Science and Technology news... :: View topic

John Jones · Guest

Charlie wrote:
[quote]On Oct 8, 3:43ï¿½pm, John Jones <jonescard...@aol.com> wrote:
Charlie wrote:
In automated logic (via computers) if (p AND q) are considered, they
are implicitly assumed to be considered at the same time and space.
The assumption that AND implies is that its inputs (p,q) are evaluated
at
the same time and in the same operator (logic element). Our computers
would not work otherwise.
Charlie
Might I suggest that it isn>t how you have described it? In a
computer/machine all events are sequenced. There is no computer/machine
that can accumulate its sequenced events. It is not possible to
represent the accumulated truths of p and q by a machine (given the
truth of p and q). We may read the machine as having accumulated its
events, but this is an anthropomorphic reading of the tasks we have
given it. A machine only ever presents sequences or lists and not
accumulations. Only a mind can synthesise events to bring a unitary
emergent property - in this case, that p and q IS true. Machines can>t
do that.

Excuse me:
Each logic operation is static (although a frightening number can be
done each second); whether done on paper, or done in a computer. All
the elements are assembled, frozen in time, and then the logic
operations are performed. Neither formal, nor mechanized Boolean logic
admits of time, sequence, or change.

That>s why we use software, to tell the machine at every step:
00010010: (Now it is time to) do W
00010100: (Now it is time to) do X
00010110: (Now it is time to) do Y
00011000: (Now it is time to) do Z

Charlie
[/quote]

see new post

Mitch · Guest

On Oct 12, 5:37 pm, John Jones <jonescard...@aol.com> wrote:
[quote]Mitch wrote:
On Oct 9, 4:17 pm, John Jones <jonescard...@aol.com> wrote:

Sorry, it is very technical tangent. '0' can be used to refer to a
particular element in an algebra with certain properties, likewise '1'
can be defined with certain other properties, and under certain other
assumptions one can show that '0' acts identically to '1'. But under
normal circumstances, the locution '0=1' is usually taken to be the
canonical false proposition.

As I was saying, 0=1 doesn>t fit in with any number statement.
[/quote]
just to be pedantic, -sure- it does, it>s just usually taken to be a
very meaningful number statement, just one that is -false-.

[quote]but one
might consider the trivial ring which has both it>s additive and
multiplicative identities equal, even though the first is usually
called '0' and the second '1'.)
That would be a different house then. So if there are different
mathematical houses that use the same signs, then I can>t say that two
and two IS four.

Sure you can. But there might be notational confusion, that is all.
You sure can say it and most people would think you well-justified in
saying it, without having to specify what exactly you meant by 'two',
'plus', 'equals', and 'four'. You can also say '2+2=5' and have it be
meaningful (and just plain false). -Different- house? not really, just
how we call things in the one big house. The name is not the thing.

I was arguing that you can>t argue for 'p and q' from 'p' and 'q', let
alone assign a truth value to it.
[/quote]
Right. We all got that from the beginning. And everyone else is saying
that that is old news, that p and q aren>t arbitrary statements for
one to infer from 'p' and 'q' to get 'p and q'. both p and q can>t
have modals, or different contexts for interpretation, or other
ambiguities.

I>m surprised you>re picking on 'and'. 'or' is much more problematic.
Cripes, what about 'if then'?

if 2 + 2 = 5, then 3 is not prime.

True, right? (Given the conversation, make sure you use traditional
number theory. Frankly, you should be using traditional logic, too,
but we>re in a skeptical mode for the moment.)

....
[quote]The nice thing about mathematical language is that it is intended to
be unambiguous.

I don>t know how far disambiguation can be trusted if it works by
eliminating irreducible distinctions.
[/quote]
I>m not sure I follow, or where that came from (there>s no context
that suggests that). I feel like we>d rather eliminate -reducible-
distinctions, you know, by reducing them.

[quote]If there is some qualm about ambiguity, then there is
a definition or clarification to be made, the ambiguity is not
tolerated.

No one likes ambiguity, but I don>t think that its elimination is a
particularly mathematical project, nor especially practised by
mathematicians.
[/quote]
Sure, but it>s the place with the least (or no) tolerance for
ambiguity.

Mitch

Mitch · Guest

On Oct 13, 6:30 pm, John Jones <jonescard...@aol.com> wrote:
[quote]Mitch wrote:
On Oct 12, 5:37 pm, John Jones <jonescard...@aol.com> wrote:
Mitch wrote:
I>m surprised you>re picking on 'and'. 'or' is much more problematic.
Cripes, what about 'if then'?

