| Topic: |
Science > Philosophy |
| User: |
"Immortalist" |
| Date: |
03 Oct 2004 12:27:34 PM |
| Object: |
THE THREE "LAWS OF THOUGHT" |
THE THREE "LAWS OF THOUGHT"
Those who have defined logic as the science of the laws of thought have often
gone on to assert that there are exactly three fundamental or basic laws of
thought necessary and sufficient for thinking to follow if it is to be "correct."
These have traditionally been called "the principle of identity," "the principle
of contradiction" (sometimes "the principle of noncontradiction"), and "the
principle of excluded middle." There are alternative formulations of these
principles, appropriate to different contexts. The formulations appropriate here
are the following:
[1] - The principle of identity asserts that if any statement is true, then it is
true.
[2] - The principle of contradiction asserts that no statement can be both true
and false.
[3] - The principle of excluded middle asserts that any statement is either true
or false.
In the terminology of the present chapter, we may rephrase them as follows. The
principle of identity asserts that every statement of the form (IF p THEREFORE p)
is true; that is, that every such statement is a tautology. The principle of
contradiction asserts that every statement of the form (p AND NOT p) is false;
that is, that every such statement is self-contradictory. The principle of
excluded middle asserts that every statement of the form (p OR NOT p) is true;
that is, that every such statement is a tautology.
Objections have been made to these principles from time to time, but for the most
part, the objections seem to be based on misunderstandings;
[1] - The principle of identity has been criticized on the grounds that things
change, for statements that were true, say, of the United States when it
consisted of the 13 original states, is no longer true of the United States today
with its 50 states. In one sense of the word "statement" this observation is
correct, but that sense is not the one with which logic is concerned. Those
"statements" whose truth values change with time are elliptical or incomplete
formulations of propositions that do not change, and it is the propositions that
do not change with which logic deals. Thus the sentence "There are only 13 states
in the United States" may be regarded as an elliptical or partial formulation of
"There were only 13 states in the United States in 1790," which is just as true
today as it was in 1790. When we confine our attention to complete or
nonelliptical formulations, the principle of identity is perfectly true and
unobjectionable.
[2] - The principle of contradiction has been criticized by Hegelians, general
semanticists, and Marxists, on the grounds that there are contradictions, real
situations in which contradictory or conflicting forces are at work. That there
are situations containing conflicting forces must be admitted; this is as true in
the realm of mechanics as in social and economic spheres. But it is a loose and
inconvenient terminology to call these conflicting forces "contradictory." The
heat applied to a contained gas, which tends to make it expand, and the
container, which tends to keep it from expanding, may be described as conflicting
with each other, but neither is the negation or denial or contradictory of the
other. The private owner of a large factory, which requires thousands of laborers
working together for its operation, may oppose and be opposed by the labor union
that could never have been organized if its members had not been brought together
to work in that factory; but neither owner nor union is the negation or denial or
contradictory of the other. When understood in the sense in which it is intended,
the principle of contradiction is unobjectionable and perfectly true.
[3] - The principle of excluded middle has been the object of more attacks than
either of the other principles. It has been urged that its acceptance leads to a
"two-valued orientation," which implies, among other things, that everything is
either white or black, with any middle ground excluded. But although the
statement "This is black" cannot be jointly true along with the statement "This i
s white" (where the word "this" refers to exactly the same thing in both
statements), one is not the denial or contradictory of the other. Admittedly they
cannot both be true, but they can both be false. They are contrary, but not
contradictory. The negation or contradictory of "This is white," is "-this is
white," and one of these statements must be true-if the word "white" is used in
precisely the same sense in both statements. When restricted to statements
containing completely unambiguous and perfetly precise terms, the principle of
excluded middle is also perfectly true.
Conclusion: These three principles-the principle of identity, the principle of
contradiction, the principle of excluded middle-are indubitably true. Some
traditional logicians assigned them a privileged and most fundamental status,[see
note below*] but the special claims sometimes made for them may be doubted. The
first (identity) and the third (excluded middle) are by no means the only forms
of tautologies, and the explicit contradiction (p AND NOT p) ruled out by the
second principle is by no means the only contradictory form of statement. Yet the
three laws of thought can be regarded as having a certain fundamental status in
relation to truth tables. As we fill in subsequent columns by referring back to
the initial columns, we are guided by the principle of identity: If a T has been
placed under a symbol in a certain row, then in filling in other columns under
expressions containing that symbol, when we come to that row we regard that
symbol as still being assigned a T. In filling out the initial columns, in each
row we put either a T or an F, being guided by the principle of excluded middle;
and nowhere do we put both T and F together, being guided by the principle of
contradiction. The three laws of thought can be regarded as the basic principles
governing the construction of truth tables.
Still, it should be remarked that when one attempts to set up logic as a system,
these three principles are no more "important" or "fruitful" than many others.
Indeed there are other tautologies that are more fruitful for purposes of
deduction-and hence more important-than the three principles discussed. A
treatment of this point, however, lies beyond the scope of this book.
[*] Plato appealed explicitly to the principle of contradiction in Book IV of his
Republic
(at nos. 436 and 439), and Aristotle discussed all three of these principles in
Books IV
and XI of his Metaphysics. Of the principle of contradiction, Aristotle wrote;
"That the same attribute cannot at the same time belong and not belong to the
same subject and in the same respect" is a principle "which every one must have
who understands anything that is," and which "every one must already have when he
comes to a special study." It is, he concluded, "the most certain of all
principles."
Introduction to Logic - by Irving M. Copi, Carl Cohen
http://www.amazon.com/exec/obidos/tg/detail/-/0130749214/qid=1096821419/
.
|
|
| User: "Tim" |
|
| Title: Re: THE THREE "LAWS OF THOUGHT" |
03 Oct 2004 12:42:59 PM |
|
|
"Immortalist" <Reanimater_2000@yahoo.com> wrote in message
news:Gr-dnaiH3JSPqv3cRVn-uA@comcast.com...
THE THREE "LAWS OF THOUGHT"
Those who have defined logic as the science of the laws of thought have
often
gone on to assert that there are exactly three fundamental or basic laws
of
thought necessary and sufficient for thinking to follow if it is to be
"correct."
These have traditionally been called "the principle of identity," "the
principle
of contradiction" (sometimes "the principle of noncontradiction"), and
"the
principle of excluded middle." There are alternative formulations of these
principles, appropriate to different contexts. The formulations
appropriate here
are the following:
[1] - The principle of identity asserts that if any statement is true,
then it is
true.
[2] - The principle of contradiction asserts that no statement can be both
true
and false.
[3] - The principle of excluded middle asserts that any statement is
either true
or false.
In the terminology of the present chapter, we may rephrase them as
follows. The
principle of identity asserts that every statement of the form (IF p
THEREFORE p)
is true; that is, that every such statement is a tautology. The principle
of
contradiction asserts that every statement of the form (p AND NOT p) is
false;
that is, that every such statement is self-contradictory. The principle of
excluded middle asserts that every statement of the form (p OR NOT p) is
true;
that is, that every such statement is a tautology.
Objections have been made to these principles from time to time, but for
the most
part, the objections seem to be based on misunderstandings;
[1] - The principle of identity has been criticized on the grounds that
things
change, for statements that were true, say, of the United States when it
consisted of the 13 original states, is no longer true of the United
States today
with its 50 states. In one sense of the word "statement" this observation
is
correct, but that sense is not the one with which logic is concerned.
