Re: truth of experience
On 12 Mar 2014, at 21:14, meekerdb wrote:
On 3/12/2014 8:33 AM, Bruno Marchal wrote:
Hello Terren,
On 12 Mar 2014, at 04:34, Terren Suydam wrote:
Hi Bruno,
Thanks, that helps. Can you expand a bit on t? Unfortunately I
haven't had the time to follow the modal logic threads, so please
forgive me but I don't understand how you could represent reality
with t.
Shortly, A most general meaning is that the proposition A is
possible.
Modal logician uses the word world in a very general sense, it
can mean situation, state, and actually it can mean anything.
To argue for example that it is possible that a dog is dangerous,
would consist in showing a situation, or a world, or a reality in
which a dog is dangerous.
so you can read A, as A is possible, or possible(A), with the
idea that this means that there is a reality in which A is true.
Reality is not represented by A, it is more the existence of a
reality verifying a proposition.
In particular, t, which is t is possible, where t is the
constant true, or 1=1 in arithmetic, simply means that there is a
reality.
t is possible looks like a category error to me.
t is equivalent with (p - p), it is the constant boolean valued
function true. So t is an admissible atomic formula and applies
to all formula.
In the arithmetical interpretation (of the modal logic G), t is
consistent('~(0=1)'), that is ~beweisbar('~(0=1)').
NOT PROVABLE FALSE = CONSISTENT TRUE.
~[]f = t
This is standard use, in both modal logic and meta-arithmetic.
A is possible means A refers to the state of some world.
No. It refers to a state, or to a world, or to a number, or to a cow.
At this abstraction level, some world looks like a 1004 distracting
pseudo-information. We are not doing metaphysics, just math, which
then is applied to formulate the comp measure problem, and get quantum
logic from there.
I don't see that t or 1=1 refers to some world, they are just
tautologies, artifacts of language.
t is indeed a tautology, that is a proposition true (by definition) in
all possible worlds (a world here is simply a function from the set
of atomic sentences letter in {0, 1}, or {false, true}.
But 1=1 cannot be deduced from logic alone, and you need primitive
terms, like s and 0, to name the non trivial object s(0), and you need
some axioms on equality, =. Usually x = x, is an axiom.
In particular 1 = 1 does refer to a reality, which is the usual
(standard) model of arithmetic, denoted by the mathematical structure
(N, +, x).
1=1 is supposed to refer to that (mathematical) reality.
This, Aristotle and Leibniz understood, but Kripke enriched the
notion of possibility by making the notion of possibility
relative to the world you actually are.
Somehow, for the machine talking in first predicate logic, like PA
and ZF, more can be said, once we interpret the modal box by the
Gödelian beweisbar('p'), which can be translated in arithmetic.
First order theories have a nice metamathematical property,
discovered by Gödel (in his PhD thesis), and know as completeness,
which (here) means that provability is equivalent with truth in all
models, where models are mathematical structure which can verify or
not, but in a well defined mathematical sense, a formula of
classical first order logical theories.
For example PA proves some sentences A, if and only if, A is true
in all models of PA.
If []A is provability (beweisbar('A')), the dual A is consistency
(~beweisbar('~A').
A = ~[]~A.
~A is equivalent with A - f (as you can verify by doing the
truth table)
A = ~[]~A = ~([](A - f))
Saying that you cannot prove a contradiction (f), from A, means
that A is consistent.
So t means, for PA, with the arithmetical translation
~beweisbar('~t'), = ~beweisbar('f'), that PA is consistent, and by
Gödel completeness theorem, this means that there is a mathematical
structure (model) verifying 1=1.
So, although ~beweisbar('~t'), is an arithmetical proposition
having some meaning in term of syntactical object (proofs)
existence, it is also a way for PA, or Löbian entities, to refer,
implicitly at first, to the existence of a reality.
But why should the failure to prove f imply anything about reality?
Because it preserves the hope that there is a reality to which you are
connected.
If you prove 1=1 in classical logic, you can prove anything, you get
inconsistent. There might still be a reality, but you are not
connected to it.
You are in a cul-de-sac world, when seen in Kripke semantics of G.
But don't take this in any literal way, except in terms of the
behavior, including discourse of the machine.
The theory is correct for any arithmetically effective machines having
sound extension beliefs of those beliefs:
0 ≠ (x + 1)
((x + 1) = (y + 1)) - x = y
x + 0 = x
x + (y + 1) = (x + y) + 1
x * 0 = 0
x * (y + 1) = (x * y) + x
+ the induction
Re: truth of experience
On 12 Mar 2014, at 21:51, LizR wrote: On 13 March 2014 04:33, Bruno Marchal marc...@ulb.ac.be wrote: Hello Terren, On 12 Mar 2014, at 04:34, Terren Suydam wrote: Hi Bruno, Thanks, that helps. Can you expand a bit on t? Unfortunately I haven't had the time to follow the modal logic threads, so please forgive me but I don't understand how you could represent reality with t. Shortly, A most general meaning is that the proposition A is possible. Modal logician uses the word world in a very general sense, it can mean situation, state, and actually it can mean anything. To argue for example that it is possible that a dog is dangerous, would consist in showing a situation, or a world, or a reality in which a dog is dangerous. so you can read A, as A is possible, or possible(A), with the idea that this means that there is a reality in which A is true. Reality is not represented by A, it is more the existence of a reality verifying a proposition. In particular, t, which is t is possible, where t is the constant true, or 1=1 in arithmetic, simply means that there is a reality. You mean t asserts there is a reality in which the relevant proposition is true (e.g. one in which the dog is dangerous) ? Exactly. (Although possible(dog is dangerous) is more (dog-is- dangerous) than t, which is more like possible(dog is dog). That's Kripke semantics: A is true in alpha IF THERE IS A REALITY beta verifying A. so t is true in alpha if there is a reality beta verifying t. Now, Kripke semantics extends classical propositional logic, and t is verified in all worlds. So, if alpha verifies t (if t is true in alpha), then t means simply that there is some world beta accessible (given that t is true in all world). t = truth is possible = I am consistent = there is a reality out there = I am connected to a reality =truth is accessible. Note that this well captured by modal logic, but also by important theorem for first order theories. In particular Gödel completeness theorem, which can put in this way: a theory is consistent if and only the theory has a model. Gödel completeness (two equivalent versions): - provable(p) (in a theory) entails p is true in all models of the theory. - consistent(p) (in a theory) entails there is at least one model in which p is verified (true). Bruno -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: truth of experience
On 3/13/2014 8:19 AM, Bruno Marchal wrote:
On 12 Mar 2014, at 21:14, meekerdb wrote:
On 3/12/2014 8:33 AM, Bruno Marchal wrote:
Hello Terren,
On 12 Mar 2014, at 04:34, Terren Suydam wrote:
Hi Bruno,
Thanks, that helps. Can you expand a bit on t? Unfortunately I haven't had the
time to follow the modal logic threads, so please forgive me but I don't understand
how you could represent reality with t.