I just picked on the first one I saw. The others will follow. But people
here have argued for 'p and q' from p and q. As does the texts I>ve
looked at.
[/quote]
Yes. They>re all considering the things that could go in for p and q
to be of a certain kind.

[quote]I argued that the object or agency 'p and q' has NOT been
properly identified to assign a truth value to it, nor is it explained
how 'p and q' can be constructed from two other objects we know about,
p, and q.
[/quote]
If you restrict p and q appropriately, then 'p and q' follow from 'p
and 'q' pretty incontrovertibly. I fit makes you feel better, just
define 'p and q' the least possible inference from 'p' and 'q'.

[quote] if 2 + 2 = 5, then 3 is not prime.

True, right? (Given the conversation, make sure you use traditional
number theory. Frankly, you should be using traditional logic, too,
but we>re in a skeptical mode for the moment.)

I suppose if my Aunty had a beard she>d be my uncle... but I can>t make
sense of 2+2=5. The project stops at that point.
[/quote]
2+2=5 is obviously a falsehood. Likewise 3 is prime, so the consequent
is false too. So, what is the truth value of 'if 2+2=5, then 3 is not
prime'?

[quote]...
The nice thing about mathematical language is that it is intended to
be unambiguous.
I don>t know how far disambiguation can be trusted if it works by
eliminating irreducible distinctions.

I>m not sure I follow, or where that came from (there>s no context
that suggests that). I feel like we>d rather eliminate -reducible-
distinctions, you know, by reducing them.

If maths is made unambiguous by eliminating essential distinctions then
I wonder how far we can trust the project of disambiguation.
[/quote]
Uh...I don>t know. Here again I don>t know were you came up with
'eliminating essential distinctions'. I do think it practical to
remove ambiguities (it reduces the number of tracks of discussion).
Are you reading 'ambiguity' as an 'essential distinction'? (I don>t)
What I think I mean by ambiguity is multiple interpretations.

[quote]No one likes ambiguity, but I don>t think that its elimination is a
particularly mathematical project, nor especially practised by
mathematicians.

Sure, but it>s the place with the least (or no) tolerance for
ambiguity.

Mathematical objects are clear by being written down and seen. But it is
what they refer to that can lead to ambiguity, despite the clarity of
syntactical presentation.

Syntax is inevitably clear, but at some point the syntax needs
translating
[/quote]
Well, just because something is typeset nicely, doesn>t mean it>s
right, or meaningful, or anything.

[quote]and at that point its clarity is of no avail.
[/quote]
Uh...I would say that if its clarity is of no avail, then it wasn>t
clear to begin with. All you can write down on paper is syntax, and
somehow it gets translated to inside your head. For the syntax to
work, the translation to your head has to work all the way through at
each syntactic step.

[quote]For example,
does 'not P' identify P-like objects or the absence of P and P-like objects?
[/quote]
Good point. Depends on the context. (if you>re curious, your specific
case could be followed). But in each context, the mathematical 'not P'
is pretty well understood, and maps well to ideas in our heads. A
particular piece of syntax may not mean much to you the individual,
but that doesn>t mean it doesn>t mean something coherent to others.

Mitch

Jesse F. Hughes · Guest

John Jones <jonescardiff@aol.com> writes:

[quote]Jesse F. Hughes wrote:
John Jones <jonescardiff@aol.com> writes:

Mitch wrote:
Which is all to say, there>s not much of a problem with 'and', or the
other connectives (at least not in this conversation), the problem is
with those examples of propositions.

Mitch
Yes, but isn>t it the case that the examples used to illustrate the
problem extend right across the board, with no exceptions?

There are plenty of well-known examples in which the natural language
"and" does not behave like the logical "and". This basic fact is very
old news, but you haven>t come up with any coherent reasoning along
these lines.

For just one example: In logic, A & B is true in exactly the same
situations in which B & A is true, but in natural language this is not
so.

"Jennie became pregnant and she got married."

has a different meaning from

"Jennie got married and she became pregnant."

This exciting observation that natural language meaning is different
than the meanings of formal connectives has been done. (To be sure,
none of these arguments bear any similarity to your odd claims.)

Any project that claims that its terms are meaningful in a way that is
different to a natural language formulation, can have no meaningful terms.