Those
"statements" whose truth values change with time are elliptical or
incomplete
formulations of propositions that do not change, and it is the
propositions that
do not change with which logic deals. Thus the sentence "There are only 13
states
in the United States" may be regarded as an elliptical or partial
formulation of
"There were only 13 states in the United States in 1790," which is just as
true
today as it was in 1790. When we confine our attention to complete or
nonelliptical formulations, the principle of identity is perfectly true
and
unobjectionable.
[2] - The principle of contradiction has been criticized by Hegelians,
general
semanticists, and Marxists, on the grounds that there are contradictions,
real
situations in which contradictory or conflicting forces are at work. That
there
are situations containing conflicting forces must be admitted; this is as
true in
the realm of mechanics as in social and economic spheres. But it is a
loose and
inconvenient terminology to call these conflicting forces "contradictory."
The
heat applied to a contained gas, which tends to make it expand, and the
container, which tends to keep it from expanding, may be described as
conflicting
with each other, but neither is the negation or denial or contradictory of
the
other. The private owner of a large factory, which requires thousands of
laborers
working together for its operation, may oppose and be opposed by the labor
union
that could never have been organized if its members had not been brought
together
to work in that factory; but neither owner nor union is the negation or
denial or
contradictory of the other. When understood in the sense in which it is
intended,
the principle of contradiction is unobjectionable and perfectly true.
[3] - The principle of excluded middle has been the object of more attacks
than
either of the other principles. It has been urged that its acceptance
leads to a
"two-valued orientation," which implies, among other things, that
everything is
either white or black, with any middle ground excluded. But although the
statement "This is black" cannot be jointly true along with the statement
"This i
s white" (where the word "this" refers to exactly the same thing in both
statements), one is not the denial or contradictory of the other.
Admittedly they
cannot both be true, but they can both be false. They are contrary, but
not
contradictory. The negation or contradictory of "This is white," is "-this
is
white," and one of these statements must be true-if the word "white" is
used in
precisely the same sense in both statements. When restricted to statements
containing completely unambiguous and perfetly precise terms, the
principle of
excluded middle is also perfectly true.
Conclusion: These three principles-the principle of identity, the
principle of
contradiction, the principle of excluded middle-are indubitably true. Some
traditional logicians assigned them a privileged and most fundamental
status,[see
note below*] but the special claims sometimes made for them may be
doubted. The
first (identity) and the third (excluded middle) are by no means the only
forms
of tautologies, and the explicit contradiction (p AND NOT p) ruled out by
the
second principle is by no means the only contradictory form of statement.
Yet the
three laws of thought can be regarded as having a certain fundamental
status in
relation to truth tables. As we fill in subsequent columns by referring
back to
the initial columns, we are guided by the principle of identity: If a T
has been
placed under a symbol in a certain row, then in filling in other columns
under
expressions containing that symbol, when we come to that row we regard
that
symbol as still being assigned a T. In filling out the initial columns, in
each
row we put either a T or an F, being guided by the principle of excluded
middle;
and nowhere do we put both T and F together, being guided by the principle
of
contradiction. The three laws of thought can be regarded as the basic
principles
governing the construction of truth tables.
Still, it should be remarked that when one attempts to set up logic as a
system,
these three principles are no more "important" or "fruitful" than many
others.
Indeed there are other tautologies that are more fruitful for purposes of
deduction-and hence more important-than the three principles discussed. A
treatment of this point, however, lies beyond the scope of this book.
[*] Plato appealed explicitly to the principle of contradiction in Book IV
of his
Republic
(at nos. 436 and 439), and Aristotle discussed all three of these
principles in
Books IV
and XI of his Metaphysics. Of the principle of contradiction, Aristotle
wrote;
"That the same attribute cannot at the same time belong and not belong to
the
same subject and in the same respect" is a principle "which every one must
have
who understands anything that is," and which "every one must already have
when he
comes to a special study." It is, he concluded, "the most certain of all
principles."
Introduction to Logic - by Irving M. Copi, Carl Cohen
http://www.amazon.com/exec/obidos/tg/detail/-/0130749214/qid=1096821419/
So if I could offer just one example to the contrary, in other words, if I
could show a situation that you or I or anyone else could possibly
experience and that situation contradicts one and all of the Three Laws,
then those Three Laws would stand refuted?
.
|
|
|
| User: "Immortalist" |
|
| Title: Re: THE THREE "LAWS OF THOUGHT" |
03 Oct 2004 01:13:22 PM |
|
|
"Tim" <abc@abc.abc> wrote in message
news:JIadnT-SvrTZp_3cRVn-iQ@edaptivity.com...
"Immortalist" <Reanimater_2000@yahoo.com> wrote in message
news:Gr-dnaiH3JSPqv3cRVn-uA@comcast.com...
THE THREE "LAWS OF THOUGHT"
Those who have defined logic as the science of the laws of thought have often
gone on to assert that there are exactly three fundamental or basic laws of
thought necessary and sufficient for thinking to follow if it is to be
"correct."
These have traditionally been called "the principle of identity," "the
principle
of contradiction" (sometimes "the principle of noncontradiction"), and "the
principle of excluded middle." There are alternative formulations of these
principles, appropriate to different contexts. The formulations appropriate
here
are the following:
[1] - The principle of identity asserts that if any statement is true, then it
is
true.
[2] - The principle of contradiction asserts that no statement can be both true
and false.
[3] - The principle of excluded middle asserts that any statement is either
true
or false.
In the terminology of the present chapter, we may rephrase them as follows. The
principle of identity asserts that every statement of the form (IF p THEREFORE
p)
is true; that is, that every such statement is a tautology. The principle of
contradiction asserts that every statement of the form (p AND NOT p) is false;
that is, that every such statement is self-contradictory. The principle of
excluded middle asserts that every statement of the form (p OR NOT p) is true;
that is, that every such statement is a tautology.
Objections have been made to these principles from time to time, but for the
most
part, the objections seem to be based on misunderstandings;
[1] - The principle of identity has been criticized on the grounds that things
change, for statements that were true, say, of the United States when it
consisted of the 13 original states, is no longer true of the United States
today
with its 50 states. In one sense of the word "statement" this observation is
correct, but that sense is not the one with which logic is concerned. Those
"statements" whose truth values change with time are elliptical or incomplete
formulations of propositions that do not change, and it is the propositions
that
do not change with which logic deals. Thus the sentence "There are only 13
states
in the United States" may be regarded as an elliptical or partial formulation
of
"There were only 13 states in the United States in 1790," which is just as true
today as it was in 1790. When we confine our attention to complete or
nonelliptical formulations, the principle of identity is perfectly true and
unobjectionable.
[2] - The principle of contradiction has been criticized by Hegelians, general
semanticists, and Marxists, on the grounds that there are contradictions, real
situations in which contradictory or conflicting forces are at work. That there
are situations containing conflicting forces must be admitted; this is as true
in
the realm of mechanics as in social and economic spheres. But it is a loose and
inconvenient terminology to call these conflicting forces "contradictory." The
heat applied to a contained gas, which tends to make it expand, and the
container, which tends to keep it from expanding, may be described as
conflicting
with each other, but neither is the negation or denial or contradictory of the
other. The private owner of a large factory, which requires thousands of
laborers
working together for its operation, may oppose and be opposed by the labor
union
that could never have been organized if its members had not been brought
together
to work in that factory; but neither owner nor union is the negation or denial
or
contradictory of the other. When understood in the sense in which it is
intended,
the principle of contradiction is unobjectionable and perfectly true.
