On 04/28/2024 11:26 AM, olcott wrote:
On 4/28/2024 1:12 PM, Ross Finlayson wrote:
On 04/28/2024 10:10 AM, olcott wrote:
On 4/28/2024 11:13 AM, Richard Damon wrote:
On 4/28/24 11:27 AM, olcott wrote:
On 4/28/2024 10:10 AM, Richard Damon wrote:
On 4/28/24 10:48 AM, olcott wrote:
On 4/28/2024 9:31 AM, Ross Finlayson wrote:
On 04/28/2024 06:10 AM, olcott wrote:
On 4/28/2024 3:36 AM, Mikko wrote:
On 2024-04-27 13:39:50 +0000, olcott said:
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On 4/27/2024 3:24 AM, Mikko wrote:
On 2024-04-26 13:54:05 +0000, olcott said:
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On 4/26/2024 3:32 AM, Mikko wrote:
On 2024-04-25 14:15:20 +0000, olcott said:
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On 4/25/2024 3:16 AM, Mikko wrote:
On 2024-04-25 00:17:57 +0000, olcott said:
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On 4/24/2024 6:01 PM, Richard Damon wrote:
On 4/24/24 11:33 AM, olcott wrote:
On 4/24/2024 3:35 AM, Mikko wrote:
On 2024-04-23 14:31:00 +0000, olcott said:
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On 4/23/2024 3:21 AM, Mikko wrote:
On 2024-04-22 17:37:55 +0000, olcott said:
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On 4/22/2024 10:27 AM, Mikko wrote:
On 2024-04-22 14:10:54 +0000, olcott said:
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On 4/22/2024 4:35 AM, Mikko wrote:
On 2024-04-21 14:44:37 +0000, olcott said:
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On 4/21/2024 2:57 AM, Mikko wrote:
On 2024-04-20 15:20:05 +0000, olcott said:
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On 4/20/2024 2:54 AM, Mikko wrote:
On 2024-04-19 18:04:48 +0000, olcott said:
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When we create a three-valued logic system
that
has these
three values: {True, False, Nonsense}
https://en.wikipedia.org/wiki/Three-valued_logic
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>
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Such three valued logic has the problem
that a
tautology of the
ordinary propositional logic cannot be
trusted to
be true. For
example, in ordinary logic A ∨ ¬A is always
true.
This means that
some ordinary proofs of ordinary theorems
are no
longer valid and
you need to accept the possibility that a
theory
that is complete
in ordinary logic is incomplete in your
logic.
>
>
I only used three-valued logic as a teaching
device. Whenever an
expression of language has the value of
{Nonsense}
then it is
rejected and not allowed to be used in any
logical
operations. It
is basically invalid input.
>
You cannot teach because you lack necessary
skills.
Therefore you
don't need any teaching device.
>
>
That is too close to ad homimen.
If you think my reasoning is incorrect then
point to
the error
in my reasoning. Saying that in your opinion I
am a
bad teacher
is too close to ad hominem because it refers to
your
opinion of
me and utterly bypasses any of my reasoning.
>
No, it isn't. You introduced youtself as a
topic of
discussion so
you are a legitimate topic of discussion.
>
I didn't claim that there be any reasoning,
incorrect
or otherwise.
>
>
If you claim I am a bad teacher you must point
out what
is wrong with
the lesson otherwise your claim that I am a bad
teacher
is essentially
an as hominem attack.
>
You are not a teacher, bad or otherwise. That you
lack
skills that
happen to be necessary for teaching is obvious
from you
postings
here. A teacher needs to understand human
psychology but
you don't.
>
>
You may be correct that I am a terrible teacher.
None-the-less Mathematicians might not have very
much
understanding
of the link between proof theory and computability.
>
Sume mathematicians do have very much
understanding of
that. But that
link is not needed for understanding and solving
problems
separately
in the two areas.
>
When I refer to rejecting an invalid input math
would
seem to construe
this as nonsense, where as computability theory
would
totally understand.