[/quote]
Right. And hence, no mathematical discipline has meaningful terms!
Topology? "Open" and "closed" are clearly different than natural
language. Analysis? "Series", "continuous" (topological, too, of
course) and so on. Geometry? "Line" and "point" are rather different
than the natural language terms.

And, of course, in logic, aside from "and", the connectives "or" and
"implies" are rather different than natural language usage.

So, enough of this twaddle! No more of these meaningless projects!
Let John Jones show us the way.

--
"I am one of those annoying people who is so good at so many things
that I can>t seem to pick one. I can seriously party. But I can also
sit for long periods concentrating profusely on some problem or
other."-- James S Harris: Thinker. Serious partyer. Renaissance man.
** Posted from http://www.teranews.com **

John Jones · Guest

Jesse F. Hughes wrote:
[quote]John Jones <jonescardiff@aol.com> writes:

Jesse F. Hughes wrote:
John Jones <jonescardiff@aol.com> writes:

Mitch wrote:
Which is all to say, there>s not much of a problem with 'and', or the
other connectives (at least not in this conversation), the problem is
with those examples of propositions.

Mitch
Yes, but isn>t it the case that the examples used to illustrate the
problem extend right across the board, with no exceptions?

There are plenty of well-known examples in which the natural language
"and" does not behave like the logical "and". This basic fact is very
old news, but you haven>t come up with any coherent reasoning along
these lines.

For just one example: In logic, A & B is true in exactly the same
situations in which B & A is true, but in natural language this is not
so.

"Jennie became pregnant and she got married."

has a different meaning from

"Jennie got married and she became pregnant."

This exciting observation that natural language meaning is different
than the meanings of formal connectives has been done. (To be sure,
none of these arguments bear any similarity to your odd claims.)

Any project that claims that its terms are meaningful in a way that is
different to a natural language formulation, can have no meaningful terms.

Right. And hence, no mathematical discipline has meaningful terms!
[/quote]
Yes. But thankfully ALL mathematical terms and concepts are rooted in
spatio-temporal (natural language), familiar examples.

[quote]Topology? "Open" and "closed" are clearly different than natural
language.
[/quote]
No. I think that the mathematical and logical proselytes get carried
away with thinking that what they are doing is unique, and so
occassionally they must be gently reminded that there is nothing new
under the sun.

[quote]Analysis? "Series", "continuous" (topological, too, of
course) and so on. Geometry? "Line" and "point" are rather different
than the natural language terms.
[/quote]
It doesn>t matter whether these terms and signs are used differently to
their natural language meanings. They still engage with the same
meanings. Just because 'dog' now refers to 'cat' doesn>t mean that a new
meaning has been created - we just have a new sign for an old meaning.

[quote]And, of course, in logic, aside from "and", the connectives "or" and
"implies" are rather different than natural language usage.
[/quote]
They are different, not that the logicians themselves can see the
difference in its entirety. But where we depart from natural meaning, we
enter confusion, and not a new language.

John Jones · Guest

Mitch wrote:
[quote]On Oct 12, 5:37 pm, John Jones <jonescard...@aol.com> wrote:
Mitch wrote:
On Oct 9, 4:17 pm, John Jones <jonescard...@aol.com> wrote:
Sorry, it is very technical tangent. '0' can be used to refer to a
particular element in an algebra with certain properties, likewise '1'
can be defined with certain other properties, and under certain other
assumptions one can show that '0' acts identically to '1'. But under
normal circumstances, the locution '0=1' is usually taken to be the
canonical false proposition.
As I was saying, 0=1 doesn>t fit in with any number statement.

just to be pedantic, -sure- it does, it>s just usually taken to be a
very meaningful number statement, just one that is -false-.

but one
might consider the trivial ring which has both it>s additive and
multiplicative identities equal, even though the first is usually
called '0' and the second '1'.)
That would be a different house then. So if there are different
mathematical houses that use the same signs, then I can>t say that two
and two IS four.
Sure you can. But there might be notational confusion, that is all.
You sure can say it and most people would think you well-justified in
saying it, without having to specify what exactly you meant by 'two',
'plus', 'equals', and 'four'. You can also say '2+2=5' and have it be
meaningful (and just plain false). -Different- house? not really, just
how we call things in the one big house. The name is not the thing.
I was arguing that you can>t argue for 'p and q' from 'p' and 'q', let
alone assign a truth value to it.