Shortly, A most general meaning is that the proposition A is possible.
Modal logician uses the word world in a very general sense, it can mean situation,
state, and actually it can mean anything.
To argue for example that it is possible that a dog is dangerous, would consist in
showing a situation, or a world, or a reality in which a dog is dangerous.
so you can read A, as A is possible, or possible(A), with the idea that this
means that there is a reality in which A is true.
Reality is not represented by A, it is more the existence of a reality verifying
a proposition.
In particular, t, which is t is possible, where t is the constant true, or 1=1
in arithmetic, simply means that there is a reality.
t is possible looks like a category error to me.
t is equivalent with (p - p), it is the constant boolean valued function true. So t
is an admissible atomic formula and applies to all formula.
In the arithmetical interpretation (of the modal logic G), t is consistent('~(0=1)'),
that is ~beweisbar('~(0=1)').
NOT PROVABLE FALSE = CONSISTENT TRUE.
~[]f = t
This is standard use, in both modal logic and meta-arithmetic.
A is possible means A refers to the state of some world.
No. It refers to a state, or to a world, or to a number, or to a cow. At this
abstraction level, some world looks like a 1004 distracting pseudo-information. We are
not doing metaphysics, just math, which then is applied to formulate the comp measure
problem, and get quantum logic from there.
I don't see that t or 1=1 refers to some world, they are just tautologies,
artifacts of language.
t is indeed a tautology, that is a proposition true (by definition) in all possible
worlds (a world here is simply a function from the set of atomic sentences letter in
{0, 1}, or {false, true}.
But 1=1 cannot be deduced from logic alone, and you need primitive terms, like s and
0, to name the non trivial object s(0), and you need some axioms on equality, =.
Usually x = x, is an axiom.
In particular 1 = 1 does refer to a reality, which is the usual (standard) model of
arithmetic, denoted by the mathematical structure (N, +, x).
1=1 is supposed to refer to that (mathematical) reality.
This, Aristotle and Leibniz understood, but Kripke enriched the notion of
possibility by making the notion of possibility relative to the world you actually are.
Somehow, for the machine talking in first predicate logic, like PA and ZF, more can be
said, once we interpret the modal box by the Gödelian beweisbar('p'), which can be
translated in arithmetic.
First order theories have a nice metamathematical property, discovered by Gödel (in
his PhD thesis), and know as completeness, which (here) means that provability is
equivalent with truth in all models, where models are mathematical structure which can
verify or not, but in a well defined mathematical sense, a formula of classical first
order logical theories.
For example PA proves some sentences A, if and only if, A is true in all models
of PA.
If []A is provability (beweisbar('A')), the dual A is consistency
(~beweisbar('~A').
A = ~[]~A.
~A is equivalent with A - f (as you can verify by doing the truth table)
A = ~[]~A = ~([](A - f))
Saying that you cannot prove a contradiction (f), from A, means that A is
consistent.
So t means, for PA, with the arithmetical translation ~beweisbar('~t'),
= ~beweisbar('f'), that PA is consistent, and by Gödel *_completeness_* theorem, this
means that there is a mathematical structure (model) verifying 1=1.
So, although ~beweisbar('~t'), is an arithmetical proposition having some meaning in
term of syntactical object (proofs) existence, it is also a way for PA, or Löbian
entities, to refer, implicitly at first, to the existence of a reality.
But why should the failure to prove f imply anything about reality?
Because it preserves the hope that there is a reality to which you are
connected.
If you prove 1=1 in classical logic, you can prove anything, you get inconsistent.
There might still be a reality, but you are not connected to it.
Above you deflect the criticism of a category error by saying, We are not doing
metaphysics, just math, which then is applied to formulate the comp measure problem, and
get quantum logic from there. But then it turns out you really are doing metaphysics.
You are taking a tautology in mathematics and using it to infer things about reality and
your relation to it.
