According to the most popular definition, logic is the study of
arguments. That is, of mental operations deriving a conclusion from one
or more premises. The premises can be combined in a conjunction and
then logic becomes the study of conditionals (if..., then...).
Accordingly, logic would prefer any deductive theory to have the form:

1. If..., then.....
2. If..., then.....
3. If..., then..... etc.

The difference between this form of the theory and the traditional one
is that the former urges the public to verify the validity of ALL the
conditionals (arguments) and the truth of ALL the premises whereas the
latter rather discourages them from attempting any logical
verification. That is the reason why the listed-conditional form will
never be adopted.

Pentcho Valev

"Pentcho Valev" wrote in message
oups.com...
According to the most popular definition, logic is the study of
arguments. That is, of mental operations deriving a conclusion from one
or more premises. The premises can be combined in a conjunction and
then logic becomes the study of conditionals (if..., then...).
Accordingly, logic would prefer any deductive theory to have the form:

1. If..., then.....
2. If..., then.....
3. If..., then..... etc.

The difference between this form of the theory and the traditional one
is that the former urges the public to verify the validity of ALL the
conditionals (arguments) and the truth of ALL the premises whereas the
latter rather discourages them from attempting any logical
verification. That is the reason why the listed-conditional form will
never be adopted.

Your "listed conditional form" is called deductive reasoning. It's
advantage is that the validity of the conclusions is assured, provided the
premises are valid. It has a down side. There is never any more
information contained in the conclusions than was already present in the
premsies. If you want to add information, you have to use inductive
reasoning. Of course, the validity of what you come up is not guaranteed,
but it does provide new information.



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Pentcho Valev wrote:
According to the most popular definition, logic is the study of
arguments.

Also sprach Wikipedia.

That is, of mental operations deriving a conclusion from one
or more premises. The premises can be combined in a conjunction and
then logic becomes the study of conditionals (if..., then...).
Accordingly, logic would prefer any deductive theory to have the form:

1. If..., then.....
2. If..., then.....
3. If..., then..... etc.

This is simply a *summary* of deductions. This "If-Then format" is the
equivalent of a mathematical statement of a theorem (a theory using
deductive logic), with the assumptions and conditions listed after the
"if" and the conclusion(s) stated after the "then."

As any mathematician can tell you, the *proof* of a theorem is where
the logic lies, and almost invariably extends well beyond the simple
statements.

http://mathworld.wolfram.com/Theorem.html

For example, there is far more to the logic (i.e. the proof) of the
Pythagorean Theorem than

a^2 + b^2 = c^2

The 'ifs' should specify a right triangle in a planar Euclidean space
with proper identification of the sides and the hypotenuse. That only
completes the 'if-then' part of the statement. The logic of the
*proof* of the Pythagorean Theorem can unfold in myriad ways, both
geometric and algebraic, and will include references to previously
established mathematical propositions (axioms, assumptions, and
theorems).

Only when the logical steps forming a valid proof have been completed
does one have in hand a theorem.

Tom Davidson
Richmond, VA

"Pentcho Valev" wrote in message
oups.com...
According to the most popular definition, logic is the study of
arguments.

I wonder if Boole would agree with that or the engineers who use it to
design switching circuits. Your silly Semitic pigeonholing does not apply
to math and logic.

That is, of mental operations deriving a conclusion from one
or more premises. The premises can be combined in a conjunction and
then logic becomes the study of conditionals (if..., then...).
Accordingly, logic would prefer any deductive theory to have the form:

1. If..., then.....
2. If..., then.....
3. If..., then..... etc.

The difference between this form of the theory and the traditional one
is that the former urges the public to verify the validity of ALL the
conditionals (arguments) and the truth of ALL the premises whereas the
latter rather discourages them from attempting any logical
verification. That is the reason why the listed-conditional form will
never be adopted.

This difference between what is printed in textbooks and what you write is
textbooks usually make sense.

Bill


Pentcho Valev

"Bill Hobba" wrote in message news

"Pentcho Valev" wrote in message
oups.com...
According to the most popular definition, logic is the study of
arguments.

I wonder if Boole would agree with that or the engineers who use it to
design switching circuits. Your silly Semitic pigeonholing does not apply
to math and logic.

.... and since a few days he lost the very reason for bringing
up this silly strawman to begin with.
Something seems to have dawned on him, but he's not yet
sure what it is. What an incredible dope.

Dirk Vdm

Pentcho Valev:
According to the most popular definition, logic is the study of
arguments.

If that were the case, then you would have invented the Stupid Logic
as a sub discipline.

That is, of mental operations deriving a conclusion from one
or more premises. The premises can be combined in a conjunction and
then logic becomes the study of conditionals (if..., then...).
Accordingly, logic would prefer any deductive theory to have the form:

1. If..., then.....
2. If..., then.....
3. If..., then..... etc.

The difference between this form of the theory and the traditional one
is that the former urges the public to verify the validity of ALL the
conditionals (arguments) and the truth of ALL the premises whereas the
latter rather discourages them from attempting any logical
verification. That is the reason why the listed-conditional form will
never be adopted.

Pentcho Valev

Dirk Van de moortel:

"Bill Hobba" wrote in message
news

"Pentcho Valev" wrote in message
oups.com...
According to the most popular definition, logic is the study of
arguments.

I wonder if Boole would agree with that or the engineers who use it to
design switching circuits. Your silly Semitic pigeonholing does not apply
to math and logic.

... and since a few days he lost the very reason for bringing
up this silly strawman to begin with.
Something seems to have dawned on him, but he's not yet
sure what it is.

Maybe we could arrange an accident before he does and posts an article
about it.

What an incredible dope.

You've vastly overestimated his talent. But, I just of a use for him,
that fits his vast interest in logic. He can be the prototype for the
Pentcho test. Its sort of like the turing test. If someone can't
tell the difference between a computer and mr. valev, the computer isn't
plugged in.

Pentcho Valev wrote:
According to the most popular definition, logic is the study of
arguments. That is, of mental operations deriving a conclusion from one
or more premises. The premises can be combined in a conjunction and
then logic becomes the study of conditionals (if..., then...).

There are many forms of implication.

Accordingly, logic would prefer any deductive theory to have the form:

1. If..., then.....
2. If..., then.....
3. If..., then..... etc.

plus a defined truth table for the particular implication, disjunction,
and conjunction


The difference between this form of the theory and the traditional one
is that the former urges the public to verify the validity of ALL the
conditionals (arguments) and the truth of ALL the premises whereas the
latter rather discourages them from attempting any logical
verification.

Who says so?

That is the reason why the listed-conditional form will
never be adopted.

I told you to look very closely at material implication and modus
ponens. The question is, How to make modus ponens a tautology.

Now, in physics, there is no necessary logical relationship between
hypothesis and conclusion. If there were, there'd be no point in
empiricism, because all conclusions would be logically contained in
their hypotheses. For example,

If I drop a stone from rest above the floor of my lab then the stone
will fall to the floor.

I do NOT know that because of any logical connection between hypothesis
and conclusion. I know it (inductively) because I performed the
experiment over and over. The relationship is material, or just because
that's the way the universe happen to be. Material implication also
includes arbitrary relationships between hypothesis and conclusion.

I can freely invent an arbitrary material implication:

If it snows tomorrow then I will go to the store.

The conclusion, I WILL GO TO THE STORE is not logically necesitated by
the hypothesis, since the hypothesis IT SNOWS TOMORROW may support
either the given conclusion or its negation depending on my whim. But
modus ponens is a tautology either way.