Right. We all got that from the beginning. And everyone else is saying
that that is old news, that p and q aren>t arbitrary statements for
one to infer from 'p' and 'q' to get 'p and q'. both p and q can>t
have modals, or different contexts for interpretation, or other
ambiguities.

I>m surprised you>re picking on 'and'. 'or' is much more problematic.
Cripes, what about 'if then'?
[/quote]
I just picked on the first one I saw. The others will follow. But people
here have argued for 'p and q' from p and q. As does the texts I>ve
looked at. I argued that the object or agency 'p and q' has NOT been
properly identified to assign a truth value to it, nor is it explained
how 'p and q' can be constructed from two other objects we know about,
p, and q.

[quote]if 2 + 2 = 5, then 3 is not prime.

True, right? (Given the conversation, make sure you use traditional
number theory. Frankly, you should be using traditional logic, too,
but we>re in a skeptical mode for the moment.)
[/quote]
I suppose if my Aunty had a beard she>d be my uncle... but I can>t make
sense of 2+2=5. The project stops at that point.

[quote]...
The nice thing about mathematical language is that it is intended to
be unambiguous.
I don>t know how far disambiguation can be trusted if it works by
eliminating irreducible distinctions.

I>m not sure I follow, or where that came from (there>s no context
that suggests that). I feel like we>d rather eliminate -reducible-
distinctions, you know, by reducing them.
[/quote]
If maths is made unambiguous by eliminating essential distinctions then
I wonder how far we can trust the project of disambiguation.

[quote]If there is some qualm about ambiguity, then there is
a definition or clarification to be made, the ambiguity is not
tolerated.
No one likes ambiguity, but I don>t think that its elimination is a
particularly mathematical project, nor especially practised by
mathematicians.

Sure, but it>s the place with the least (or no) tolerance for
ambiguity.
[/quote]
Mathematical objects are clear by being written down and seen. But it is
what they refer to that can lead to ambiguity, despite the clarity of
syntactical presentation.

Syntax is inevitably clear, but at some point the syntax needs
translating and at that point its clarity is of no avail. For example,
does 'not P' identify P-like objects or the absence of P and P-like objects?

John Jones · Guest

Mitch wrote:
[quote]On Oct 13, 6:30 pm, John Jones <jonescard...@aol.com> wrote:
Mitch wrote:
On Oct 12, 5:37 pm, John Jones <jonescard...@aol.com> wrote:
Mitch wrote:
I>m surprised you>re picking on 'and'. 'or' is much more problematic.
Cripes, what about 'if then'?
I just picked on the first one I saw. The others will follow. But people
here have argued for 'p and q' from p and q. As does the texts I>ve
looked at.

Yes. They>re all considering the things that could go in for p and q
to be of a certain kind.

I argued that the object or agency 'p and q' has NOT been
properly identified to assign a truth value to it, nor is it explained
how 'p and q' can be constructed from two other objects we know about,
p, and q.

If you restrict p and q appropriately, then 'p and q' follow from 'p
and 'q' pretty incontrovertibly. I fit makes you feel better, just
define 'p and q' the least possible inference from 'p' and 'q'.
[/quote]
The least possible inference is that 'p and q' is 'p', and 'q' but
written down in another way. That cannot be of any logical significance.

The other least possible inference is that 'p and q' is an object (or
statement etc) with a truth value; just as 'p' and 'q' are also objects
with truth values. But what sort of object is 'p and q'?
That>s my point. 'P and q' is not identified as anything, yet it is
identified as an object. How? It is merely assumed that if there are two
truths then they, and their objects, can be 'conjunctioned'. This 'truth
conjunctioning' is not easily understood, in fact, I would say that it
is incomprehensible.

[quote]If maths is made unambiguous by eliminating essential distinctions then
I wonder how far we can trust the project of disambiguation.

Uh...I don>t know. Here again I don>t know were you came up with
'eliminating essential distinctions'. I do think it practical to
remove ambiguities (it reduces the number of tracks of discussion).
Are you reading 'ambiguity' as an 'essential distinction'? (I don>t)
What I think I mean by ambiguity is multiple interpretations.
[/quote]
I don>t want to identify the task of removing ambiguity with the task of
of eliminating differences.

[quote]For example,
does 'not P' identify P-like objects or the absence of P and P-like objects?

Good point. Depends on the context. (if you>re curious, your specific
case could be followed). But in each context, the mathematical 'not P'
is pretty well understood,
[/quote]
It is syntactically presented, but the translation of that syntax poses
problems. Not-P can refer to the complete (necessary) absence of the
framework of P and P-like objects, or refer to the absence of only P, or
refer to the presence of another object in the framework of P.