[3] - The principle of excluded middle has been the object of more attacks than
either of the other principles. It has been urged that its acceptance leads to
a
"two-valued orientation," which implies, among other things, that everything is
either white or black, with any middle ground excluded. But although the
statement "This is black" cannot be jointly true along with the statement "This
i
s white" (where the word "this" refers to exactly the same thing in both
statements), one is not the denial or contradictory of the other. Admittedly
they
cannot both be true, but they can both be false. They are contrary, but not
contradictory. The negation or contradictory of "This is white," is "-this is
white," and one of these statements must be true-if the word "white" is used in
precisely the same sense in both statements. When restricted to statements
containing completely unambiguous and perfetly precise terms, the principle of
excluded middle is also perfectly true.
Conclusion: These three principles-the principle of identity, the principle of
contradiction, the principle of excluded middle-are indubitably true. Some
traditional logicians assigned them a privileged and most fundamental
status,[see
note below*] but the special claims sometimes made for them may be doubted. The
first (identity) and the third (excluded middle) are by no means the only forms
of tautologies, and the explicit contradiction (p AND NOT p) ruled out by the
second principle is by no means the only contradictory form of statement. Yet
the
three laws of thought can be regarded as having a certain fundamental status in
relation to truth tables. As we fill in subsequent columns by referring back to
the initial columns, we are guided by the principle of identity: If a T has
been
placed under a symbol in a certain row, then in filling in other columns under
expressions containing that symbol, when we come to that row we regard that
symbol as still being assigned a T. In filling out the initial columns, in each
row we put either a T or an F, being guided by the principle of excluded
middle;
and nowhere do we put both T and F together, being guided by the principle of
contradiction. The three laws of thought can be regarded as the basic
principles
governing the construction of truth tables.
Still, it should be remarked that when one attempts to set up logic as a
system,
these three principles are no more "important" or "fruitful" than many others.
Indeed there are other tautologies that are more fruitful for purposes of
deduction-and hence more important-than the three principles discussed. A
treatment of this point, however, lies beyond the scope of this book.
[*] Plato appealed explicitly to the principle of contradiction in Book IV of
his
Republic(at nos. 436 and 439), and Aristotle discussed all three of
these principles in Books IV and XI of his Metaphysics. Of the principle
of contradiction, Aristotle wrote; "That the same attribute cannot at the
same time belong and not belong to the same subject and in the same respect"
is a principle "which every one must have who understands anything that
is," and which "every one must already have when he comes to a special
study." It is, he concluded, "the most certain of all
principles."
Introduction to Logic - by Irving M. Copi, Carl Cohen
http://www.amazon.com/exec/obidos/tg/detail/-/0130749214/qid=1096821419/
So if I could offer just one example to the contrary, in other words, if I
could show a situation that you or I or anyone else could possibly
experience and that situation contradicts one and all of the Three Laws,
then those Three Laws would stand refuted?
Possibly since if we suppose, that there are basic empirical beliefs, that is,
emperical beliefs which are epistemically justified, and whose justification does
not depend on that of any further emperical beliefs, since for a belief to be
episemically justified requires that there be a reason why it is likely to be
true and a belief is justified for a person only if he is in cognitive possession
of such a reason, then a person is in cognitive possession of such a reason only
if he believes with justification the premises from which it follows that the
belief is likely to be true, but the premises of such a justifying argument must
include at least one empirical premise, whence the justification of a supposed
basic empirical belief depends on the justification of at least one other
empirical belief, contradicting that there are basic empirical beliefs, that is,
emperical beliefs which are epistemically justified, making it so there can be no
basic empirical beliefs including completely justified sceptical beliefs, but
unlikely, who knows you got the example?
.
|
|
|
| User: "Tim" |
|
| Title: Re: THE THREE "LAWS OF THOUGHT" |
03 Oct 2004 03:13:15 PM |
|
|
"Immortalist" <Reanimater_2000@yahoo.com> wrote in message
news:Q5SdnTUuHNFT3P3cRVn-jg@comcast.com...
"Tim" <abc@abc.abc> wrote in message
news:JIadnT-SvrTZp_3cRVn-iQ@edaptivity.com...
"Immortalist" <Reanimater_2000@yahoo.com> wrote in message
news:Gr-dnaiH3JSPqv3cRVn-uA@comcast.com...
THE THREE "LAWS OF THOUGHT"
Those who have defined logic as the science of the laws of thought have
often
gone on to assert that there are exactly three fundamental or basic laws
of
thought necessary and sufficient for thinking to follow if it is to be
"correct."
These have traditionally been called "the principle of identity," "the
principle
of contradiction" (sometimes "the principle of noncontradiction"), and
"the
principle of excluded middle." There are alternative formulations of
these
principles, appropriate to different contexts. The formulations
appropriate
here
are the following:
[1] - The principle of identity asserts that if any statement is true,
then it
is
true.
[2] - The principle of contradiction asserts that no statement can be
both true
and false.
[3] - The principle of excluded middle asserts that any statement is
either
true
or false.
In the terminology of the present chapter, we may rephrase them as
follows. The
principle of identity asserts that every statement of the form (IF p
THEREFORE
p)
is true; that is, that every such statement is a tautology. The
principle of
contradiction asserts that every statement of the form (p AND NOT p) is
false;
that is, that every such statement is self-contradictory. The principle
of
excluded middle asserts that every statement of the form (p OR NOT p) is
true;
that is, that every such statement is a tautology.
Objections have been made to these principles from time to time, but for
the
most
part, the objections seem to be based on misunderstandings;
[1] - The principle of identity has been criticized on the grounds that
things
change, for statements that were true, say, of the United States when it
consisted of the 13 original states, is no longer true of the United
States
today
with its 50 states. In one sense of the word "statement" this
observation is
correct, but that sense is not the one with which logic is concerned.
Those
"statements" whose truth values change with time are elliptical or
incomplete
formulations of propositions that do not change, and it is the
propositions
that
do not change with which logic deals. Thus the sentence "There are only
13
states
in the United States" may be regarded as an elliptical or partial
formulation
of
"There were only 13 states in the United States in 1790," which is just
as true
today as it was in 1790. When we confine our attention to complete or
nonelliptical formulations, the principle of identity is perfectly true
and
unobjectionable.
[2] - The principle of contradiction has been criticized by Hegelians,
general
semanticists, and Marxists, on the grounds that there are
contradictions, real
situations in which contradictory or conflicting forces are at work.
That there
are situations containing conflicting forces must be admitted; this is
as true
in
the realm of mechanics as in social and economic spheres. But it is a
loose and
inconvenient terminology to call these conflicting forces
"contradictory." The
heat applied to a contained gas, which tends to make it expand, and the
container, which tends to keep it from expanding, may be described as
conflicting
with each other, but neither is the negation or denial or contradictory
of the
other. The private owner of a large factory, which requires thousands of
laborers
working together for its operation, may oppose and be opposed by the
labor
union
that could never have been organized if its members had not been brought
together
to work in that factory; but neither owner nor union is the negation or
denial
or
contradictory of the other. When understood in the sense in which it is
intended,
the principle of contradiction is unobjectionable and perfectly true.
[3] - The principle of excluded middle has been the object of more
attacks than
either of the other principles. It has been urged that its acceptance
leads to
a
"two-valued orientation," which implies, among other things, that
everything is
either white or black, with any middle ground excluded. But although the
statement "This is black" cannot be jointly true along with the
statement "This
i
s white" (where the word "this" refers to exactly the same thing in both
statements), one is not the denial or contradictory of the other.
Admittedly
they
cannot both be true, but they can both be false. They are contrary, but
not
contradictory. The negation or contradictory of "This is white," is
"-this is
white," and one of these statements must be true-if the word "white" is
used in
precisely the same sense in both statements. When restricted to
statements
containing completely unambiguous and perfetly precise terms, the
principle of
excluded middle is also perfectly true.
