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John Jones · Guest

"And" (also called a conjunction, "^") is employed in logic. For
example, the conjunction p and q, (p ^ q) of two propositions is true
when both p and q are true, false otherwise. It would be tedious to even
begin to think otherwise. But Tedium is the name of the dragon who
guards a treasure:

PROPOSAL
If p is true, and if q is true, it does not follow that p and q (as
p^q)IS true. We cannot even say that p and q ARE true. The distinction
here, of course, is that the former is a 'logical' necessity ('p and q'
'is'...) and the latter appears to be merely a grammatical necessity (p
and q 'are'...), a necessity which does not take 'are true' as a truth
evaluation.

DISCUSSION
Consider
q "Itâ€™s raining" is true
p "Itâ€™s Monday" is true
It does not follow that p ^ q, "Itâ€™s Monday and itâ€™s raining", is true.

This is because no reason has been given to consider the conjunction
"and" as occuring in any form other than as a listing of the truths of p
and q. In which case '"Itâ€™s Monday and itâ€™s raining", is true' is not
only bad grammar, but grammatical necessities are not necessary truths
(this is why I said that we cannot say that it is a necessity that p and
q ARE true).

We must take another step if we want to show that, given the truth of p,
q, p ^ q IS true. To make that step we must take p 'it is Monday' and q
'it is raining' as arising in the same context and as referring to a
common event p and q "it is Monday and it is raining"; ..but we cannot
really make any assumptions.

CONCLUSION
The logical necessity of "if p, q, then p ^ q is true", is a necessity
that is based on one of the following conditions

1) an assumption that p and q arise in the same context (e.g. it>s
raining and Monday in the same spatiotemporal location). Given that this
context is not represented, then p ^ q is true (in this context) is not
a necessary truth but a dependent truth or a problematic assumed truth;
2) the identity of context of p and q is not assumed. Hence the
necessary truth of their conjunction (and) is only a possible truth (eg.
p and q may, or may not refer to days and times on different planets);
3) Necessary truth is defined circularly as being logical truth (we have
heard that argument before);
4) p and q, as propositional variables, are contextless. Hence, they are
semantically void.

None of these cases allows us to say that: the conjunction p and q, (p ^
q) of two propositions is true when both p and q are true, false otherwise.

Herbert Newman · Guest

On Wed, 08 Oct 2008 00:20:40 +0100 John Jones wrote:

[quote]Consider

q "It¢s raining" is true,
p "It¢s Monday" is true.

It does not follow that p ^ q, "It>s Monday and it¢s raining", is true.

That>s indeed fascinating. So if it>s Monday and it>s raining, (i.e. if it[/quote]
is true that it is Monday and is true that it is raining) you would not
agree that it is true that it is Monday and it is raining. Fascinating,
indeed.

Herb

James Burns · Guest

Herbert Newman wrote:
[quote]On Wed, 08 Oct 2008 00:20:40 +0100 John Jones wrote:

Consider

q "It¢s raining" is true,
p "It¢s Monday" is true.

It does not follow that p ^ q, "It>s Monday and it¢s raining",
is true.

That>s indeed fascinating. So if it>s Monday and it>s raining,
(i.e. if it is true that it is Monday and is true that it is
raining) you would not agree that it is true that it is Monday
and it is raining. Fascinating, indeed.
[/quote]
You are, apparently, following the path blazed by John Jones
and using "fascinating" in the sense of "not remotely fascinating".
Am I correct(*)?

(*) I am using "correct" here in the sense of "correct".

Jim Burns

Mitch · Guest

On Oct 8, 2:34 pm, John Jones <jonescard...@aol.com> wrote:
[quote]Herbert Newman wrote:
On Wed, 08 Oct 2008 00:20:40 +0100 John Jones wrote:

Consider

q "It¢s raining" is true,
p "It¢s Monday" is true.

It does not follow that p ^ q, "It>s Monday and it¢s raining", is true.

That>s indeed fascinating. So if it>s Monday and it>s raining, (i.e. if it
is true that it is Monday and is true that it is raining) you would not
agree that it is true that it is Monday and it is raining. Fascinating,
indeed.

Yes, I would not agree that if it is true that it is Monday and is true
that it is raining, then it is true that it is Monday and it is raining.
I will summarise why I say that:

1) Two truths (Monday, raining) only obtain as one truth if the context
of each truth is the same.
[/quote]
The context for both separately and together is not the universe?