Here>s another one. If ambiguity is removed by declaring that reference
and self-reference are the same then this particular process of
disambiguation leads us into error: 'This sentence' is an act of
self-reference or an act of reference. The former act is not surveyable
because it is internal, while the latter act refers to a missing or
unidentified statement. If we try to formalise 'this sentence' and make
its syntax unambiguous by declaring that reference and self-reference
mean the same thing then, as they don>t mean the same thing, a
simplified, disambiguated syntax will increase ambiguity by being unable
to distinguish internal (self-reference) from hidden (reference).

[quote]and maps well to ideas in our heads. A
particular piece of syntax may not mean much to you the individual,
but that doesn>t mean it doesn>t mean something coherent to others.
[/quote]
Yes, but I would have thought that the assumptions we make in everyday
life don>t make an appearance in logic or maths. In everyday life we are
immersed in contexts and frameworks and so are rarely at a loss to know
what it is we are talking about and their possibilities. But in maths
and logic we are taken out of these contexts.

Mitch · Guest

On Oct 14, 5:16 pm, John Jones <jonescard...@aol.com> wrote:
[quote]Mitch wrote:
On Oct 13, 6:30 pm, John Jones <jonescard...@aol.com> wrote:
Mitch wrote:
On Oct 12, 5:37 pm, John Jones <jonescard...@aol.com> wrote:
Mitch wrote:
I>m surprised you>re picking on 'and'. 'or' is much more problematic.
Cripes, what about 'if then'?
I just picked on the first one I saw. The others will follow. But people
here have argued for 'p and q' from p and q. As does the texts I>ve
looked at.

Yes. They>re all considering the things that could go in for p and q
to be of a certain kind.

I argued that the object or agency 'p and q' has NOT been
properly identified to assign a truth value to it, nor is it explained
how 'p and q' can be constructed from two other objects we know about,
p, and q.

If you restrict p and q appropriately, then 'p and q' follow from 'p
and 'q' pretty incontrovertibly. I fit makes you feel better, just
define 'p and q' the least possible inference from 'p' and 'q'.

The least possible inference is that 'p and q' is 'p', and 'q' but
written down in another way. That cannot be of any logical significance.
[/quote]
I think you>ve made a case by example that it is not entirely obvious,
if one is skeptical enough, that from 'p' and 'q' one should be able
to infer 'p and q'.

[quote]The other least possible inference is that 'p and q' is an object (or
statement etc)
[/quote]
or concept.

[quote]with a truth value; just as 'p' and 'q' are also objects
with truth values. But what sort of object is 'p and q'?
That>s my point. 'P and q' is not identified as anything, yet it is
identified as an object. How? It is merely assumed that if there are two
truths then they, and their objects, can be 'conjunctioned'. This 'truth
conjunctioning' is not easily understood, in fact, I would say that it
is incomprehensible.
[/quote]
There>s a difference between skepticism and not even trying.

[quote]If maths is made unambiguous by eliminating essential distinctions then
I wonder how far we can trust the project of disambiguation.

Uh...I don>t know. Here again I don>t know were you came up with
'eliminating essential distinctions'. I do think it practical to
remove ambiguities (it reduces the number of tracks of discussion).
Are you reading 'ambiguity' as an 'essential distinction'? (I don>t)
What I think I mean by ambiguity is multiple interpretations.

I don>t want to identify the task of removing ambiguity with the task of
of eliminating differences.
[/quote]
OK. Fine. But you>re the one who brought up elimination of
differences, and I>m just trying to figure out what that really means
for you.

[quote]For example,
does 'not P' identify P-like objects or the absence of P and P-like objects?

Good point. Depends on the context. (if you>re curious, your specific
case could be followed). But in each context, the mathematical 'not P'
is pretty well understood,

It is syntactically presented, but the translation of that syntax poses
problems.
[/quote]
Sure. Negation is not obvious.

[quote]Not-P can refer to the complete (necessary) absence of the
framework of P and P-like objects,
[/quote]
Oh. hm. maybe. that>s one I>ve never heard before.

[quote]or refer to the absence of only P, or
refer to the presence of another object in the framework of P.
[/quote]
Usually, it>s as simple as 'not p' means true if 'p' is false, and
vice versa. That is, in the cases where 'p' has a truth value, 'not p'
has the opposite truth value.