Brent
You are in a cul-de-sac world, when seen in Kripke semantics of G. But
Re: truth of experience
On 3/13/2014 8:33 AM, Bruno Marchal wrote: On 12 Mar 2014, at 21:51, LizR wrote: On 13 March 2014 04:33, Bruno Marchal marc...@ulb.ac.be mailto:marc...@ulb.ac.be wrote: Hello Terren, On 12 Mar 2014, at 04:34, Terren Suydam wrote: Hi Bruno, Thanks, that helps. Can you expand a bit on t? Unfortunately I haven't had the time to follow the modal logic threads, so please forgive me but I don't understand how you could represent reality with t. Shortly, A most general meaning is that the proposition A is possible. Modal logician uses the word world in a very general sense, it can mean situation, state, and actually it can mean anything. To argue for example that it is possible that a dog is dangerous, would consist in showing a situation, or a world, or a reality in which a dog is dangerous. so you can read A, as A is possible, or possible(A), with the idea that this means that there is a reality in which A is true. Reality is not represented by A, it is more the existence of a reality verifying a proposition. In particular, t, which is t is possible, where t is the constant true, or 1=1 in arithmetic, simply means that there is a reality. You mean t asserts there is a reality in which the relevant proposition is true (e.g. one in which the dog is dangerous) ? Exactly. (Although possible(dog is dangerous) is more (dog-is-dangerous) than t, which is more like possible(dog is dog). That's Kripke semantics: A is true in alpha IF THERE IS A REALITY beta verifying A. so t is true in alpha if there is a reality beta verifying t. Now, Kripke semantics extends classical propositional logic, and t is verified in all worlds. This is a point that confuses me in trying your exercises (which I'm attempting to do without reading your exchanges with Liz). There you refer to a formula being respected when it is true in all worlds for all valuations. But does all valuations of a formula A include f when A=p-p? Are we to assume that t is a formula in all worlds and it's value is always t? And then is f also a formula in every world? Brent So, if alpha verifies t (if t is true in alpha), then t means simply that there is some world beta accessible (given that t is true in all world). t = truth is possible = I am consistent = there is a reality out there = I am connected to a reality =truth is accessible. Note that this well captured by modal logic, but also by important theorem for first order theories. In particular Gödel completeness theorem, which can put in this way: a theory is consistent if and only the theory has a model. Gödel completeness (two equivalent versions): - provable(p) (in a theory) entails p is true in all models of the theory. - consistent(p) (in a theory) entails there is at least one model in which p is verified (true). Bruno -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com mailto:everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com mailto:everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. http://iridia.ulb.ac.be/~marchal/ http://iridia.ulb.ac.be/%7Emarchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com mailto:everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com mailto:everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: truth of experience
On 13 Mar 2014, at 17:56, meekerdb wrote:
On 3/13/2014 8:19 AM, Bruno Marchal wrote:
On 12 Mar 2014, at 21:14, meekerdb wrote:
On 3/12/2014 8:33 AM, Bruno Marchal wrote:
Hello Terren,
On 12 Mar 2014, at 04:34, Terren Suydam wrote:
Hi Bruno,
Thanks, that helps. Can you expand a bit on t? Unfortunately
I haven't had the time to follow the modal logic threads, so
please forgive me but I don't understand how you could represent
reality with t.
Shortly, A most general meaning is that the proposition A
is possible.
Modal logician uses the word world in a very general sense, it
can mean situation, state, and actually it can mean anything.
To argue for example that it is possible that a dog is
dangerous, would consist in showing a situation, or a world, or a
reality in which a dog is dangerous.
so you can read A, as A is possible, or possible(A), with
the idea that this means that there is a reality in which A is
true.
Reality is not represented by A, it is more the existence of
a reality verifying a proposition.
In particular, t, which is t is possible, where t is the
constant true, or 1=1 in arithmetic, simply means that there is
a reality.
t is possible looks like a category error to me.
t is equivalent with (p - p), it is the constant boolean valued
function true. So t is an admissible atomic formula and
applies to all formula.
In the arithmetical interpretation (of the modal logic G), t is
consistent('~(0=1)'), that is ~beweisbar('~(0=1)').
NOT PROVABLE FALSE = CONSISTENT TRUE.
~[]f = t
This is standard use, in both modal logic and meta-arithmetic.
A is possible means A refers to the state of some world.
No. It refers to a state, or to a world, or to a number, or to a
cow. At this abstraction level, some world looks like a 1004
distracting pseudo-information. We are not doing metaphysics, just
math, which then is applied to formulate the comp measure problem,
and get quantum logic from there.
I don't see that t or 1=1 refers to some world, they are just
tautologies, artifacts of language.
t is indeed a tautology, that is a proposition true (by definition)
in all possible worlds (a world here is simply a function from
the set of atomic sentences letter in {0, 1}, or {false, true}.
But 1=1 cannot be deduced from logic alone, and you need
primitive terms, like s and 0, to name the non trivial object s(0),
and you need some axioms on equality, =. Usually x = x, is an
axiom.
In particular 1 = 1 does refer to a reality, which is the usual
(standard) model of arithmetic, denoted by the
mathematical structure (N, +, x).
1=1 is supposed to refer to that (mathematical) reality.
This, Aristotle and Leibniz understood, but Kripke enriched the
notion of possibility by making the notion of possibility
relative to the world you actually are.
Somehow, for the machine talking in first predicate logic, like
PA and ZF, more can be said, once we interpret the modal box by
the Gödelian beweisbar('p'), which can be translated in
arithmetic.
First order theories have a nice metamathematical property,
discovered by Gödel (in his PhD thesis), and know as
completeness, which (here) means that provability is equivalent
with truth in all models, where models are mathematical structure
which can verify or not, but in a well defined mathematical
sense, a formula of classical first order logical theories.
For example PA proves some sentences A, if and only if, A is true
in all models of PA.
If []A is provability (beweisbar('A')), the dual A is
consistency (~beweisbar('~A').
A = ~[]~A.
~A is equivalent with A - f (as you can verify by doing the
truth table)
A = ~[]~A = ~([](A - f))
Saying that you cannot prove a contradiction (f), from A, means
that A is consistent.
So t means, for PA, with the arithmetical translation
~beweisbar('~t'), = ~beweisbar('f'), that PA is consistent, and
by Gödel completeness theorem, this means that there is a
mathematical structure (model) verifying 1=1.
So, although ~beweisbar('~t'), is an arithmetical proposition
having some meaning in term of syntactical object (proofs)
existence, it is also a way for PA, or Löbian entities, to refer,
implicitly at first, to the existence of a reality.
But why should the failure to prove f imply anything about reality?
Because it preserves the hope that there is a reality to which you
are connected.
If you prove 1=1 in classical logic, you can prove anything, you
get inconsistent. There might still be a reality, but you are not
connected to it.
Above you deflect the criticism of a category error by saying, We
are not doing metaphysics, just math, which then is applied to
formulate the comp measure problem, and get quantum logic from
there. But then it turns out you really are doing metaphysics.