Mitch

Charlie · Guest

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

On Oct 7, 4:20 pm, John Jones <jonescard...@aol.com> wrote:
[quote]"And" (also called a conjunction, "^") is employed inlogic. For
example, the conjunction p and q, (p ^ q) of two propositions is true
when both p and q are true, false otherwise. It would be tedious to even
begin to think otherwise. But Tedium is the name of the dragon who
guards a treasure:

PROPOSAL
If p is true, and if q is true, it does not follow that p and q (as
p^q)IS true. We cannot even say that p and q ARE true. The distinction
here, of course, is that the former is a 'logical' necessity ('p and q'
'is'...) and the latter appears to be merely a grammatical necessity (p
and q 'are'...), a necessity which does not take 'are true' as a truth
evaluation.

DISCUSSION
Consider
q "It’s raining" is true
p "It’s Monday" is true
It does not follow that p ^ q, "It’s Monday and it’s raining", is true.

This is because no reason has been given to consider the conjunction
"and" as occuring in any form other than as a listing of the truths of p
and q. In which case '"It’s Monday and it’s raining", is true' is not
only bad grammar, but grammatical necessities are not necessary truths
(this is why I said that we cannot say that it is a necessity that p and
q ARE true).

We must take another step if we want to show that, given the truth of p,
q, p ^ q IS true. To make that step we must take p 'it is Monday' and q
'it is raining' as arising in the same context and as referring to a
common event p and q "it is Monday and it is raining"; ..but we cannot
really make any assumptions.

CONCLUSION
The logical necessity of "if p, q, then p ^ q is true", is a necessity
that is based on one of the following conditions

1) an assumption that p and q arise in the same context (e.g. it>s
raining and Monday in the samespatiotemporallocation). Given that this
context is not represented, then p ^ q is true (in this context) is not
a necessary truth but a dependent truth or a problematic assumed truth;
2) the identity of context of p and q is not assumed. Hence the
necessary truth of their conjunction (and) is only a possible truth (eg.
p and q may, or may not refer to days and times on different planets);
3) Necessary truth is defined circularly as being logical truth (we have
heard that argument before);
4) p and q, as propositional variables, are contextless. Hence, they are
semantically void.

None of these cases allows us to say that: the conjunction p and q, (p ^
q) of two propositions is true when both p and q are true, false otherwise.[/quote]

John Jones · Guest

Herbert Newman wrote:
[quote]On Wed, 08 Oct 2008 00:20:40 +0100 John Jones wrote:

Consider

q "It¢s raining" is true,
p "It¢s Monday" is true.

It does not follow that p ^ q, "It>s Monday and it¢s raining", is true.

That>s indeed fascinating. So if it>s Monday and it>s raining, (i.e. if it
is true that it is Monday and is true that it is raining) you would not
agree that it is true that it is Monday and it is raining. Fascinating,
indeed.

[/quote]
Yes, I would not agree that if it is true that it is Monday and is true
that it is raining, then it is true that it is Monday and it is raining.
I will summarise why I say that:

1) Two truths (Monday, raining) only obtain as one truth if the context
of each truth is the same.

2) If we wriggle out of 1) by saying that we are merely restating the
two truths in a different way, then there is a grammatically correct way
of putting it. We ought to say 'they are true that it is Monday and it
is raining', and NOT 'it is true that it is Monday and it is raining.
But note this, in any case, the truth referred to in the correct,
grammatically, presented case is not a truth arising from the
application of a logical conjunction against two true propositions.

John Jones · Guest

James Burns wrote:
[quote]Herbert Newman wrote:
On Wed, 08 Oct 2008 00:20:40 +0100 John Jones wrote:

Consider

q "It¢s raining" is true,
p "It¢s Monday" is true.

It does not follow that p ^ q, "It>s Monday and it¢s raining",
is true.

That>s indeed fascinating. So if it>s Monday and it>s raining,
(i.e. if it is true that it is Monday and is true that it is
raining) you would not agree that it is true that it is Monday
and it is raining. Fascinating, indeed.

You are, apparently, following the path blazed by John Jones
and using "fascinating" in the sense of "not remotely fascinating".
Am I correct(*)?

(*) I am using "correct" here in the sense of "correct".

Jim Burns
[/quote]
Two truths obtain as one truth through a unifying context. Without that
context, two truths do not so obtain, or only obtain it as a
possibility. That>s all I>m saying folks.