You might be confusing it with set-complement ('absence of only P'?),
which has a lot of algebraic similarities with logical not, and there
are interpretations where each can be implemented with the other.

As to 'framework', I think you>re laying a lot of your own meaning
onto 'not'...er....or maybe you>re really taking about one of the many
varieties of the English 'not' (and narrowmindedly, all I>m talking
about is the logical, stipulated version).

....
[quote]and maps well to ideas in our heads. A
particular piece of syntax may not mean much to you the individual,
but that doesn>t mean it doesn>t mean something coherent to others.

Yes, but I would have thought that the assumptions we make in everyday
life don>t make an appearance in logic or maths.
[/quote]
I wouldn>t go that far. I think there>s -some- rationality in everyday
life.

[quote]In everyday life we are
immersed in contexts and frameworks and so are rarely at a loss to know
what it is we are talking about and their possibilities.
[/quote]
I wouldn>t go that far here either. I think we>re often at a loss (or
rather, many every day contexts are entertaining myths) but we get by
anyway.

[quote]But in maths and logic we are taken out of these contexts.
[/quote]
How about just a different context?

Mitch

herbzet · Guest

Mitch wrote:
[quote]John Jones wrote:

I was arguing that you can>t argue for 'p and q' from 'p' and 'q', let
alone assign a truth value to it.

Right. We all got that from the beginning. And everyone else is saying
that that is old news, that p and q aren>t arbitrary statements for
one to infer from 'p' and 'q' to get 'p and q'. both p and q can>t
have modals, or different contexts for interpretation, or other
ambiguities.

I>m surprised you>re picking on 'and'. 'or' is much more problematic.
Cripes, what about 'if then'?
[/quote]
It is precisely because 'and' is *less* problematic than 'or' or
'if then' that it is the place for a really fundamental critique
of (symbolic?) logic.

About the only thing that is about as un-problematic as 'and'
in logic is 'not', which I assume JJ will get around to in due
course.

It is worth noting, John, that 'and' and 'not', when taken as
primitive, are a sufficient basis for defining all the other
propositional operators -- '(inclusive) or', '(exclusive) or',
'if then', 'if and only if', etc.

(A propositional operator takes propositions as arguments and
returns a proposition as a value. Witt says (somewhere in
Tractatus) that they might be better regarded as taking truth-
values as arguments and returning a truth-value as a value
(I>ll look it up).

[quote]From an algebraic point of view, the variables of a Boolean algebra
could take as arguments and values propositions, truth-values, or[/quote]
any one of many other sorts of things, e.g., switches (open or closed),
sets of points in a plane, etc.)

--
hz

herbzet · Guest

herbzet wrote:

[quote]From an algebraic point of view, the variables of a Boolean algebra
could take as arguments and values propositions, truth-values, or
any one of many other sorts of things, e.g., switches (open or closed),
sets of points in a plane, etc.)
[/quote]
I meant, from an algebraic point of view, the /operators/ of a Boolean
algebra take as arguments and values ... etc.

--
hz

John Jones · Guest

Mitch wrote:
[quote]On Oct 14, 5:16 pm, John Jones <jonescard...@aol.com> wrote:
Mitch wrote:
On Oct 13, 6:30 pm, John Jones <jonescard...@aol.com> wrote:
Mitch wrote:
On Oct 12, 5:37 pm, John Jones <jonescard...@aol.com> wrote:
Mitch wrote:
I>m surprised you>re picking on 'and'. 'or' is much more problematic.
Cripes, what about 'if then'?
I just picked on the first one I saw. The others will follow. But people
here have argued for 'p and q' from p and q. As does the texts I>ve
looked at.
Yes. They>re all considering the things that could go in for p and q
to be of a certain kind.
I argued that the object or agency 'p and q' has NOT been
properly identified to assign a truth value to it, nor is it explained
how 'p and q' can be constructed from two other objects we know about,
p, and q.
If you restrict p and q appropriately, then 'p and q' follow from 'p
and 'q' pretty incontrovertibly. I fit makes you feel better, just
define 'p and q' the least possible inference from 'p' and 'q'.
The least possible inference is that 'p and q' is 'p', and 'q' but
written down in another way. That cannot be of any logical significance.

I think you>ve made a case by example that it is not entirely obvious,
if one is skeptical enough, that from 'p' and 'q' one should be able
to infer 'p and q'.
[/quote]
I don>t know if you believe me, but it>s true that I don>t know what is
meant, or could be meant by "'p and q' is true".