You are taking a tautology in mathematics and using it to infer
Re: truth of experience
On 13 Mar 2014, at 18:03, meekerdb wrote: On 3/13/2014 8:33 AM, Bruno Marchal wrote: On 12 Mar 2014, at 21:51, LizR wrote: On 13 March 2014 04:33, Bruno Marchal marc...@ulb.ac.be wrote: Hello Terren, On 12 Mar 2014, at 04:34, Terren Suydam wrote: Hi Bruno, Thanks, that helps. Can you expand a bit on t? Unfortunately I haven't had the time to follow the modal logic threads, so please forgive me but I don't understand how you could represent reality with t. Shortly, A most general meaning is that the proposition A is possible. Modal logician uses the word world in a very general sense, it can mean situation, state, and actually it can mean anything. To argue for example that it is possible that a dog is dangerous, would consist in showing a situation, or a world, or a reality in which a dog is dangerous. so you can read A, as A is possible, or possible(A), with the idea that this means that there is a reality in which A is true. Reality is not represented by A, it is more the existence of a reality verifying a proposition. In particular, t, which is t is possible, where t is the constant true, or 1=1 in arithmetic, simply means that there is a reality. You mean t asserts there is a reality in which the relevant proposition is true (e.g. one in which the dog is dangerous) ? Exactly. (Although possible(dog is dangerous) is more (dog-is- dangerous) than t, which is more like possible(dog is dog). That's Kripke semantics: A is true in alpha IF THERE IS A REALITY beta verifying A. so t is true in alpha if there is a reality beta verifying t. Now, Kripke semantics extends classical propositional logic, and t is verified in all worlds. This is a point that confuses me in trying your exercises (which I'm attempting to do without reading your exchanges with Liz). There you refer to a formula being respected when it is true in all worlds for all valuations. But does all valuations of a formula A include f when A=p-p? No, the valuations are defined only on the atomic p, q, r, (in modal propositional logic). Then the arbitrary formula get their value by the truth table, and the modal formula get their value by the Kripke semantics, that is, the truth values of the boxed an diamonded propositions depends on the locally accessible worlds. Are we to assume that t is a formula in all worlds and it's value is always t? Yes. It is a boolean constant. You can suppress it and replaced it by (p - p), as this is true in all words (as this is true in the worlds where p is true, and is true in the worlds where p is false). And then is f also a formula in every world? You can represent it by (p ~p), or just ~t, and it is false in every world. The cul-de-sac worlds get close, as they verify []f. Fortunately they don't verify []A - A. f is never met, in any world, but you can met []f, [][]f, [][][]f, ... G* proves ◊[]f, ◊[][]f,◊[][][]f, ... in the G-worlds. (Do everyone see a lozenge here: ◊ ?) Bruno Brent So, if alpha verifies t (if t is true in alpha), then t means simply that there is some world beta accessible (given that t is true in all world). t = truth is possible = I am consistent = there is a reality out there = I am connected to a reality =truth is accessible. Note that this well captured by modal logic, but also by important theorem for first order theories. In particular Gödel completeness theorem, which can put in this way: a theory is consistent if and only the theory has a model. Gödel completeness (two equivalent versions): - provable(p) (in a theory) entails p is true in all models of the theory. - consistent(p) (in a theory) entails there is at least one model in which p is verified (true). Bruno -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com . Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything- l...@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email
Re: truth of experience
On 3/13/2014 11:43 AM, Bruno Marchal wrote: On 13 Mar 2014, at 18:03, meekerdb wrote: On 3/13/2014 8:33 AM, Bruno Marchal wrote: On 12 Mar 2014, at 21:51, LizR wrote: On 13 March 2014 04:33, Bruno Marchal marc...@ulb.ac.be mailto:marc...@ulb.ac.be wrote: Hello Terren, On 12 Mar 2014, at 04:34, Terren Suydam wrote: Hi Bruno, Thanks, that helps. Can you expand a bit on t? Unfortunately I haven't had the time to follow the modal logic threads, so please forgive me but I don't understand how you could represent reality with t. Shortly, A most general meaning is that the proposition A is possible. Modal logician uses the word world in a very general sense, it can mean situation, state, and actually it can mean anything. To argue for example that it is possible that a dog is dangerous, would consist in showing a situation, or a world, or a reality in which a dog is dangerous. so you can read A, as A is possible, or possible(A), with the idea that this means that there is a reality in which A is true. Reality is not represented by A, it is more the existence of a reality verifying a proposition. In particular, t, which is t is possible, where t is the constant true, or 1=1 in arithmetic, simply means that there is a reality. You mean t asserts there is a reality in which the relevant proposition is true (e.g. one in which the dog is dangerous) ? Exactly. (Although possible(dog is dangerous) is more (dog-is-dangerous) than t, which is more like possible(dog is dog). That's Kripke semantics: A is true in alpha IF THERE IS A REALITY beta verifying A. so t is true in alpha if there is a reality beta verifying t. Now, Kripke semantics extends classical propositional logic, and t is verified in all worlds. This is a point that confuses me in trying your exercises (which I'm attempting to do without reading your exchanges with Liz). There you refer to a formula being respected when it is true in all worlds for all valuations. But does all valuations of a formula A include f when A=p-p? No, the valuations are defined only on the atomic p, q, r, (in modal propositional logic). Then the arbitrary formula get their value by the truth table, and the modal formula get their value by the Kripke semantics, that is, the truth values of the boxed an diamonded propositions depends on the locally accessible worlds. Then t and f cannot be treated as atomic propositions, which was my objection to writing t. In such a formula, t can only be regarded as shorthand for some tautology. So t doesn't mean There is some reality it means There is some tautology: a proposition that is t in virtue of the definition of relations , V, ~, etc. Are we to assume that t is a formula in all worlds and it's value is always t? Yes. It is a boolean constant. You can suppress it and replaced it by (p - p), as this is true in all words (as this is true in the worlds where p is true, and is true in the worlds where p is false). And then is f also a formula in every world? You can represent it by (p ~p), or just ~t, and it is false in every world. The cul-de-sac worlds get close, as they verify []f. Fortunately they don't verify []A - A. f is never met, in any world, but you can met []f, [][]f, [][][]f, ... G* proves ◊[]f, ◊[][]f,◊[][][]f, ... in the G-worlds. You say (p ~p) is false in every world, but f is never met in any world. That seems contradictory. If p is a proposition in some world, are we not always allowed to form (p ~p), which will have the value f for all valuations of p? (Do everyone see a lozenge here: ◊ ?) I see it. Brent -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: truth of experience