Conclusion: These three principles-the principle of identity, the
principle of
contradiction, the principle of excluded middle-are indubitably true.
Some
traditional logicians assigned them a privileged and most fundamental
status,[see
note below*] but the special claims sometimes made for them may be
doubted. The
first (identity) and the third (excluded middle) are by no means the
only forms
of tautologies, and the explicit contradiction (p AND NOT p) ruled out
by the
second principle is by no means the only contradictory form of
statement. Yet
the
three laws of thought can be regarded as having a certain fundamental
status in
relation to truth tables. As we fill in subsequent columns by referring
back to
the initial columns, we are guided by the principle of identity: If a T
has
been
placed under a symbol in a certain row, then in filling in other columns
under
expressions containing that symbol, when we come to that row we regard
that
symbol as still being assigned a T. In filling out the initial columns,
in each
row we put either a T or an F, being guided by the principle of excluded
middle;
and nowhere do we put both T and F together, being guided by the
principle of
contradiction. The three laws of thought can be regarded as the basic
principles
governing the construction of truth tables.
Still, it should be remarked that when one attempts to set up logic as a
system,
these three principles are no more "important" or "fruitful" than many
others.
Indeed there are other tautologies that are more fruitful for purposes
of
deduction-and hence more important-than the three principles discussed.
A
treatment of this point, however, lies beyond the scope of this book.
[*] Plato appealed explicitly to the principle of contradiction in Book
IV of
his
Republic(at nos. 436 and 439), and Aristotle discussed all three of
these principles in Books IV and XI of his Metaphysics. Of the principle
of contradiction, Aristotle wrote; "That the same attribute cannot at
the
same time belong and not belong to the same subject and in the same
respect"
is a principle "which every one must have who understands anything that
is," and which "every one must already have when he comes to a special
study." It is, he concluded, "the most certain of all
principles."
Introduction to Logic - by Irving M. Copi, Carl Cohen
http://www.amazon.com/exec/obidos/tg/detail/-/0130749214/qid=1096821419/
So if I could offer just one example to the contrary, in other words, if
I
could show a situation that you or I or anyone else could possibly
experience and that situation contradicts one and all of the Three Laws,
then those Three Laws would stand refuted?
Possibly since if we suppose, that there are basic empirical beliefs, that
is,
emperical beliefs which are epistemically justified, and whose
justification does
not depend on that of any further emperical beliefs, since for a belief to
be
episemically justified requires that there be a reason why it is likely to
be
true and a belief is justified for a person only if he is in cognitive
possession
of such a reason, then a person is in cognitive possession of such a
reason only
if he believes with justification the premises from which it follows that
the
belief is likely to be true, but the premises of such a justifying
argument must
include at least one empirical premise, whence the justification of a
supposed
basic empirical belief depends on the justification of at least one other
empirical belief, contradicting that there are basic empirical beliefs,
that is,
emperical beliefs which are epistemically justified, making it so there
can be no
basic empirical beliefs including completely justified sceptical beliefs,
but
unlikely, who knows you got the example?
The above sounds like a paraphrasing of BonJour's antifoundationalist arg.
The Three Polarizer Paradox.
The Particle-Wave Duality of Light.
It is night time.
It is day time.
Statement 1) (way above) needs to be ammended or my third and fourth eg's
stand. ie. it must make spatio-temporal restrictions.
Ditto for #2 (way above). #3 holds in some cases but not all cases. -
America: love it or leave it. Is there no room for a centrist position in
there somewhere?
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| User: "block" |
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| Title: Re: THE THREE "LAWS OF THOUGHT" |
03 Oct 2004 01:10:01 PM |
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"Immortalist" <Reanimater_2000@yahoo.com> wrote in message
news:Gr-dnaiH3JSPqv3cRVn-uA@comcast.com...
[1] - The principle of identity asserts that if any statement is true,
then it is
true.
Is there such thing as a true statement? Isn't the closest thing
"probable"? (maybe, possible, likely, worth a thought, hold on a minute
I'll get back to you)...................... etc
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| User: "|-|erc" |
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| Title: Re: THE THREE "LAWS OF THOUGHT" |
04 Oct 2004 07:56:30 AM |
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"block" <block@nowhere.com> wrote in >
"Immortalist" <Reanimater_2000@yahoo.com> wrote in >
[1] - The principle of identity asserts that if any statement is true,
then it is
true.
Is there such thing as a true statement? Isn't the closest thing
"probable"? (maybe, possible, likely, worth a thought, hold on a minute
I'll get back to you)...................... etc
the class of statements that have an answer as either True or False are called propositions.
propositions are common, and some are contradictory when the value is False.
statements that are true simply by the act of making them are always true in all domains.
"I am telling you something." is always true.
"I am a liar" is always true.
"this statement has no proof that it is true" is always true.
Herc
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| User: "Immortalist" |
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| Title: Re: THE THREE "LAWS OF THOUGHT" |
04 Oct 2004 12:01:29 PM |
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"|-|erc" <spam@fodder.abc> wrote in message
news:2Mb8d.14110$5O5.3436@news-server.bigpond.net.au...
"block" <block@nowhere.com> wrote in >
"Immortalist" <Reanimater_2000@yahoo.com> wrote in >
[1] - The principle of identity asserts that if any statement is true,
then it is
true.
Is there such thing as a true statement? Isn't the closest thing
"probable"? (maybe, possible, likely, worth a thought, hold on a minute
I'll get back to you)...................... etc
the class of statements that have an answer as either True or False are called
propositions.
propositions are common, and some are contradictory when the value is False.
statements that are true simply by the act of making them are always true in
all domains.
"I am telling you something." is always true.
"I am a liar" is always true.
But all times are not claimed to be times when you are telling something
therefore it is contingent and not necessary that it is always true that you are
a liar.
"this statement has no proof that it is true" is always true.
False. If that statement has no proof then it may or may not be true or false and
hence is again contingent upon something other that elements of the subject "by
definition."
There is a solution to the Epimenides Paradox (a.k.a. the Liar's Paradox).
The paradox goes like this:
1. Epimenides is a Cretan.
2. Epimenides states, "All Cretans are liars."
On the face of it, this appears to be a paradox. Epimenides, being a Cretan, must
either be a liar or a truth-teller. Thus his statement must be either true or
false. But if it's true, then he (being a Cretan) must be a liar, so the
statement can't be true. On the other hand, his statement is false, then he can't
be a liar, so the statement must be true. This is a paradox.
Or so it would seem. Actually, the trouble lies in the interpretation of the
statement "The statement 'All Cretans are liars' is false".
The solution goes like this:
p1. Epimenides is a Cretan.
p2. Epimenides is either a liar or a truth-teller.
p3. His statement is either true or false.
Assume that there is more than one Cretan:
p4. There is more than one Cretan.
Also assume that Epimenides is indeed a liar:
p5. Epimenides is a liar.
p6. Thus Epimenides's statement is false.
p7. Thus "All Cretans are liars" is false.
p8. Thus not all Cretans are liars.
p9. Thus some (one or more but not all) Cretans are not liars.
p10. Thus at least one (but not all) of them is a liar.
p11. Thus Epimenides, a Cretan, could be a liar.
We assumed that Epimenides was a Cretan (p1) and a liar (p5). Therefore, there is
no paradox.
Another way of looking at it is to realize that, unless there is only one member
of a set, then the negation of "all members of the set", i.e., "not all members
of the set", is not "no members" but "some members".