In fact, though its a bit late in the day, I challenge anyone to say
what it means.

[quote]Usually, it>s as simple as 'not p' means true if 'p' is false, and
vice versa. That is, in the cases where 'p' has a truth value, 'not p'
has the opposite truth value.
[/quote]
Perhaps instead of looking for an alternative to P if P is false, I
should just accept the fact that P is false, and that whatever else is
around is no-one>s interest as far as P is false is concerned..

[quote]You might be confusing it with set-complement ('absence of only P'?),
which has a lot of algebraic similarities with logical not, and there
are interpretations where each can be implemented with the other.
[/quote]
I don>t know.

[quote]As to 'framework', I think you>re laying a lot of your own meaning
onto 'not'...er....or maybe you>re really taking about one of the many
varieties of the English 'not' (and narrowmindedly, all I>m talking
about is the logical, stipulated version).
[/quote]
I>m not inventing anything or being prescriptive. P, and P-like objects
such as R occur in the framework of P but not in another framework. For
example, red and yellow are found in the framework of colour but not in
the framework of sound. Now, if P is red, does not-P refer to yellow
etc, or to loud, etc?

[quote]
But in maths and logic we are taken out of these contexts.

How about just a different context?

[/quote]
I would argue that that is an impossibility. A context that was
different in that way would meet all the criteria for something being
impossible.

John Jones · Guest

herbzet wrote:
[quote]
Mitch wrote:
John Jones wrote:

I was arguing that you can>t argue for 'p and q' from 'p' and 'q', let
alone assign a truth value to it.
Right. We all got that from the beginning. And everyone else is saying
that that is old news, that p and q aren>t arbitrary statements for
one to infer from 'p' and 'q' to get 'p and q'. both p and q can>t
have modals, or different contexts for interpretation, or other
ambiguities.

I>m surprised you>re picking on 'and'. 'or' is much more problematic.
Cripes, what about 'if then'?
[/quote]
.... I thought I responded to this post but I can>t see my post.
Er...yes, I will take a look at those others soon.

[quote]It is precisely because 'and' is *less* problematic than 'or' or
'if then' that it is the place for a really fundamental critique
of (symbolic?) logic.
[/quote]
I think that 'and' in logic is a mysterious operation or power that
allows two truths to be reduced to one truth. How is that possible? It
breaks the link between truth and the object of truth. It says that two
true objects are one true object. But what object is that?

[quote]About the only thing that is about as un-problematic as 'and'
in logic is 'not', which I assume JJ will get around to in due
course.

It is worth noting, John, that 'and' and 'not', when taken as
primitive, are a sufficient basis for defining all the other
propositional operators -- '(inclusive) or', '(exclusive) or',
'if then', 'if and only if', etc.

(A propositional operator takes propositions as arguments and
returns a proposition as a value.
[/quote]
It looks to me like an argument is a value. 'P' is not an argument or a
value but a presentation of P. If I append or operate upon it with 'not'
as in not-P, or if/then, as in 'if P' then these are arguments and
values; in the sense that it must be either true or false. But 'P' per
se is not true/false or argument/value.

[quote]Witt says (somewhere in
Tractatus) that they might be better regarded as taking truth-
values as arguments and returning a truth-value as a value
(I>ll look it up).

From an algebraic point of view, the variables of a Boolean algebra
could take as arguments and values propositions, truth-values, or
any one of many other sorts of things, e.g., switches (open or closed),
sets of points in a plane, etc.)

--
hz[/quote]

John Jones · Guest

herbzet wrote:
[quote]
herbzet wrote:

From an algebraic point of view, the variables of a Boolean algebra
could take as arguments and values propositions, truth-values, or
any one of many other sorts of things, e.g., switches (open or closed),
sets of points in a plane, etc.)

I meant, from an algebraic point of view, the /operators/ of a Boolean
algebra take as arguments and values ... etc.

--
hz
[/quote]
Arguments, values, operators and variables look like another thing to
look at.

Mitch · Guest

On Oct 14, 10:10 pm, herbzet <herb...@gmail.com> wrote:
[quote]Mitch wrote:
I>m surprised you>re picking on 'and'. 'or' is much more problematic.
Cripes, what about 'if then'?

It is precisely because 'and' is *less* problematic than 'or' or
'if then' that it is the place for a really fundamental critique
of (symbolic?) logic.
[/quote]
Yes, I see that.

