Re: The philosophy of logic reformulates existing ideas on a new basis ---

olcott <polcott333@gmail.com> wrote:

On 11/8/2024 5:58 AM, Alan Mackenzie wrote:

In comp.theory olcott <polcott333@gmail.com> wrote:

On 11/6/2024 2:34 PM, Alan Mackenzie wrote:

In comp.theory olcott <polcott333@gmail.com> wrote:

On 11/6/2024 10:45 AM, Alan Mackenzie wrote:

[ .... ]

There is another sense in which something could be a lie.  If, for
example, I emphatically asserted some view about the minutiae of
medical surgery, in opposition to the standard view accepted by
practicing surgeons, no matter how sincere I might be in that
belief, I would be lying.  Lying by ignorance.

That is a lie unless you qualify your statement with X is a
lie(unintentional false statement). It is more truthful to
say that statement X is rejected as untrue by a consensus of
medical opinion.

No, as so often, you've missed the nuances.  The essence of the
scenario is making emphatic statements in a topic which requires
expertise, but that expertise is missing.  Such as me laying down the
law about surgery or you doing the same in mathematical logic.

It is not at all my lack of expertise on mathematical logic
it is your ignorance of philosophy of logic as shown by you
lack of understanding of the difference between "a priori"
and "a posteriori" knowledge.

Garbage.

Surgical procedures and mathematical logic are in fundamentally
different classes of knowledge.

But the necessity of expertise is present in both, equally.  Emphatically
to assert falsehoods when expertise is lacking is a form of lying.  That
is what you do.

This allows for the possibility that the consensus is not
infallible. No one here allows for the possibility that the
current received view is not infallible. Textbooks on the
theory of computation are NOT the INFALLIBLE word of God.

Gods have got nothing to do with it.  2 + 2 = 4, the fact that the
world is a ball, not flat, Gödel's theorem, and the halting problem,
have all been demonstrated beyond any doubt whatsoever.

Regarding the last two they would have said the same thing about
Russell's Paradox and what is now known as naive set theory at the
time.

There's no "would have said" regarding Russell's paradox.  Nobody would
have asserted the correctness of naive set theory, a part of mathematics
then at the forefront of research and still in flux.  We've moved beyond
that point in the last hundred years.

And you are continually stating that theorems like 2 + 2 = 4 are false.

That is a lie. I never said anything like that and you know it.

Now who's lying?  You have frequently denied the truth of proven
mathematical facts like 2 + 2 = 4.  As I have continually made clear in
my posts "like 2 + 2 = 4" includes the halting theorem, Gödel's theorem,
and Tarski's theorem.

Here is what I actually said:

When the operations are limited to applying truth preserving
operations to expressions of language that are stipulated to
be true then
True(L,x) ≡ (L ⊢ x) and False(L, x) ≡ (L ⊢ ~x)

Then
(Incomplete(L) ≡  ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
becomes
(¬TruthBearer(L,x) ≡  ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
Incompleteness utterly ceases to exist

Incompleteness is an essential property of logic systems which can do
anything at all.  If what you assert is true (which I doubt), then your
system would be incapable of doing anything useful.

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

--
Alan Mackenzie (Nuremberg, Germany).