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herbzet
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 Posted: Tue Oct 21, 2008 7:45 am Post subject: Re: The problematic connective |
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John Jones wrote:
[quote]herbzet wrote:
John Jones wrote:
herbzet wrote:
John Jones wrote:
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'.
'P' or P, offers only itself, while not-P, if P, or etc, offer others.
And, not, if, or, are convenient ways of expressing other objects or
proposals other than the proposal 'operated' on. In other words,
operators are objects or proposals. They are not logical powers or
agencies that act upon a proposal, object or proposition etc. I don>t
see any distinction between operators and what they operate on.
"what they operate on" = operand
Or doer and done to. It>s strange that we describe the former as an
agency or operator but not the latter. After all, it>s always both that
change. The reason is that doer and done to are a priviliged binary.
This means that a privilege, or favoured status, is granted from outside
the binary to one of the pair. In this case the operator or doer is
classed as a superior sort of object - an agency, while the done to, or
operand, is not so favoured. All we have to do then is give a reason for
granting this privilege, which shouldn>t be hard to find.
It wouldn>t hurt, I think, to ascribe, for convenience, a purely
grammatical existence to operators, e.g., "the" is an operator
(in this case, an article) that takes a noun phrase as an argument
and returns a noun phrase.
I would have to see some examples. I know latin doesn>t have a word for
'the'.
[/quote]
Oh, come on. Get an english grammar and find your own examples.
How about an adjective, for example?
[quote]In any case, it>s sometimes helpful to keep in mind the distinction
between the language and what is denoted by the language, if anything.
After all, the language is a pretty concrete object, while what,
presumably, is being denoted (especially in logic/mathematics)
is not, particularly.
--
hz[/quote] |
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John Jones
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| Posted: Sat Oct 25, 2008 7:22 am Post subject: Re: The problematic connective |
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Mitch wrote:
[quote]On Oct 15, 8:55 pm, herbzet <herb...@gmail.com> wrote:
John Jones wrote:
herbzet wrote:
Mitch wrote:
I>m surprised you>re picking on 'and'. 'or' is much more problematic.
Cripes, what about 'if then'?
...
Er...yes, I will take a look at those others soon.
Stick with "and" till you beat it death, is my advice. You
can>t get much more fundamental than that, and "not".
OK, but now I realize that all the substantive discussion so far
really has only said things about 'and' that are also the case for
other operators...um...logical connectors. That is, the discussion has
been about operators, what a proposition -is-, 'combining' values.
Anything special about that simplest of connectors 'and', different
from the others?
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.
(substituting 'or', or 'then' or 'xor' doesn>t make much difference in
the above)
Can anything be said about 'and' that is special? (-is- there a
difference between classical and intuitionistic 'and'? (I don>t think
so))
Mitch
[/quote]
Logical 'and' cannot be distinguished from logical 'or'. That>s the
plain fact of it.
This is not because they are not the same, but because they are
underdetermined - vague or incoherent. |
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Mitch Harris
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| Posted: Sat Oct 25, 2008 8:25 pm Post subject: Re: The problematic connective |
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On Oct 24, 10:22 pm, John Jones <jonescard...@aol.com> wrote:
[quote]Mitch wrote:
On Oct 15, 8:55 pm, herbzet <herb...@gmail.com> wrote:
John Jones wrote:
herbzet wrote:
Mitch wrote:
I>m surprised you>re picking on 'and'. 'or' is much more problematic.
Cripes, what about 'if then'?
...
Er...yes, I will take a look at those others soon.
Stick with "and" till you beat it death, is my advice. You
can>t get much more fundamental than that, and "not".
OK, but now I realize that all the substantive discussion so far
really has only said things about 'and' that are also the case for
other operators...um...logical connectors. That is, the discussion has
been about operators, what a proposition -is-, 'combining' values.
Anything special about that simplest of connectors 'and', different
from the others?
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.
(substituting 'or', or 'then' or 'xor' doesn>t make much difference in
the above)
Can anything be said about 'and' that is special? (-is- there a
difference between classical and intuitionistic 'and'? (I don>t think
so))
Mitch
Logical 'and' cannot be distinguished from logical 'or'. That>s the
plain fact of it.