(Do everyone see a lozenge here: ◊ ?) Yes I do! -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: truth of experience
On Fri, Mar 14, 2014 at 10:10:45AM +1300, LizR wrote: (Do everyone see a lozenge here: ◊ ?) Yes I do! Not me (alas). Although it is visible when typing my response. Cheers -- Prof Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Professor of Mathematics hpco...@hpcoders.com.au University of New South Wales http://www.hpcoders.com.au -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: truth of experience
On 13 Mar 2014, at 20:05, meekerdb wrote: On 3/13/2014 11:43 AM, Bruno Marchal wrote: On 13 Mar 2014, at 18:03, meekerdb wrote: On 3/13/2014 8:33 AM, Bruno Marchal wrote: On 12 Mar 2014, at 21:51, LizR wrote: On 13 March 2014 04:33, Bruno Marchal marc...@ulb.ac.be wrote: Hello Terren, On 12 Mar 2014, at 04:34, Terren Suydam wrote: Hi Bruno, Thanks, that helps. Can you expand a bit on t? Unfortunately I haven't had the time to follow the modal logic threads, so please forgive me but I don't understand how you could represent reality with t. Shortly, A most general meaning is that the proposition A is possible. Modal logician uses the word world in a very general sense, it can mean situation, state, and actually it can mean anything. To argue for example that it is possible that a dog is dangerous, would consist in showing a situation, or a world, or a reality in which a dog is dangerous. so you can read A, as A is possible, or possible(A), with the idea that this means that there is a reality in which A is true. Reality is not represented by A, it is more the existence of a reality verifying a proposition. In particular, t, which is t is possible, where t is the constant true, or 1=1 in arithmetic, simply means that there is a reality. You mean t asserts there is a reality in which the relevant proposition is true (e.g. one in which the dog is dangerous) ? Exactly. (Although possible(dog is dangerous) is more (dog-is- dangerous) than t, which is more like possible(dog is dog). That's Kripke semantics: A is true in alpha IF THERE IS A REALITY beta verifying A. so t is true in alpha if there is a reality beta verifying t. Now, Kripke semantics extends classical propositional logic, and t is verified in all worlds. This is a point that confuses me in trying your exercises (which I'm attempting to do without reading your exchanges with Liz). There you refer to a formula being respected when it is true in all worlds for all valuations. But does all valuations of a formula A include f when A=p-p? No, the valuations are defined only on the atomic p, q, r, (in modal propositional logic). Then the arbitrary formula get their value by the truth table, and the modal formula get their value by the Kripke semantics, that is, the truth values of the boxed an diamonded propositions depends on the locally accessible worlds. Then t and f cannot be treated as atomic propositions, Why? Pi is constant, but still a (real) number. Why could we not have constant proposition? which was my objection to writing t. In such a formula, t can only be regarded as shorthand for some tautology. If you want. Any simple provable proposition would do. So t doesn't mean There is some reality it means There is some tautology: a proposition that is t in virtue of the definition of relations , V, ~, etc. t means, in Kripke semantics, that there is a world in which t is true (and as t is true in any world, it does mean that there is a world. Then when A is the diamond consistency of A, it means that there is a model verufying A, by Gödel's completeness theorem. Bruno Are we to assume that t is a formula in all worlds and it's value is always t? Yes. It is a boolean constant. You can suppress it and replaced it by (p - p), as this is true in all words (as this is true in the worlds where p is true, and is true in the worlds where p is false). And then is f also a formula in every world? You can represent it by (p ~p), or just ~t, and it is false in every world. The cul-de-sac worlds get close, as they verify []f. Fortunately they don't verify []A - A. f is never met, in any world, but you can met []f, [][]f, [][] []f, ... G* proves ◊[]f, ◊[][]f,◊[][][]f, ... in the G- worlds. You say (p ~p) is false in every world, but f is never met in any world. That seems contradictory. If p is a proposition in some world, are we not always allowed to form (p ~p), which will have the value f for all valuations of p? (Do everyone see a lozenge here: ◊ ?) I see it. Brent -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group
Re: truth of experience
On 13 Mar 2014, at 22:10, LizR wrote: (Do everyone see a lozenge here: ◊ ?) Yes I do! Nice, I hope everyone see it. Does someone not see a lozenge? Here: ◊ Do someone not see Gödel's second theorem here: ◊t - ~[]◊t ? Bruno -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: truth of experience
On 14 Mar 2014, at 01:49, Russell Standish wrote: On Fri, Mar 14, 2014 at 10:10:45AM +1300, LizR wrote: (Do everyone see a lozenge here: ◊ ?) Yes I do! Not me (alas). Damned. I will need to use the more ugly instead of the cute ◊ ! No problem. Bruno Although it is visible when typing my response. Cheers -- Prof Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Professor of Mathematics hpco...@hpcoders.com.au University of New South Wales http://www.hpcoders.com.au -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: truth of experience
On 3/13/2014 9:54 PM, Bruno Marchal wrote: which was my objection to writing t. In such a formula, t can only be regarded as shorthand for some tautology. If you want. Any simple provable proposition would do. Then f also occurs in every world since (p ~p) can be formed in every world. But you say we never meet f in any world? Brent So t doesn't mean There is some reality it means There is some tautology: a proposition that is t in virtue of the definition of relations , V, ~, etc. t means, in Kripke semantics, that there is a world in which t is true (and as t is true in any world, it does mean that there is a world. Then when A is the diamond consistency of A, it means that there is a model verufying A, by Gödel's completeness theorem. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: truth of experience
On 14 Mar 2014, at 06:08, meekerdb wrote: On 3/13/2014 9:54 PM, Bruno Marchal wrote: which was my objection to writing t. In such a formula, t can only be regarded as shorthand for some tautology. If you want. Any simple provable proposition would do. Then f also occurs in every world since (p ~p) can be formed in every world. But you say we never meet f in any world? I meant that f, like (p ~p), is FALSE in every world. By met it I mean met it true. Bruno Brent So t doesn't mean There is some reality it means There is some tautology: a proposition that is t in virtue of the definition of relations , V, ~, etc. t means, in Kripke semantics, that there is a world in which t is true (and as t is true in any world, it does mean that there is a world. Then when A is the diamond consistency of A, it means that there is a model verufying A, by Gödel's completeness theorem. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: truth of experience