Mitch · Guest

On Oct 8, 6:29 pm, John Jones <jonescard...@aol.com> wrote:
[quote]Mitch wrote:
On Oct 8, 2:34 pm, John Jones <jonescard...@aol.com> wrote:
Herbert Newman wrote:
On Wed, 08 Oct 2008 00:20:40 +0100 John Jones wrote:
Consider
q "It¢s raining" is true,
p "It¢s Monday" is true.
It does not follow that p ^ q, "It>s Monday and it¢s raining", is true.
That>s indeed fascinating. So if it>s Monday and it>s raining, (i.e. if it
is true that it is Monday and is true that it is raining) you would not
agree that it is true that it is Monday and it is raining. Fascinating,
indeed.
Yes, I would not agree that if it is true that it is Monday and is true
that it is raining, then it is true that it is Monday and it is raining.
I will summarise why I say that:

1) Two truths (Monday, raining) only obtain as one truth if the context
of each truth is the same.

The context for both separately and together is not the universe?

Mitch

Definitely not. It>s raining on Mars, and Monday on earth, may be true
at this time, but we can>t say that, therefore, it IS true that it is
Monday and it is raining. We wouldn>t know what was true. On the other
hand, we can say THEY ARE true that it is raining and it is Monday; but
the truth of that is not significant - it is not the truth of the
conjunction (raining and Monday) but refers vaguely to some truth that
the list (raining, Monday) possesses.
[/quote]
Oh. So I think what you>ve really done is show how those two sentences
('it is raining' and 'it is monday') aren>t true propositions by
themselves, each one requires a lot more information to be a
proposition. Most informal expositions do expect some sort of context
like 'it is monday, right here right now' and 'it is obviously raining
right here right now' (plus any other particulars you might imagine).
Propositional logic works best with mathematical statements.

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

John Jones · Guest

Mitch wrote:
[quote]On Oct 8, 2:34 pm, John Jones <jonescard...@aol.com> wrote:
Herbert Newman wrote:
On Wed, 08 Oct 2008 00:20:40 +0100 John Jones wrote:
Consider
q "It¢s raining" is true,
p "It¢s Monday" is true.
It does not follow that p ^ q, "It>s Monday and it¢s raining", is true.
That>s indeed fascinating. So if it>s Monday and it>s raining, (i.e. if it
is true that it is Monday and is true that it is raining) you would not
agree that it is true that it is Monday and it is raining. Fascinating,
indeed.
Yes, I would not agree that if it is true that it is Monday and is true
that it is raining, then it is true that it is Monday and it is raining.
I will summarise why I say that:

1) Two truths (Monday, raining) only obtain as one truth if the context
of each truth is the same.

The context for both separately and together is not the universe?

Mitch
[/quote]
Definitely not. It>s raining on Mars, and Monday on earth, may be true
at this time, but we can>t say that, therefore, it IS true that it is
Monday and it is raining. We wouldn>t know what was true. On the other
hand, we can say THEY ARE true that it is raining and it is Monday; but
the truth of that is not significant - it is not the truth of the
conjunction (raining and Monday) but refers vaguely to some truth that
the list (raining, Monday) possesses.

John Jones · Guest

Charlie wrote:
[quote]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

[/quote]
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.

Jan Burse · Guest

I would not like to touch, even with my fingertip:

John Jones schrieb:
[quote]1) an assumption that p and q arise in the same context (e.g. it>s
raining and Monday in the same spatiotemporal location). Given that this
context is not represented, then p ^ q is true (in this context) is not
a necessary truth but a dependent truth or a problematic assumed truth;
2) the identity of context of p and q is not assumed. Hence the
necessary truth of their conjunction (and) is only a possible truth (eg.
p and q may, or may not refer to days and times on different planets);
3) Necessary truth is defined circularly as being logical truth (we have
heard that argument before);
4) p and q, as propositional variables, are contextless. Hence, they are
semantically void.

None of these cases allows us to say that: the conjunction p and q, (p ^
q) of two propositions is true when both p and q are true, false otherwise.
[/quote]
BUT! (watch your butt)

The word "and2 does not always mean conjunction
in natural language. Here is an example:

"Fred, please choose between the left stack and the right stack!"

James Burns · Guest

John Jones wrote:
[quote]James Burns wrote:

Herbert Newman wrote:

On Wed, 08 Oct 2008 00:20:40 +0100 John Jones wrote:

Consider

q "It¢s raining" is true,
p "It¢s Monday" is true.

It does not follow that p ^ q, "It>s Monday and it¢s raining",
is true.