[quote]About the only thing that is about as un-problematic as 'and'
in logic is 'not'...
[/quote]
There I>d say there>s quite a bit more problematic about
'not' than 'and'.

(p and p) <-> p is a lot more obvious and uncontestable than --p -> p

Mitch

herbzet · Guest

John Jones wrote:
[quote]herbzet wrote:
Mitch wrote:
John Jones wrote:

I was arguing that you can>t argue for 'p and q' from 'p' and 'q', let
alone assign a truth value to it.

Right. We all got that from the beginning. And everyone else is saying
that that is old news, that p and q aren>t arbitrary statements for
one to infer from 'p' and 'q' to get 'p and q'. both p and q can>t
have modals, or different contexts for interpretation, or other
ambiguities.

I>m surprised you>re picking on 'and'. 'or' is much more problematic.
Cripes, what about 'if then'?

... I thought I responded to this post but I can>t see my post.
[/quote]
Yes, you responded to Mitch>s post on Monday; I>m about 24 hours
behind you. Your post was news:gd0i50$jnk$1@aioe.org .

Then I responded to Mitch>s comment (just above) on Tuesday.

[quote]Er...yes, I will take a look at those others soon.
[/quote]
Stick with "and" till you beat it death, is my advice. You
can>t get much more fundamental than that, and "not".

Me talking to Mitch:

[quote]It is precisely because 'and' is *less* problematic than 'or' or
'if then' that it is the place for a really fundamental critique
of (symbolic?) logic.

I think that 'and' in logic is a mysterious operation or power that
allows two truths to be reduced to one truth. How is that possible? It
breaks the link between truth and the object of truth.
[/quote]
I don>t know what you mean by "the object of truth"; a wild guess
is that you might mean the object that bears or possesses truth.

[quote]It says that two
true objects are one true object. But what object is that?
[/quote]
A proposition.

[quote]About the only thing that is about as un-problematic as 'and'
in logic is 'not', which I assume JJ will get around to in due
course.

It is worth noting, John, that 'and' and 'not', when taken as
primitive, are a sufficient basis for defining all the other
propositional operators -- '(inclusive) or', '(exclusive) or',
'if then', 'if and only if', etc.

(A propositional operator takes propositions as arguments and
returns a proposition as a value.

It looks to me like an argument is a value.
[/quote]
This does not contradict my assertion in any way.

[quote]'P' is not an argument or a
value but a presentation of P. If I append or operate upon it with 'not'
as in not-P, or if/then, as in 'if P' then these are arguments and
values; in the sense that it must be either true or false. But 'P' per
se is not true/false or argument/value.
[/quote]
If P is something that can be true or false, what else could it be
but a proposition?

If P is a proposition, and 'P' is the presentation of P, I wouldn>t
necessarily expect 'P' to be true or false, though I would expect
P to be true or false.

It>s unclear from what you wrote just above whether you mean to
assert that by "not-P" whether you consider the propositional
operator 'not' as operating on P or 'P'.

[quote]Witt says (somewhere in
Tractatus) that they might be better regarded as taking truth-
values as arguments and returning a truth-value as a value
(I>ll look it up).
[/quote]
I have to kind of retract this -- I mis-remembered it. Having discussed
an elementary proposition

4.21 The simplist kind of proposition, an elementary proposition,
assets the existence of a state of affairs.

4.22 An elementary proposition consists of names. It is a nexus,
a concantenation, of names.

4.23 It is only in the nexus of an elementary proposition that
a name occurs in a proposition.

he then says

5 A proposition is a truth-function of elementary propositions.
(An elementary proposition is a truth-function of itself.)

5.01 Elementary propositions are the truth-arguments of propositions.

and develops from there.

(Pears, McGuinness translation)

[quote]From an algebraic point of view, the [operators] of a Boolean algebra
could take as arguments and values propositions, truth-values, or
any one of many other sorts of things, e.g., switches (open or closed),
sets of points in a plane, etc.)
[/quote]
--
hz


www.GetXFactor.com Leading Technology, Science, Agriculture News and information	Part of the Identityscape.com network... getxfactor.com jmoodmusic.com smartbusinesschoices.com mintdepot.com lowfaresalways.com evangelicalview.com shoppingpodder.com soproudlywehail.com webnews.ws currenthumor.com

Science and Technology news... Forum Index -> Logic Forum	Goto page Previous 1, 2, 3, 4, 5 Next
Page 3 of 5