If Epimenides is the only Cretan (so the set of Cretans has only one member),
then there would be a paradox, since "not all Cretans" would mean "no Cretans".
................
(1) This sentence is false.
If (1) is true, then (1) is false. On the other hand, assume (1) is false.
Because the Liar Sentence is saying precisely that (namely that it is false), the
Liar Sentence is true, so (1) is true. We've now shown that (1) is true if and
only if it is false. Since (1) is one or the other, it is both.
http://david.tribble.com/text/liar.htm
http://www.google.com/search?hl=en&ie=UTF-8&oe=UTF-8&q=solution+to+the+liars+paradox
Herc
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| User: "Barb Knox" |
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| Title: Re: THE THREE "LAWS OF THOUGHT" |
04 Oct 2004 09:48:17 AM |
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In article <2Mb8d.14110$5O5.3436@news-server.bigpond.net.au>,
"_|erc" <spam@fodder.abc> wrote:
"block" <block@nowhere.com> wrote in >
"Immortalist" <Reanimater_2000@yahoo.com> wrote in >
[1] - The principle of identity asserts that if any statement is true,
then it is
true.
Is there such thing as a true statement? Isn't the closest thing
"probable"? (maybe, possible, likely, worth a thought, hold on a minute
I'll get back to you)...................... etc
the class of statements that have an answer as either True or False are called
propositions.
propositions are common, and some are contradictory when the value is False.
statements that are true simply by the act of making them are always true in
all domains.
"I am telling you something." is always true.
Not necessarily -- I might not be listening. "I am attempting to tell you
something" would be better.
"I am a liar" is always true.
Not even close. You HAVE heard of the Liar Paradox, I assume.
"this statement has no proof that it is true" is always true.
Not necessarily -- it's true only if the system of proof being used is
consistent.
--
---------------------------
| BBB b \ Barbara at LivingHistory stop co stop uk
| B B aa rrr b |
| BBB a a r bbb | Quidquid latine dictum sit,
| B B a a r b b | altum viditur.
| BBB aa a r bbb |
-----------------------------
.
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| User: "|-|erc" |
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| Title: Re: THE THREE "LAWS OF THOUGHT" |
04 Oct 2004 06:43:49 PM |
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"Barb Knox" <see@sig.below> wrote in
In article <2Mb8d.14110$5O5.3436@news-server.bigpond.net.au>,
"_|erc" <spam@fodder.abc> wrote:
"block" <block@nowhere.com> wrote in >
"Immortalist" <Reanimater_2000@yahoo.com> wrote in >
[1] - The principle of identity asserts that if any statement is true,
then it is
true.
Is there such thing as a true statement? Isn't the closest thing
"probable"? (maybe, possible, likely, worth a thought, hold on a minute
I'll get back to you)...................... etc
the class of statements that have an answer as either True or False are called
propositions.
propositions are common, and some are contradictory when the value is False.
statements that are true simply by the act of making them are always true in
all domains.
"I am telling you something." is always true.
Not necessarily -- I might not be listening. "I am attempting to tell you
something" would be better.
he could be talking to himself!
"You're fired!" is another, there's a whole class of statements where the logic parser
could get the truth value for *free*, like a core of godel statments, they are common enough,
anything where the act of speech performs the verb, firing, ordering, praising, many many
subtypes of verbs that are acts of speech, crucial for natural language interpretation.
"if you call people stupid you are stupid" ... this statement is a call, the verb is self referencing here.
hence without any outside knowledge we can deduce the speaker is stupid (pun expected)
"I am a liar" is always true.
Not even close. You HAVE heard of the Liar Paradox, I assume.
from Immortalist's post, you seem to define Liar wrongly as always lying. A liar is
someone who atleast once lied. The statement cannot be false.
"this statement has no proof that it is true" is always true.
Not necessarily -- it's true only if the system of proof being used is
consistent.
the antithesis of which is non logical.
Herc
I tend to generalise
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| User: "Immortalist" |
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| Title: Re: THE THREE "LAWS OF THOUGHT" |
03 Oct 2004 01:15:04 PM |
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"block" <block@nowhere.com> wrote in message
news:ZfX7d.188$24.126@newsfe3-win.ntli.net...
"Immortalist" <Reanimater_2000@yahoo.com> wrote in message
news:Gr-dnaiH3JSPqv3cRVn-uA@comcast.com...
[1] - The principle of identity asserts that if any statement is true,
then it is
true.
Is there such thing as a true statement? Isn't the closest thing
"probable"? (maybe, possible, likely, worth a thought, hold on a minute
I'll get back to you)...................... etc
If A = "question about a statement" and you ask if it is possible that "A" is the
same thing as "NOT A" I would have to claim there's_no_question_about_it?
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| User: "Luis A. Rodriguez" |
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| Title: Re: THE THREE "LAWS OF THOUGHT" |
12 Oct 2004 02:43:52 PM |
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"Immortalist" <Reanimater_2000@yahoo.com> wrote in message news:<Gr-dnaiH3JSPqv3cRVn-uA@comcast.com>...
THE THREE "LAWS OF THOUGHT"
Those who have defined logic as the science of the laws of thought have often
gone on to assert that there are exactly three fundamental or basic laws of
thought necessary and sufficient for thinking to follow if it is to be "correct."
In the terminology of the present chapter, we may rephrase them as follows. The principle of identity asserts that every statement of the form (IF p THEREFORE p) is true; that is, that every such statement is a tautology.
The principle of contradiction asserts that every statement of the
form (p AND NOT p) is false; that is, that every such statement is
self-contradictory.
The principle of excluded middle asserts that every statement of the
form (p OR NOT p) is true; that is, that every such statement is a
tautology.
tg
In equations:
1.- P = P P is identical to P
2.- P * P' = 0 It is false that occurs P AND NOT P
3.- (P + P')' = 0 It is false that NOT occurs P OR NOT
P
It is possible to develop an algebra of logic with equations equaled
to 0.
But your three axioms are unsufficient.
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| User: "Immortalist" |
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| Title: Re: THE THREE "LAWS OF THOUGHT" |
13 Oct 2004 12:25:11 AM |
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"Luis A. Rodriguez" <luiroto@yahoo.com> wrote in message
news:c9ba0a0b.0410121143.1593c062@posting.google.com...
"Immortalist" <Reanimater_2000@yahoo.com> wrote in message
news:<Gr-dnaiH3JSPqv3cRVn-uA@comcast.com>...
THE THREE "LAWS OF THOUGHT"
Those who have defined logic as the science of the laws of thought have often
gone on to assert that there are exactly three fundamental or basic laws of
thought necessary and sufficient for thinking to follow if it is to be
"correct."
In the terminology of the present chapter, we may rephrase them as follows.
The principle of identity asserts that every statement of the form (IF p
THEREFORE p) is true; that is, that every such statement is a tautology.
The principle of contradiction asserts that every statement of the
form (p AND NOT p) is false; that is, that every such statement is
self-contradictory.
The principle of excluded middle asserts that every statement of the
form (p OR NOT p) is true; that is, that every such statement is a
tautology.
tg
In equations:
1.- P = P P is identical to P
2.- P * P' = 0 It is false that occurs P AND NOT P
3.- (P + P')' = 0 It is false that NOT occurs P OR NOT
P
It is possible to develop an algebra of logic with equations equaled
to 0.
But your three axioms are unsufficient.