to the question if we are dreaming or not, or more generally, if we are wrong or not. Brains that are defective in this manner result in schizophrenia and presumably other dissociative pathologies. OK. For me it all casts doubt on whether Bp p is an accurate formalization for experience, but I might be missing something. As I said above, it is a simplest meta definition which capture the main thing (the truth of the experience) without needing to define it. Also, for the physical first person *experience*, Bp p, which is only the knower, is not enough, you will need Bp t p, which by incompleteness has its own logic, quantum like when restricted to the sigma_1 truth. You need a reality (t). Can you make sense of Bp p for a schizophrenic who hears voices? If a schizophrenic says that he hears voices, and if he hears voice (mentally, virtually, arithmetically, brain-biologically, ...), then he knows he hears voice. An insane guy who says that he is Napoleon does not know that he is napoleon, but he believes it only. He still might know that he believes being Napoleon, and be only ignorant or denying that this is false. How about your own salvia experiences? It is very hard to describe, even more to interpret. And I am biased. It is indeed: [](... what-the-f.) and ... what the f. Most plausibly. It is like remembering forgotten qualia since eons. It might confirms the idea that brains, machines, words, theories filter consciousness only. Consciousness would be a close sister of (arithmetical) truth. Salvia might open the appetite for platonism, but of course it is also a question of taste. Bruno T On Mon, Mar 10, 2014 at 3:26 PM, Bruno Marchal marc...@ulb.ac.be wrote: On 10 Mar 2014, at 16:28, Terren Suydam wrote: Question for you Bruno:. You say (with help from Theaetetus) that 1p experience is given by Bp p. Yet, our experience is often deluded, as in optical illusions, or in various kinds of emotional psychological denial. Can we ever really say that our knowledge, even 1p experience, refers to anything True? In public? No. In private? Yes. I would say. Then in the frame of theories about such 1p things, like consciousness, we can decide to agree on some property of the notion. Then, consciousness-here-and-now might be a candidate for a possible true reference, if you agree consciousness-here-and-now is undoubtable or incorrigible. Then we can approximate many sort of truth, by the very plausible, the probable, the relatively expectable, etc. If someone complains, is the pain real or fake? Eventually it is a question for a judge. The truth is what no machine can really grasp the whole truth, but all machines can know very well some aspect of it, I think, but very few in justifiable modes. Bruno -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything- l...@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: truth of experience
On 3/12/2014 8:33 AM, Bruno Marchal wrote:
Hello Terren,
On 12 Mar 2014, at 04:34, Terren Suydam wrote:
Hi Bruno,
Thanks, that helps. Can you expand a bit on t? Unfortunately I haven't had the time
to follow the modal logic threads, so please forgive me but I don't understand how you
could represent reality with t.
Shortly, A most general meaning is that the proposition A is possible.
Modal logician uses the word world in a very general sense, it can mean situation,
state, and actually it can mean anything.
To argue for example that it is possible that a dog is dangerous, would consist in
showing a situation, or a world, or a reality in which a dog is dangerous.
so you can read A, as A is possible, or possible(A), with the idea that this means
that there is a reality in which A is true.
Reality is not represented by A, it is more the existence of a reality verifying a
proposition.
In particular, t, which is t is possible, where t is the constant true, or 1=1 in
arithmetic, simply means that there is a reality.
t is possible looks like a category error to me. A is possible means A refers to the
state of some world. I don't see that t or 1=1 refers to some world, they are just
tautologies, artifacts of language.
This, Aristotle and Leibniz understood, but Kripke enriched the notion of possibility
by making the notion of possibility relative to the world you actually are.
Somehow, for the machine talking in first predicate logic, like PA and ZF, more can be
said, once we interpret the modal box by the Gödelian beweisbar('p'), which can be
translated in arithmetic.
First order theories have a nice metamathematical property, discovered by Gödel (in his
PhD thesis), and know as completeness, which (here) means that provability is equivalent
with truth in all models, where models are mathematical structure which can verify or
not, but in a well defined mathematical sense, a formula of classical first order
logical theories.
For example PA proves some sentences A, if and only if, A is true in all models
of PA.
If []A is provability (beweisbar('A')), the dual A is consistency
(~beweisbar('~A').
A = ~[]~A.
~A is equivalent with A - f (as you can verify by doing the truth table)
A = ~[]~A = ~([](A - f))
Saying that you cannot prove a contradiction (f), from A, means that A is
consistent.
So t means, for PA, with the arithmetical translation ~beweisbar('~t'),
= ~beweisbar('f'), that PA is consistent, and by Gödel *_completeness_* theorem, this
means that there is a mathematical structure (model) verifying 1=1.
So, although ~beweisbar('~t'), is an arithmetical proposition having some meaning in
term of syntactical object (proofs) existence, it is also a way for PA, or Löbian
entities, to refer, implicitly at first, to the existence of a reality.
But why should the failure to prove f imply anything about reality?
Brent
Of course, when asked about t, the sound machines stay mute (Gödel's *_first
incompleteness_* theorem), and eventually, the Löbian one, like PA and ZF, explains why
they stay mute, by asserting
t - ~[]t (Gödel's *_second_* *_incompleteness_*).
This is capital, as it means that []p, although it implies p, that implication cannot
be proved by the machine, so that to a get a probability on the relative consistent
extension, the less you can ask, is p, and by incompleteness, although both []p and
[]p p, will prove the same arithmetical propositions, they will obey different logics.
More on this later. When you grasp the link between modal logic and Gödel, you can see
that modal logic can save a lot of work. Modal logic does not add anything to the
arithmetical reality, nor even to self-reference, but it provides a jet to fly above the
arithmetical abysses, even discover them, including their different panorama, when
filtered by local universal machines/numbers. As there are also modal logics capable of
representing quantum logic(s), modal logics can help to compare the way nature selects
the observable-possibilities, and the computable, or sigma_1 arithmetical selection
enforced, I think, by computationalism.