That>s indeed fascinating. So if it>s Monday and it>s raining,
(i.e. if it is true that it is Monday and is true that it is
raining) you would not agree that it is true that it is Monday
and it is raining. Fascinating, indeed.

You are, apparently, following the path blazed by John Jones
and using "fascinating" in the sense of "not remotely fascinating".
Am I correct(*)?

(*) I am using "correct" here in the sense of "correct".

Jim Burns

Two truths obtain as one truth through a unifying context.
Without that context, two truths do not so obtain, or only
obtain it as a possibility. That>s all I>m saying folks.
[/quote]
A proposition which is composed of two propositions
and the connective "and", using the proper syntax,
is true if and only if both of the propositions
of which it is composed are true.

That>s all I>m saying.

Jim Burns

Mitch · Guest

On Oct 9, 1:57 pm, John Jones <jonescard...@aol.com> wrote:
[quote]Mitch wrote:
On Oct 8, 6:29 pm, John Jones <jonescard...@aol.com> wrote:
Mitch wrote:
On Oct 8, 2:34 pm, John Jones <jonescard...@aol.com> wrote:
Herbert Newman wrote:
On Wed, 08 Oct 2008 00:20:40 +0100 John Jones wrote:
Consider
q "It¢s raining" is true,
p "It¢s Monday" is true.
It does not follow that p ^ q, "It>s Monday and it¢s raining", is true.
That>s indeed fascinating. So if it>s Monday and it>s raining, (i.e.. if it
is true that it is Monday and is true that it is raining) you would not
agree that it is true that it is Monday and it is raining. Fascinating,
indeed.
Yes, I would not agree that if it is true that it is Monday and is true
that it is raining, then it is true that it is Monday and it is raining.
I will summarise why I say that:
1) Two truths (Monday, raining) only obtain as one truth if the context
of each truth is the same.
The context for both separately and together is not the universe?
Mitch
Definitely not. It>s raining on Mars, and Monday on earth, may be true
at this time, but we can>t say that, therefore, it IS true that it is
Monday and it is raining. We wouldn>t know what was true. On the other
hand, we can say THEY ARE true that it is raining and it is Monday; but
the truth of that is not significant - it is not the truth of the
conjunction (raining and Monday) but refers vaguely to some truth that
the list (raining, Monday) possesses.

Oh. So I think what you>ve really done is show how those two sentences
('it is raining' and 'it is monday') aren>t true propositions by
themselves, each one requires a lot more information to be a
proposition. Most informal expositions do expect some sort of context
like 'it is monday, right here right now' and 'it is obviously raining
right here right now' (plus any other particulars you might imagine).
Propositional logic works best with mathematical statements.

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?
[/quote]
I>m not sure what you mean. What does it mean for an example, like
'it>s raining' to extend right across the board no exceptions? Do you
mean for -any- example? Or some example like 'it>s raining' with
properties that is bad? Across the board over what set?

An example like '2 + 2 = 5' is specific enough to be called a
proposition, not having the contextual difficulties you point out. So
not -all- statements have the problem (but, with the great worry that
this will be trying to put out a fire with gasoline even statements of
mathematics can have polysemy, e.g. '0=1' is under normal
circumstances, considered to always be a false proposition, 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'.)

Mitch

Mitch · Guest

On Oct 9, 4:17 pm, John Jones <jonescard...@aol.com> wrote:
[quote]Mitch wrote:
On Oct 9, 1:57 pm, John Jones <jonescard...@aol.com> wrote:
Mitch wrote:
On Oct 8, 6:29 pm, John Jones <jonescard...@aol.com> wrote:
Mitch wrote:
On Oct 8, 2:34 pm, John Jones <jonescard...@aol.com> wrote:
Herbert Newman wrote:
On Wed, 08 Oct 2008 00:20:40 +0100 John Jones wrote:
Consider
q "It¢s raining" is true,
p "It¢s Monday" is true.
It does not follow that p ^ q, "It>s Monday and it¢s raining", is true.
That>s indeed fascinating. So if it>s Monday and it>s raining, (i..e. if it
is true that it is Monday and is true that it is raining) you would not
agree that it is true that it is Monday and it is raining. Fascinating,
indeed.
Yes, I would not agree that if it is true that it is Monday and is true
that it is raining, then it is true that it is Monday and it is raining.
I will summarise why I say that:
1) Two truths (Monday, raining) only obtain as one truth if the context
of each truth is the same.
The context for both separately and together is not the universe?
Mitch
Definitely not. It>s raining on Mars, and Monday on earth, may be true
at this time, but we can>t say that, therefore, it IS true that it is
Monday and it is raining. We wouldn>t know what was true. On the other
hand, we can say THEY ARE true that it is raining and it is Monday; but
the truth of that is not significant - it is not the truth of the
conjunction (raining and Monday) but refers vaguely to some truth that
the list (raining, Monday) possesses.
Oh. So I think what you>ve really done is show how those two sentences
('it is raining' and 'it is monday') aren>t true propositions by
themselves, each one requires a lot more information to be a
proposition. Most informal expositions do expect some sort of context
like 'it is monday, right here right now' and 'it is obviously raining
right here right now' (plus any other particulars you might imagine).
Propositional logic works best with mathematical statements.
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?