The three axioms are the foundation you are building the other ones on. You are
just looking at it wrongly. It all starts with one rule; the law of identity
where we agree to agree that A=A and then we deduce from that A is not equal to
not A, and from there all of logic math and whatever is added like words are
formed from letters and sentences from paragraphs. You move into the realm of the
synthetic apriori or I mean the partial values of SOME when you harp on grey
areas and the fuzzy logic. Its all good bro... but i predict you lose sense with
ALL and SOME when you protest and yea know it not, aaaaaa?
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| User: "T.M." |
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| Title: Re: THE THREE "LAWS OF THOUGHT" |
13 Oct 2004 12:10:14 PM |
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Immortalist wrote:
[...]
1.- P = P P is identical to P
2.- P * P' = 0 It is false that occurs P AND NOT P
3.- (P + P')' = 0 It is false that NOT occurs P OR NOT
You move into the realm of the synthetic apriori [...]
Immortalist,
Thank you for the thread.
Tom
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| User: "raydpratt" |
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| Title: Re: THE THREE "LAWS OF THOUGHT" |
13 Oct 2004 09:55:08 PM |
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(T.M.) wrote in message news:<686adb54.0410130910.3da517ad@posting.google.com>...
Immortalist wrote:
[...]
1.- P = P P is identical to P
2.- P * P' = 0 It is false that occurs P AND NOT P
3.- (P + P')' = 0 It is false that NOT occurs P OR NOT
You move into the realm of the synthetic apriori [...]
Immortalist,
Thank you for the thread.
Tom
0/Infinity = X/Infinity (X does not equal 0 or Infinity).
No part of Infinity, not even the most infinitesimal fraction of
Infinity, can ever be subtracted from 0 or any other finite number.
Were a fraction of Infinity to be subtracted from a finite numerator,
the fraction of Infinity would have to be one or more of the numerable
parts of Infinity, but Infinity by definition does not have numerable
parts, and therefore no finite fraction of Infinity can ever be
conceived or subtracted from a finite number.
Ergo, 0 = X (X does not equal 0 or Infinity) in relation to division
by Infinity.
Very Respectfully,
Ray
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| User: "raydpratt" |
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| Title: Re: THE THREE "LAWS OF THOUGHT" |
13 Oct 2004 09:13:17 PM |
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(T.M.) wrote in message news:<686adb54.0410130910.3da517ad@posting.google.com>...
Immortalist wrote:
[...]
1.- P = P P is identical to P
2.- P * P' = 0 It is false that occurs P AND NOT P
3.- (P + P')' = 0 It is false that NOT occurs P OR NOT
You move into the realm of the synthetic apriori [...]
Immortalist,
Thank you for the thread.
Tom
If X/0 = Infinity (X does not = 0), and if the inverse operations of 0
x Infinity = X and 0 x Infinity = 0 are both true, then X = 0 even
when X does not equal 0.
How could this be? It's true in relation to the unit of measure
called Infinity, for you cannot say that X is farther away than 0 from
the center of Infinity. Any finite number is equal to zero in its
distance in any direction towards the bounds of infinity.
Thus, to say that 0 x Infinity = X (X does not = 0) and that 0 x
Infinity = 0 does not say two different things in relation to
infinity. Both values are absolutely equal in their distance from the
bounds of infinity.
Very Respectfully,
Ray
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| User: "raydpratt" |
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| Title: Re: THE THREE "LAWS OF THOUGHT" |
13 Oct 2004 12:15:42 AM |
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I studied logic in Mr. Copi's 2nd Edition of Introduction to Logic for
the purpose of identifying and crucifying the fallacious lies told by
both the Nevada Attorney General's Office and the Arizona Attorney
General's Office in prisoners-rights litigation for myself and other
prisoners while I was incarcerated for 14 years, 7 months, and 12
days, and for a brief time after I was free. I went on to get an
AAS-Legal Assistant degree through an ABA-approved course of study.
For me, logic is a cold hard tool. The metaphysics of this thread
were entertaining and somewhat beyond me, but I'm truly mystified
about why the discussions might be deemed useful.
Well, I suppose that I have to throw in my two cents: X/0.
I have no logical problems with X/0 which equals infinity, and my
argument fits neatly with the discussion around intuititionistic logic
providing the synthetic truth of mathematical derivations.
Specifically, the argument against X/0 is flawed by an
overgeneralization that attributes the unique quality of finite
numbers to the unbounded quality of infinity. The argument against
X/0 = Infinity is that the inverse operation of 0 x Infinity = any
given X, which allegedly cannot be if the algebraic laws surrounding
inverse operations on finite numbers are to remain true.
My intuitionistic reasoning, however, tells me that infinity carries
an extra term in its meaning that goes beyond the meaning of a finite
number, and, thus, that the extra meaning allows infinity to multiply
out to a particular number, including zero, as well as to infinity
itself, for any given X. The fact that 0 x Infinity = X is merely an
instance of the extra properties of Infinity expressing itself in a
particular circumstance, and I have no logical or mathematical problem
with that whatsoever.
Very Respectfully,
Ray Donald Pratt
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| User: "|-|erc" |
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| Title: Re: THE THREE "LAWS OF THOUGHT" |
13 Oct 2004 12:24:35 AM |
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"raydpratt" <raydpratt@hotmail.com> wrote in message
For me, logic is a cold hard tool. The metaphysics of this thread
were entertaining and somewhat beyond me, but I'm truly mystified
about why the discussions might be deemed useful.
In the cold hard world you deal with truths of statements.
In pure logic you deal with truth. A computer doesn't have
your common sense to give value of truth to a statement, we
have to look deeper.
Herc
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| User: "Dan" |
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| Title: Re: THE THREE "LAWS OF THOUGHT" |
13 Oct 2004 07:29:18 PM |
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On 10/13/2004 12:15 AM, raydpratt wrote:
I studied logic in Mr. Copi's 2nd Edition of Introduction to Logic for
the purpose of identifying and crucifying the fallacious lies told by
both the Nevada Attorney General's Office and the Arizona Attorney
General's Office in prisoners-rights litigation for myself and other
prisoners while I was incarcerated for 14 years, 7 months, and 12
days, and for a brief time after I was free. I went on to get an
AAS-Legal Assistant degree through an ABA-approved course of study.
For me, logic is a cold hard tool. The metaphysics of this thread
were entertaining and somewhat beyond me, but I'm truly mystified
about why the discussions might be deemed useful.
Well, I suppose that I have to throw in my two cents: X/0.
I have no logical problems with X/0 which equals infinity, and my
argument fits neatly with the discussion around intuititionistic logic
providing the synthetic truth of mathematical derivations.
Specifically, the argument against X/0 is flawed by an
overgeneralization that attributes the unique quality of finite
numbers to the unbounded quality of infinity. The argument against
X/0 = Infinity is that the inverse operation of 0 x Infinity = any
given X, which allegedly cannot be if the algebraic laws surrounding
inverse operations on finite numbers are to remain true.
My intuitionistic reasoning, however, tells me that infinity carries
an extra term in its meaning that goes beyond the meaning of a finite
number, and, thus, that the extra meaning allows infinity to multiply
out to a particular number, including zero, as well as to infinity
itself, for any given X. The fact that 0 x Infinity = X is merely an
instance of the extra properties of Infinity expressing itself in a
particular circumstance, and I have no logical or mathematical problem
with that whatsoever.
Very Respectfully,
Ray Donald Pratt
Mathematically there are two classes of infinity: countable and
uncountable. Think integers and real numbers. Also, infinity can be
bound mathematically speaking.