Bruno
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Re: truth of experience
On 13 March 2014 04:33, Bruno Marchal marc...@ulb.ac.be wrote: Hello Terren, On 12 Mar 2014, at 04:34, Terren Suydam wrote: Hi Bruno, Thanks, that helps. Can you expand a bit on t? Unfortunately I haven't had the time to follow the modal logic threads, so please forgive me but I don't understand how you could represent reality with t. Shortly, A most general meaning is that the proposition A is possible. Modal logician uses the word world in a very general sense, it can mean situation, state, and actually it can mean anything. To argue for example that it is possible that a dog is dangerous, would consist in showing a situation, or a world, or a reality in which a dog is dangerous. so you can read A, as A is possible, or possible(A), with the idea that this means that there is a reality in which A is true. Reality is not represented by A, it is more the existence of a reality verifying a proposition. In particular, t, which is t is possible, where t is the constant true, or 1=1 in arithmetic, simply means that there is a reality. You mean t asserts there is a reality in which the relevant proposition is true (e.g. one in which the dog is dangerous) ? -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
truth of experience
Hi Bruno, Sure, consciousness here-and-now is undoubtable. But the p refers to the contents of consciousness, which is not undoubtable in many cases. I am in pain cannot be doubted when one is feeling it, but other felt sensations can be doubted, e.g. see http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2956899/ Such illusions of experience can even be helpful, as in Ramachandran's Mirror Box therapy for phantom limb sufferers, see http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3468806/ Illusions of experience are evidence that what we experience is of our brains' constructions, like a waking dream, guided in healthy brains by the patterns of information streaming from our sense organs. Brains that are defective in this manner result in schizophrenia and presumably other dissociative pathologies. For me it all casts doubt on whether Bp p is an accurate formalization for experience, but I might be missing something. Can you make sense of Bp p for a schizophrenic who hears voices? How about your own salvia experiences? T On Mon, Mar 10, 2014 at 3:26 PM, Bruno Marchal marc...@ulb.ac.be wrote: On 10 Mar 2014, at 16:28, Terren Suydam wrote: Question for you Bruno:. You say (with help from Theaetetus) that 1p experience is given by Bp p. Yet, our experience is often deluded, as in optical illusions, or in various kinds of emotional psychological denial. Can we ever really say that our knowledge, even 1p experience, refers to anything True? In public? No. In private? Yes. I would say. Then in the frame of theories about such 1p things, like consciousness, we can decide to agree on some property of the notion. Then, consciousness-here-and-now might be a candidate for a possible true reference, if you agree consciousness-here-and-now is undoubtable or incorrigible. Then we can approximate many sort of truth, by the very plausible, the probable, the relatively expectable, etc. If someone complains, is the pain real or fake? Eventually it is a question for a judge. The truth is what no machine can really grasp the whole truth, but all machines can know very well some aspect of it, I think, but very few in justifiable modes. Bruno -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: truth of experience
On Tuesday, March 11, 2014 12:10:31 PM UTC-4, Terren Suydam wrote: Hi Bruno, Sure, consciousness here-and-now is undoubtable. But the p refers to the contents of consciousness, which is not undoubtable in many cases. I am in pain cannot be doubted when one is feeling it, but other felt sensations can be doubted, e.g. see http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2956899/ Such illusions of experience can even be helpful, as in Ramachandran's Mirror Box therapy for phantom limb sufferers, see http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3468806/ Illusions of experience are evidence that what we experience is of our brains' constructions, Illusions are only evidence that experience has multiple layers of reference and expectation, and the brain conditions affect those layers. That doesn't mean that the brain is constructing anything though (except for neurotransmitters). If what we experience is a construction, then that means the entire universe could be a construction, including the expectation of a universe which is either 'illusory' or not. like a waking dream, guided in healthy brains by the patterns of information streaming from our sense organs. Brains that are defective in this manner result in schizophrenia and presumably other dissociative pathologies. For me it all casts doubt on whether Bp p is an accurate formalization for experience, but I might be missing something. Can you make sense of Bp p for a schizophrenic who hears voices? How about your own salvia experiences? As far as I can tell, Bp p is a fragile notion that has been generalized from from formalities within communication and has very little to do with experience. It is a radically normative and narrow consideration of only one aspect of consciousness. Craig T On Mon, Mar 10, 2014 at 3:26 PM, Bruno Marchal mar...@ulb.ac.bejavascript: wrote: On 10 Mar 2014, at 16:28, Terren Suydam wrote: Question for you Bruno:. You say (with help from Theaetetus) that 1p experience is given by Bp p. Yet, our experience is often deluded, as in optical illusions, or in various kinds of emotional psychological denial. Can we ever really say that our knowledge, even 1p experience, refers to anything True? In public? No. In private? Yes. I would say. Then in the frame of theories about such 1p things, like consciousness, we can decide to agree on some property of the notion. Then, consciousness-here-and-now might be a candidate for a possible true reference, if you agree consciousness-here-and-now is undoubtable or incorrigible. Then we can approximate many sort of truth, by the very plausible, the probable, the relatively expectable, etc. If someone complains, is the pain real or fake? Eventually it is a question for a judge. The truth is what no machine can really grasp the whole truth, but all machines can know very well some aspect of it, I think, but very few in justifiable modes. Bruno -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: truth of experience