>
People working on computability theory do not
understand
"invalid input"
as "impossible input".
>
The proof then shows, for any program f that might
determine whether
programs halt, that a "pathological" program g,
called with
some input,
can pass its own source and its input to f and then
specifically do the
opposite of what f predicts g will do. No f can exist
that
handles this
case, thus showing undecidability.
https://en.wikipedia.org/wiki/Halting_problem#
>
So then they must believe that there exists an H that
does
correctly
determine the halt status of every input, some inputs
are
simply
more difficult than others, no inputs are impossible.
>
That "must" is false as it does not follow from
anything.
>
>
Sure it does. If there are no "impossible" inputs that
entails
that all inputs are possible. When all inputs are
possible then
the halting problem proof is wrong.
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*Termination Analyzer H is Not Fooled by Pathological
Input D*
https://www.researchgate.net/publication/369971402_Termination_Analyzer_H_is_Not_Fooled_by_Pathological_Input_D
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Everyone that objects to the statement that H(D,D)
correctly
determines the halt status of its inputs say that
believe
that H(D,D) must report on the behavior of the D(D) that
invokes H(D,D).
>
Right, because that IS the definition of a Halt Decider.
>
>
Everyone here takes the definition of a halt decider to be
required to determine the halt status of the program that
invokes this halt decider, knowing full well that the
program
that invokes this halt decider IS NOT ITS INPUT.
>
All these same people also know the computable functions
only
operate on their inputs and are not allowed to consider
anything
else.
>
Computable functions are the formalized analogue of the
intuitive notion
of algorithms, in the sense that a function is computable
if there
exists an algorithm that can do the job of the function,
i.e.
given an
input of the function domain it can return the
corresponding
output.
https://en.wikipedia.org/wiki/Computable_function
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When the definition of a halt decider contradicts the
definition of
a computable function they can't both be right.
>
When the definitions of a term contradicts the
definition of
another term
then both of them are wrong. A correct definition does not
contradict
anything other than a different definition of the same
term.
>
>
*Wrong*
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That "Wrong" is wrong as it refers to a true statement.
>
>
>>> then both of them are wrong.
No it only proves that at least one of them are wrong.
>
A correct definition cannot contradict any other sentence,
including
other defintions as well as any true and false claims. If a
"defintion"
contradicts something then it is not really a definition.
>
>
*That is not the way that it works*
>
Yes, it is. A correct definition does not claim anything, so it
cannot
contradict anything.
>
If a pair of existing definitions
contradict each other then at least one of them is incorrect.
>
If a definition contradicts anything then it is incorrect.
If both of them contradict something then both are incorrect.
>
>
Are you actually paying attention or just glancing at a few
words and then spouting off something?
>
*Here is your reasoning*
Cats are animals
Cats are not animals
therefore Cats are Neither Animals nor Not Animals
>
It might
be the one that you thought was correct.
>
One should not think it was correct as it is not.
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>
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There are at least two kinds of Tertium Non Datur,
>
A xor B
both A and B
neither A nor B
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Notice that it's just Tertium Non Datur about Tertium Non Datur,
and exhausts all possibilities.
>
If you replace terms that are so referential in their types,
or aren't, or in consequence otherwise of the entire structure
of relation all of them together, are and aren't, they do
not model each other and it's thusly not a proof, the same.
>
>
You never got around to saying that I am correct.
When a contradiction arises between two expressions
then at most one of them is correct.
>
Depends on the logic system.
>
Some logic systems allow for two contradictory expressions to both
be correct.
>
Of course, those logic system have a lot of different rules for how
you do logic in them.
>
>
Language can be a mere game where incoherence is allowed or it
can establish the foundation for {true on the basis of meaning}.
In the latter contradictions prove falsehood.
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But there CAN be real meaning even in the presence of "Contradiction".
>
For instance, take the statements:
Light Behaves like a Particle
Light Behaves like a Wave
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These are contradictory, as things acting like a particle do not act
like waves.
