematical platonism to
arrive at a stronger and justified logicist positivism.
Much of what is called classical is after contradiction,
or when "contradiction, lack thereof", yet usual linear
inductive accounts suffer the "see rule 1" and "see rule end"
bit in the usual accounts of proof-by-contradiction,
thusly instead there's considered that "inverse" beats
"contradiction", because a wider and fuller dialectic,
arrives at turning things over as a knackbaut,
instead of running right down the trails as of
the inductive impasse, when induction may not
complete itself.
Then, usual classical expositions of the superclassical,
like Zeno, establish super-classical (infinitary) reasoning,
since in the infinitary then there are multiple models of
continuous domains, and multiple law(s) of large numbers,
helping advise that some of what are considered well-posed
conjectures, and actually neither way not independent number
theory, so, they're not actually well-posed.
Then, yeah, mathematics is ubiquitously successful in physics,
yet, it's subject the above, and furthermore, a quite thorough
deconstructive account of mathematics.
Perhaps take a look at Derrida and Husserl about
the pre-geometric (then, geometric) world.
Science: is merely not-falsified,
like statistics, is merely not-invalidated.
Then we all have quite a bit of _data_ to keep coherent,
where it makes sense as well that then there's something
at all reasonable, rational, real, and natural about it,
"true".
Thusly this sort "Principle of Sufficient, and Thorough, Reason"
then with "Inverse Contradiction", can help rehabilitate quite
the entire theory for a "paradox-free reason".
That there's a theory at all.