Dan
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| User: "T.M." |
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| Title: Re: THE THREE "LAWS OF THOUGHT" |
04 Oct 2004 07:36:57 AM |
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Immortalist wrote:
THE THREE "LAWS OF THOUGHT"
[1] - The principle of identity
[2] - The principle of contradiction
[3] - The principle of excluded middle
Incredible. I am working on lecture 6 of Heidegger's "The principle of
ground", opening: "The principle of ground says: nihil est sine
ratione". Thus, imho, there is a case for at least adding:
[4] - The principle of ground
to the list. Moreover, Heidegger claims that this principle deserves
to placed at the top of the list. He also makes a mention of another
principle:
[5] - The principle of difference
and the list assembled from His work reads therefore:
[1] The principle of ground
[2] The principle of difference
[3] The principle of identity
[4] The principle of contradiction
[5] The principle of excluded middle
Those principle are, of course, universal and Heidegger calls them the
principles of philosophy.
If I may, I shall make an attempt to demonstrate my interpretation of
these principles which allude directly to that which interests me
most, i.e. FOL (and Russell's PM).
[1] *I will not manage without Your kind guidenance (on this one)*
[2] If an object exists and doesn't exist then it is not the same object
[3] Every object exists (=satisfies some propositional function) iff it exists
[4] No object may exist and not exist
[5] Every object either exists or doesn't exist
Still wondering, however, about the meaning of word "object".
Heidegger's "Die Frage nach den Ding" is still out of (intellectual)
reach, unfortunately.
(As regards I.M.Copi's work, it is *excellent*). :-)
Thank you.
Tom
P.S. Understanding of those principles has been *most eye opening for
me* (it's the first time I encountered them all together and _so
clearly_ explained. They are the most general knowledge about the
world one can acquire (I am, of course, aware of the existence non
classical approaches).
Still more, thanks to M. Heidegger I finally understood the rule of
MP:
[6] If object O exists then object O' exists, then if object O
exists, then O' exists, too.
Formally MP: (O -> O')^O
-----------
O'
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| User: "Tron Furu" |
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| Title: Re: THE THREE "LAWS OF THOUGHT" |
04 Oct 2004 06:54:25 PM |
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"T.M." <tmyslovsky@yahoo.com> skrev i melding
news:686adb54.0410040436.2020f0e5@posting.google.com...
Immortalist wrote:
THE THREE "LAWS OF THOUGHT"
[1] - The principle of identity
[2] - The principle of contradiction
[3] - The principle of excluded middle
Incredible. I am working on lecture 6 of Heidegger's "The principle of
ground", opening: "The principle of ground says: nihil est sine
ratione". Thus, imho, there is a case for at least adding:
[4] - The principle of ground
to the list. Moreover, Heidegger claims that this principle deserves
to placed at the top of the list.
(her had You should probably read the dissertation of Schopenhauer on this
one, "Über die vierfache Wurzel des Satzes vom zureichenden Grunde" (He had
Kant's knack for catchy titles ...).
S. takes his version from Wolff (Ontologia, § 70), since it is, as he says,
the most general one:
"Nihil est sine ratione cur poitus sit, quam non sit": Nothing is without
reason why it is, rather than that it is not (Properly: "Nothing is without
reason why it rather is, than that it is not", but that doesn't - to my
non-native ears - sound english; I hope the two are equivalent).
According to http://www.phillex.de/satzgd2.htm, the law of sufficient reason
has a long and venerable ancestry reaching back from Leibniz to classical
Greek philosophy. For those who don't read German, the site states something
like that as a law of logic it is considered to be the law of empirical
truth, in the same way that the law of contradiction is the law of
analytical truth. I.e., everything we encounter has to be explained by
reference to something else. Everything must have a reason.
Note that the German word "Grund" covers two subspecies of "reason", "cause"
and "fundament" ("basis"? "foundation"? ... some sort of support, anyway).
HTH
T
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| User: "T.M." |
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| Title: Re: THE THREE "LAWS OF THOUGHT" |
05 Oct 2004 08:45:16 AM |
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Tron Furu wrote:
(her had You should probably read the dissertation of Schopenhauer on this
one, "Über die vierfache Wurzel des Satzes vom zureichenden Grunde" (He had
Kant's knack for catchy titles ...).
Is there an English translation?
S. takes his version from Wolff (Ontologia, § 70), since it is, as he says,
the most general one:
"Nihil est sine ratione cur poitus sit, quam non sit": Nothing is without
reason why it is, rather than that it is not (Properly: "Nothing is without
reason why it rather is, than that it is not", but that doesn't - to my
non-native ears - sound english; I hope the two are equivalent).
According to http://www.phillex.de/satzgd2.htm, the law of sufficient reason
has a long and venerable ancestry reaching back from Leibniz to classical
Greek philosophy.
Right. And Heidegger mentions it (often).
For those who don't read German, the site states something
like that as a law of logic it is considered to be the law of empirical
truth, in the same way that the law of contradiction is the law of
analytical truth. I.e., everything we encounter has to be explained by
reference to something else. Everything must have a reason.
Note that the German word "Grund" covers two subspecies of "reason", "cause"
and "fundament" ("basis"? "foundation"? ... some sort of support, anyway).
I see. Thank you.
Speaking of Wolff. Browsing the net, I found nearly no mention of his
"Quod possible est, ens est". And is this not the rule math is based
on, vis. "what is not contradictory, exists"?
Tom
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| User: "Tron Furu" |
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| Title: Re: THE THREE "LAWS OF THOUGHT" |
05 Oct 2004 12:06:32 PM |
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"T.M." <tmyslovsky@yahoo.com> skrev i melding
news:686adb54.0410050545.1d43c091@posting.google.com...
Tron Furu wrote:
(her had You should probably read the dissertation of Schopenhauer on
this
one, "Über die vierfache Wurzel des Satzes vom zureichenden Grunde" (He
had
Kant's knack for catchy titles ...).
Is there an English translation?
Dozens, if Amazon is to be trusted; but I couldn't find one on the net
(didn't go through all of the Google hits, mind you).
Speaking of Wolff. Browsing the net, I found nearly no mention of his
"Quod possible est, ens est". And is this not the rule math is based
on, vis. "what is not contradictory, exists"?
AFAIK that is Parmenides: "Whatever is conceivable, exists".
I couldn't tell whether Wolff uses it (I quoted Wolff from Schopenhauer).
Also, I couldn't tell whether this is the rule of math; except that
logicians (at least; and: I hope) are very careful with the existential
quantifier. A lot of things in logic or math are conceivable in the sense
that one may form a concept of them, for instance in order to ascertain that
there is no existing object to fall under the concept. So there are some
logical entities in use in math which are conceivable and yet cannot be said
to exist in a, so to speak, etymological sense of "real", i.e. a res, a
thing, a substance, that to which we attribute existence, in an Aritotelian
sense.
You could try to ask this question in sci.logic.
All the white around the black lettering in this post are pinches of salt,
btw.
T
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| User: "Tron Furu" |
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| Title: Re: THE THREE "LAWS OF THOUGHT" |
05 Oct 2004 12:08:07 PM |
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"Tron Furu" <tronfuru@frisurf.no> skrev i melding
news:uwA8d.326$Km6.6625@news4.e.nsc.no...
Sorry, didn't check the groups.
T
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| User: "Keynes" |
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| Title: Re: THE THREE "LAWS OF THOUGHT" |
05 Oct 2004 04:47:32 PM |
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On Tue, 5 Oct 2004 19:06:32 +0200, "Tron Furu" <tronfuru@frisurf.no> wrote:
"T.M." <tmyslovsky@yahoo.com> skrev i melding
news:686adb54.0410050545.1d43c091@posting.google.com...