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I think that the problem is that you are not in the ballpark of
sufficiently precise in your use of language. This causes you
to continue to make all kinds of fallacy of equivocation errors
that you blame on me.
>
Light behaves lie a particle and light behaves like a wave
cannot possibly be mutually exclusive of they are both true.
>
Light behave like a particle and light never behaves like
a particle is an actual contradiction.
>
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Actually the notion of particle is a nice little concession
or conceit to the theory of atomism, that the real nature
of the objects is as for a phenomenology and including the
finite, the objects of atomism as otherwise vanishing,
in substance, in essence, their existence.
>
It's generally figured that "it's waves", whereas,
besides particle/wave duality, there's also a sort
of, wave/particle wave/resonance dichotomy, as
with regards to molecular mechanics above atomic
mechanics, resonances, with regards to sub-atomic mechanics
and electron physics, field theories.
>
So, that then requires a theory of mathematical
infinities and infinitesimals, and about how
there are at least three definitions of continuous
domains, linear continuums, real numbers, at
least since the time of Aristotle after Euxodox
and for Archimedes and the complete ordered field,
R as it's called, Aristotle and Anaximander and
Archimedes' ring, line-reals, standard infinitesimals
drawing a line from zero to one, then as for since
Poincare and Dirichlet, after Fourier, the signal-reals,
as for Nyquist/Shannon, and signal and information theory.
>
The standard modern mathematics today has one,
it's called R, there are at least three,
definitions of continuous domains, the other
two these days being called "complete metrizing ultrafilters".
Then, fixing that up from resolving the issues in
the foundations proper, as continuity should be very
central and primary in a theory of mathematical objects,
makes for a better theory of the discrete and continuous,
for a better theory of the particle and wave.
>
I think that your problem is that while at the same
time something's broken, you broke something else.
>
Instead, and it's the same criticism for all the
ordinary and the quasi-modal both, there's an
extra-ordinary with a true modality and it's temporality
and a continuum, about infinity, in a theory with
a universe, in a universe.
>
So, particle mechanics, is a stochastic model,
of continuum mechanics.
>
Thusly, the metaphor about it being contradictory,
is contrived, and moot.
>
>
Great !
>
You'll want to stick to exactly, "logical paradoxes",
to solve, with regards to otherwise the usual otherwise
notions of clear-cut decide-ability in closed-categories.
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Sure it's great, it's part of the universe of mathematical
objects and the resulting theory of physics and what's
the science of it given our limitations of observables
in finite time of finite quantities as finite beings.
It's so arrived at from the fuller dialectic of the
thinkers in philosophy, logic, mathematics, science,
probability, and physics, their metaphysics, since
antiquity, and pre-history, as that's thinking for itself,
their schools.
That it _has_ a resolution to _attain_ to, then,
variously does or does not make for that a given
theory does or does not win when there are only
pieces of fragments of shadows of bits,
of those theories.
There is one where it does, though.
It has all of them together, "yet" and since "was".
Thus, this object sense, limns the noumenon
and phenomenon, with abstract theories of
atomism and continuity, and the whole and parts,
and continuous and discrete, and all the great
dichotomies and dualisms, that in the theory
of all what otherwise are, "facts", express
that those are merely, though, strongly as
they may be, "scientific observations".
There is though that the object sense, of
a conscientious (and informed) sort logically
and scientifically, is more than conscious,
and has logic and science as first-class,
and primary, and central objects of the
theory.
I.e. there is never only "read-out",
yet always "interpretation".
This raises us above bacteria and stimulus-response.
Just like some ... scientists, generously,
have "particles a grainy self-contradictory
discrete quantized continuum mechanics",
then, some, ... scientists, grudgingly,
have "my observations entail facts",
that aren't so in metaphor, except as metaphor,
and only the strong metonymy, which is
only accessible and phenomenal with a
conscientious and informed logically
and scientifically object-sense,
for the universe of logical objects.
"Truth", that is.
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