I>m not sure what you mean. What does it mean for an example, like
'it>s raining' to extend right across the board no exceptions? Do you
mean for -any- example? Or some example like 'it>s raining' with
properties that is bad? Across the board over what set?

Across the board in the sense that logic>s presentation of truth values
takes place in an assumed universe of discourse where all logical
objects live in the same house, as it were.
[/quote]
Yeah, I>d go along with that. Logic talks about everything. So, no the
-problems- with the examples (of 'it>s raining' and 'it>s monday') do
not extend right across the board across the entire universe of
possible propositions (and most people are OK with assuming that,
e.g., 'it>s raining' refers to right here, right now). '2+2=5' is
pretty definitely a proposition.

[quote]An example like '2 + 2 = 5' is specific enough to be called a
proposition, not having the contextual difficulties you point out.

I can>t see how that example ... yes I can. Is it two and two is, or
are, four? All mathematical objects live in the same house. So I can>t
have different, unknown contexts that prevent me from saying two and two
IS four...but
[/quote]
Well, you -could- but it>d be either silly (in our context) or a very
specific notational situation (say addition mod 4, or where '+' really
means concatenate the two strings to get '22'. Math uses mathematical
language so there are contexts of language that can change (like the
following thing about rings).

[quote]So
not -all- statements have the problem (but, with the great worry that
this will be trying to put out a fire with gasoline even statements of
mathematics can have polysemy, e.g. '0=1' is under normal
circumstances, considered to always be a false proposition,

not sure where this is going. 0=1 is false... do we say that it is
'false'? Granted, it doesn>t fit in with any other number statement. I
don>t think it is false, but it might not be a significant expression.
[/quote]
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.

[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.
[/quote]
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.

Under certain circumstances, one might refer to the integer 17 and
the rational 17 (= 17/1) and be pedantic that these are -not- the same
thing (e.g. there are certain operations allowable on the rational 17
that are not on the integer 17). There is surely a morphism that
preserves the properties you>d expect of the integer 17 in the
rationals and so it is easy to just think of the integers as a subset
of the rationals or one could make the case (or define) the integers
as that particular subset of the rationals with the appropriate
properties.

The nice thing about mathematical language is that it is intended to
be unambiguous. If there is some qualm about ambiguity, then there is
a definition or clarification to be made, the ambiguity is not
tolerated. Of course there are inevitable cultural differences between
subtribes, but those are petty differences that are overcome by a
strict transform between the languages.

Mitch

John Jones · Guest

James Burns wrote:
[quote]John Jones wrote:
James Burns wrote:

Herbert Newman wrote:

On Wed, 08 Oct 2008 00:20:40 +0100 John Jones wrote:

Consider

q "It¢s raining" is true,
p "It¢s Monday" is true.

It does not follow that p ^ q, "It>s Monday and it¢s raining",
is true.

That>s indeed fascinating. So if it>s Monday and it>s raining,
(i.e. if it is true that it is Monday and is true that it is
raining) you would not agree that it is true that it is Monday
and it is raining. Fascinating, indeed.

You are, apparently, following the path blazed by John Jones
and using "fascinating" in the sense of "not remotely fascinating".
Am I correct(*)?

(*) I am using "correct" here in the sense of "correct".

Jim Burns

Two truths obtain as one truth through a unifying context.
Without that context, two truths do not so obtain, or only
obtain it as a possibility. That>s all I>m saying folks.

A proposition which is composed of two propositions
and the connective "and", using the proper syntax,
is true if and only if both of the propositions
of which it is composed are true.

That>s all I>m saying.

Jim Burns
[/quote]
Yes.
It>s wrong. To the plain man, tired of being led astray by logical
platitudes, its clearly wrong, plain and simple.


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