[/quote]
Oh.
[quote]This is not because they are not the same, but because they are
underdetermined - vague or incoherent.
[/quote]
To the extent that the following can be formalized in logical 'and'
and 'or':
'Give me a hammer and a nail'
'Give me a hammer or a nail'
....these, under certain very determined, precise, and coherent
circumstances, have different outcomes.
Can you elaborate on how logical 'and' and 'or' are either vague or
incoherent (please, explain both)? (your discussion so far has not
given any indication of that)
Mitch |
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John Jones
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| Posted: Sun Oct 26, 2008 12:55 am Post subject: Re: The problematic connective |
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herbzet wrote:
[quote]
John Jones wrote:
herbzet wrote:
John Jones wrote:
herbzet wrote:
John Jones wrote:
herbzet wrote:
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.
Arguments, values, operators and variables look like another thing to
look at.
Yes, also functions.
Witt, btw, distinguishes between an operator and a function, in
5.23, 5.251, 5.3, which I believe many people do, but the discussion
gets pretty abstruse. I use "operator" in a pretty loose way.
I don>t know about these arguments and values etc. The ideas never took
root with me. Every time I see the words I must look them up, time after
time. Something must be wrong. I suspect that they are convoluted ways
of presenting objects. The idea that there are objects that are acted
upon by logical force is a strange one.
Just think of them as grammatical devices. Like "John>s wife" is a
way of indicating a particular person. Or "the (positive) square root
of two" indicates a particular real number.
I don>t know. It appears as if the distinction between an argument or
operation, and an object, is that the former refers to an object while
the latter
An object?
presents an object.
An object presents an object? Unhelpful.
Also, there is a distinction to be observed between an operation
and an argument: the thing (or things) an operation operates on is
called its argument (or arguments).
The thing an argument returns, having operated on its argument(s),
is called its value.
"Refers" is a concept I understand. I have no idea what you
might be meaning by "presents".
'Square root of' tells us how we should
look for an object, while 'square root of 9' tells us where to find it,
and '3' presents the object.
[/quote]
I was saying that 3 is presented and sqrt9 is one of a myriad of ways
that tell us where 3 can be found. So sqrt9 and 3 is like a library
location reference for a book.
[quote]In math, I>ve never heard of "presenting".
[/quote]
When you start an application, you might write a sign or number down.
You present it. Also, a presentation is the result of an application,
the end-product, the number you are looking for and wish to use.
Unless we keep the idea of presentation, as the object itself, it makes
no sense to have the idea of refering to it.
[quote]In math "sqrt(9) = 3" means
that the expression on the left of the identity symbol '=' refers to the
same object as the expression to the right of the identity symbol.
[/quote]
[quote]I will grant the the expression on the left is a rather more indirect
referring expression than the expression on the right.
But so what? "My sister-in-law" is a less direct reference than "Sue Smith",
but no one seems to have a problem with "My sister-in-law is Sue Smith".
--
hz
[/quote]
But then the object that is referenced doesn>t have an identity at all. |
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herbzet
Guest
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| Posted: Sun Oct 26, 2008 7:29 am Post subject: Re: The problematic connective |
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John Jones wrote:
[quote]herbzet wrote:
John Jones wrote:
herbzet wrote:
John Jones wrote:
herbzet wrote:
John Jones wrote:
herbzet wrote:
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.
Arguments, values, operators and variables look like another thing to
look at.
Yes, also functions.
Witt, btw, distinguishes between an operator and a function, in
5.23, 5.251, 5.3, which I believe many people do, but the discussion
gets pretty abstruse. I use "operator" in a pretty loose way.
I don>t know about these arguments and values etc. The ideas never took
root with me. Every time I see the words I must look them up, time after
time. Something must be wrong. I suspect that they are convoluted ways
of presenting objects. The idea that there are objects that are acted
upon by logical force is a strange one.
Just think of them as grammatical devices. Like "John>s wife" is a
way of indicating a particular person. Or "the (positive) square root
of two" indicates a particular real number.
I don>t know. It appears as if the distinction between an argument or
operation, and an object, is that the former refers to an object while
the latter
An object?
presents an object.
An object presents an object? Unhelpful.