Hi Terran, On 11 Mar 2014, at 17:10, Terren Suydam wrote: Hi Bruno, Sure, consciousness here-and-now is undoubtable. But the p refers to the contents of consciousness, which is not undoubtable in many cases. I am in pain cannot be doubted when one is feeling it, but other felt sensations can be doubted, e.g. see http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2956899/ Such illusions of experience can even be helpful, as in Ramachandran's Mirror Box therapy for phantom limb sufferers, see http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3468806/ Illusions of experience are evidence that what we experience is of our brains' constructions, like a waking dream, guided in healthy brains by the patterns of information streaming from our sense organs. Exactly: like a walking dream. That's the root of the Bp p idea, in the Theaetetus. To do the math I concentrate to rich (Löbian) machine for the B, but the idea of defining knowledge by true belief is an act of modesty with respect to the question if we are dreaming or not, or more generally, if we are wrong or not. Brains that are defective in this manner result in schizophrenia and presumably other dissociative pathologies. OK. For me it all casts doubt on whether Bp p is an accurate formalization for experience, but I might be missing something. As I said above, it is a simplest meta definition which capture the main thing (the truth of the experience) without needing to define it. Also, for the physical first person *experience*, Bp p, which is only the knower, is not enough, you will need Bp t p, which by incompleteness has its own logic, quantum like when restricted to the sigma_1 truth. You need a reality (t). Can you make sense of Bp p for a schizophrenic who hears voices? If a schizophrenic says that he hears voices, and if he hears voice (mentally, virtually, arithmetically, brain-biologically, ...), then he knows he hears voice. An insane guy who says that he is Napoleon does not know that he is napoleon, but he believes it only. He still might know that he believes being Napoleon, and be only ignorant or denying that this is false. How about your own salvia experiences? It is very hard to describe, even more to interpret. And I am biased. It is indeed: [](... what-the-f.) and ... what the f. Most plausibly. It is like remembering forgotten qualia since eons. It might confirms the idea that brains, machines, words, theories filter consciousness only. Consciousness would be a close sister of (arithmetical) truth. Salvia might open the appetite for platonism, but of course it is also a question of taste. Bruno T On Mon, Mar 10, 2014 at 3:26 PM, Bruno Marchal marc...@ulb.ac.be wrote: On 10 Mar 2014, at 16:28, Terren Suydam wrote: Question for you Bruno:. You say (with help from Theaetetus) that 1p experience is given by Bp p. Yet, our experience is often deluded, as in optical illusions, or in various kinds of emotional psychological denial. Can we ever really say that our knowledge, even 1p experience, refers to anything True? In public? No. In private? Yes. I would say. Then in the frame of theories about such 1p things, like consciousness, we can decide to agree on some property of the notion. Then, consciousness-here-and-now might be a candidate for a possible true reference, if you agree consciousness-here-and-now is undoubtable or incorrigible. Then we can approximate many sort of truth, by the very plausible, the probable, the relatively expectable, etc. If someone complains, is the pain real or fake? Eventually it is a question for a judge. The truth is what no machine can really grasp the whole truth, but all machines can know very well some aspect of it, I think, but very few in justifiable modes. Bruno -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: truth of experience
Hi Bruno, Thanks, that helps. Can you expand a bit on t? Unfortunately I haven't had the time to follow the modal logic threads, so please forgive me but I don't understand how you could represent reality with t. Thanks, T On Tue, Mar 11, 2014 at 2:18 PM, Bruno Marchal marc...@ulb.ac.be wrote: Hi Terran, On 11 Mar 2014, at 17:10, Terren Suydam wrote: Hi Bruno, Sure, consciousness here-and-now is undoubtable. But the p refers to the contents of consciousness, which is not undoubtable in many cases. I am in pain cannot be doubted when one is feeling it, but other felt sensations can be doubted, e.g. see http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2956899/ Such illusions of experience can even be helpful, as in Ramachandran's Mirror Box therapy for phantom limb sufferers, see http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3468806/ Illusions of experience are evidence that what we experience is of our brains' constructions, like a waking dream, guided in healthy brains by the patterns of information streaming from our sense organs. Exactly: like a walking dream. That's the root of the Bp p idea, in the Theaetetus. To do the math I concentrate to rich (Löbian) machine for the B, but the idea of defining knowledge by true belief is an act of modesty with respect to the question if we are dreaming or not, or more generally, if we are wrong or not. Brains that are defective in this manner result in schizophrenia and presumably other dissociative pathologies. OK. For me it all casts doubt on whether Bp p is an accurate formalization for experience, but I might be missing something. As I said above, it is a simplest meta definition which capture the main thing (the truth of the experience) without needing to define it. Also, for the physical first person *experience*, Bp p, which is only the knower, is not enough, you will need Bp t p, which by incompleteness has its own logic, quantum like when restricted to the sigma_1 truth. You need a reality (t). Can you make sense of Bp p for a schizophrenic who hears voices? If a schizophrenic says that he hears voices, and if he hears voice (mentally, virtually, arithmetically, brain-biologically, ...), then he knows he hears voice. An insane guy who says that he is Napoleon does not know that he is napoleon, but he believes it only. He still might know that he believes being Napoleon, and be only ignorant or denying that this is false. How about your own salvia experiences? It is very hard to describe, even more to interpret. And I am biased. It is indeed: [](... what-the-f.) and ... what the f. Most plausibly. It is like remembering forgotten qualia since eons. It might confirms the idea that brains, machines, words, theories filter consciousness only. Consciousness would be a close sister of (arithmetical) truth. Salvia might open the appetite for platonism, but of course it is also a question of taste. Bruno T On Mon, Mar 10, 2014 at 3:26 PM, Bruno Marchal marc...@ulb.ac.be wrote: On 10 Mar 2014, at 16:28, Terren Suydam wrote: Question for you Bruno:. You say (with help from Theaetetus) that 1p experience is given by Bp p. Yet, our experience is often deluded, as in optical illusions, or in various kinds of emotional psychological denial. Can we ever really say that our knowledge, even 1p experience, refers to anything True? In public? No. In private? Yes. I would say. Then in the frame of theories about such 1p things, like consciousness, we can decide to agree on some property of the notion. Then, consciousness-here-and-now might be a candidate for a possible true reference, if you agree consciousness-here-and-now is undoubtable or incorrigible. Then we can approximate many sort of truth, by the very plausible, the probable, the relatively expectable, etc. If someone complains, is the pain real or fake? Eventually it is a question for a judge. The truth is what no machine can really grasp the whole truth, but all machines can know very well some aspect of it, I think, but very few in justifiable modes. Bruno -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http