Also, there is a distinction to be observed between an operation
and an argument: the thing (or things) an operation operates on is
called its argument (or arguments).
The thing an argument returns, having operated on its argument(s),
is called its value.
"Refers" is a concept I understand. I have no idea what you
might be meaning by "presents".
'Square root of' tells us how we should
look for an object, while 'square root of 9' tells us where to find it,
and '3' presents the object.
I was saying that 3 is presented and sqrt9 is one of a myriad of ways
that tell us where 3 can be found.
[/quote]
You seem to think that '3' does not refer. A standard response would
be to ask if the word 'three', the Roman numeral 'III', the binary
numeral '11' etc. are similarly non-referring, or do they all refer
to the same abstract object?
[quote]So sqrt9 and 3 is like a library
location reference for a book.
In math, I>ve never heard of "presenting".
When you start an application, you might write a sign or number down.
You present it. Also, a presentation is the result of an application,
the end-product, the number you are looking for and wish to use.
Unless we keep the idea of presentation, as the object itself, it makes
no sense to have the idea of referring to it.
[/quote]
Well, the thesis that the numerals are, in fact, the numbers, would
be an interesting one to defend. There are philosophical precedents,
I think. I>m not sure that>s exactly what you>re intending.
[quote]In math "sqrt(9) = 3" means
that the expression on the left of the identity symbol '=' refers to the
same object as the expression to the right of the identity symbol.
I will grant the the expression on the left is a rather more indirect
referring expression than the expression on the right.
But so what? "My sister-in-law" is a less direct reference than "Sue Smith",
but no one seems to have a problem with "My sister-in-law is Sue Smith".
--
hz
But then the object that is referenced doesn>t have an identity at all.
[/quote]
That is an interesting remark.
--
hz |
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herbzet
Guest
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| Posted: Sun Oct 26, 2008 7:29 am Post subject: Re: The problematic connective |
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John Jones wrote:
[quote]
Mitch wrote:
herbzet wrote:
John Jones wrote:
herbzet wrote:
Mitch wrote:
I>m surprised you>re picking on 'and'. 'or' is much more problematic.
Cripes, what about 'if then'?
...
Er...yes, I will take a look at those others soon.
Stick with "and" till you beat it death, is my advice. You
can>t get much more fundamental than that, and "not".
OK, but now I realize that all the substantive discussion so far
really has only said things about 'and' that are also the case for
other operators...um...logical connectors. That is, the discussion has
been about operators, what a proposition -is-, 'combining' values.
Anything special about that simplest of connectors 'and', different
from the others?
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.
(substituting 'or', or 'then' or 'xor' doesn>t make much difference in
the above)
Can anything be said about 'and' that is special? (-is- there a
difference between classical and intuitionistic 'and'? (I don>t think
so))
Mitch
Logical 'and' cannot be distinguished from logical 'or'. That>s the
plain fact of it.
This is not because they are not the same, but because they are
underdetermined - vague or incoherent.
[/quote]
If that>s true, than we may ask if either can be distinguished from slithy toves.
--
hz |
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John Jones
Guest
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| Posted: Sun Oct 26, 2008 7:25 pm Post subject: Re: The problematic connective |
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herbzet wrote:
[quote]
John Jones wrote:
herbzet wrote:
John Jones wrote:
I was saying that 3 is presented and sqrt9 is one of a myriad of ways
that tell us where 3 can be found.
You seem to think that '3' does not refer. A standard response would
be to ask if the word 'three', the Roman numeral 'III', the binary
numeral '11' etc. are similarly non-referring, or do they all refer
to the same abstract object?
[/quote]
As long as a numeral is employed in an application as a number, and is
not simply a stand-alone numeral, then all these examples would be
equivalent.
[quote]So sqrt9 and 3 is like a library
location reference for a book.
But so what? "My sister-in-law" is a less direct reference than "Sue Smith",
but no one seems to have a problem with "My sister-in-law is Sue Smith".
--
hz
But then the object that is referenced doesn>t have an identity at all.
That is an interesting remark.
[/quote]
We can>t keep declaring a sign to be a reference to something else. If
everything is a reference, then the something else doesn>t have an identity. |
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