Tron Furu wrote:
(her had You should probably read the dissertation of Schopenhauer on
this
one, "Ãœber die vierfache Wurzel des Satzes vom zureichenden Grunde" (He
had
Kant's knack for catchy titles ...).
Is there an English translation?
Dozens, if Amazon is to be trusted; but I couldn't find one on the net
(didn't go through all of the Google hits, mind you).
Speaking of Wolff. Browsing the net, I found nearly no mention of his
"Quod possible est, ens est". And is this not the rule math is based
on, vis. "what is not contradictory, exists"?
AFAIK that is Parmenides: "Whatever is conceivable, exists".
I couldn't tell whether Wolff uses it (I quoted Wolff from Schopenhauer).
Also, I couldn't tell whether this is the rule of math; except that
logicians (at least; and: I hope) are very careful with the existential
quantifier. A lot of things in logic or math are conceivable in the sense
that one may form a concept of them, for instance in order to ascertain that
there is no existing object to fall under the concept. So there are some
logical entities in use in math which are conceivable and yet cannot be said
to exist in a, so to speak, etymological sense of "real", i.e. a res, a
thing, a substance, that to which we attribute existence, in an Aritotelian
sense.
You could try to ask this question in sci.logic.
All the white around the black lettering in this post are pinches of salt,
btw.
T
If exerience is the real ground of all things,
then even mistaken concepts have an existence.
What is not experienced can't exist. Even if we
recognize a hierarchy of value (truth) to mental things,
if we can think them, there they are.
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| User: "Chris Degnen" |
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| Title: Re: THE THREE "LAWS OF THOUGHT" |
07 Oct 2004 05:18:22 PM |
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Tron Furu wrote:
AFAIK that is Parmenides: "Whatever is conceivable, exists".
I couldn't tell whether Wolff uses it (I quoted Wolff from Schopenhauer).
Also, I couldn't tell whether this is the rule of math; except that
logicians (at least; and: I hope) are very careful with the existential
quantifier. A lot of things in logic or math are conceivable in the sense
that one may form a concept of them, for instance in order to ascertain that
there is no existing object to fall under the concept. So there are some
logical entities in use in math which are conceivable and yet cannot be said
to exist in a, so to speak, etymological sense of "real", i.e. a res, a
thing, a substance, that to which we attribute existence, in an Aritotelian
sense.
In the Kantian sense, whatever is possible (whatever is conceivable) is a real
possibility, and is in reality, which he defines as the sum of all real possibilities.
It's down to the equation of perception to bring existence to any of these 'real'
things, making them 'actual.' In this sense, the logical entities which you say are
conceivable would not be in use.
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| User: "T.M." |
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| Title: Re: THE THREE "LAWS OF THOUGHT" |
06 Oct 2004 09:30:25 AM |
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Tron Furu wrote:
Schopenhauer "Über die vierfache Wurzel des Satzes vom zureichenden
Grunde"
Is there an English translation?
Dozens, if Amazon is to be trusted; but I couldn't find one on the net
(didn't go through all of the Google hits, mind you).
All I meant was, really, the English version of the title. I am sorry.
Speaking of Wolff. Browsing the net, I found nearly no mention of his
"Quod possible est, ens est". And is this not the rule math is based
on, vis. "what is not contradictory, exists"?
AFAIK that is Parmenides: "Whatever is conceivable, exists".
I see. Again, I recall Heidegger mention it (in one of his works).
I couldn't tell whether Wolff uses it (I quoted Wolff from Schopenhauer).
And I quoted Wolff from Heidegger. :-)
Also, I couldn't tell whether this is the rule of math;
AFAIK, Hilbert was involved in an argument whether it is sufficient to
say of an object that it is not contradictory to assert its existence.
Sorry, I am a complete novice.
except that logicians (at least; and: I hope) are very careful
with the existential quantifier.
A lot of things in logic or math are conceivable in the sense
that one may form a concept of them, for instance in order to ascertain that
there is no existing object to fall under the concept. So there are some
logical entities in use in math which are conceivable and yet cannot be said
to exist in a, so to speak, etymological sense of "real", i.e. a res, a
thing, a substance, that to which we attribute existence, in an Aritotelian
sense.
I see. Thank you for these comments.
You could try to ask this question in sci.logic.
Do we, actually, not crosspost to it?
All the white around the black lettering in this post are pinches of salt,
btw.
I see.
Thank you.
Tom
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| User: "Tron Furu" |
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| Title: Re: THE THREE "LAWS OF THOUGHT" |
06 Oct 2004 02:03:37 PM |
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"T.M." <tmyslovsky@yahoo.com> skrev i melding
news:686adb54.0410060630.bce6cf7@posting.google.com...
Tron Furu wrote:
Schopenhauer "Über die vierfache Wurzel des Satzes vom zureichenden
Grunde"
Is there an English translation?
Dozens, if Amazon is to be trusted; but I couldn't find one on the net
(didn't go through all of the Google hits, mind you).
All I meant was, really, the English version of the title. I am sorry.
Don't be. Here i sthe title.
"On the Fourfold Root of the Principle of sufficient reason".
Sorry, I am a complete novice.
I'm completer.
Dawned upon me too late.
T
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| User: "T.M." |
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| Title: Re: THE THREE "LAWS OF THOUGHT" |
07 Oct 2004 12:08:54 PM |
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Tron Furu wrote:
[...] Here is the title.
"On the Fourfold Root of the Principle of sufficient reason".
Thank You.
Sorry, I am a complete novice.
I'm completer.
No. Because I am the completest. :-)
Dawned upon me too late.
I have always found everything you say not just interesting, but
Religion. My final Thank You (my intention is not to spam Sci.Logic,
the most wonderful place in the Universe) shall be recursive with NO
TERMINATION CONDITION:
My_Thanks_To_You -> Thank You. My_Thanks_To_You
Thank You.
Tom
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| User: "tuckpointer" |
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| Title: Re: THE THREE "LAWS OF THOUGHT" |
09 Oct 2004 09:55:19 AM |
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"T.M." <tmyslovsky@yahoo.com> wrote in message
news:686adb54.0410050545.1d43c091@posting.google.com...
[snip]
Speaking of Wolff. Browsing the net, I found nearly no mention of his
"Quod possible est, ens est". And is this not the rule math is based
on, vis. "what is not contradictory, exists"?
The "basis for mathematics" was never decided. Early twentieth century
participants discussing such matters were unable to come to agreement. The
debates had become tiresome and no longer seem to interest practicing
mathematicians to any great extent. This means that the question has been
left to individuals who are far less likely to study mathematics with skill
and passion.
Perhaps the best way to think about this is to differentiate between the
"semantic problem" and the "applicability problem." I use these terms in
context given by Mark Steiner's published work (something like "The
Applicability of Mathematics as a Philosophical Problem") For my part, I
prefer the terms "semantic problem" and "effectiveness problem" delineated
in Warren Weaver's introductory remarks to Claude Shannon's seminal work on
information theory.
In terms of the early twentieth century mathematicians who debated these
matters, this issue resolves to a debate between "intuitionism" and
"logicism." The latter term corresponds to the positions advocated by Frege
and Russell while the former term corresponds to the dissent from
individuals like Brouwer and Heyting. I have not read any of Brouwer's
original opinions, but I have been led to believe his ideas are grounded in
the works of Immanuel Kant (whence "intuitionism").
Learning about these topics takes a great deal of work. For example, I have
not yet had the opportunity to read Russell yet. Nevertheless, what little
I have read makes it clear that Russell is taking the concept of number
(more precisely, natural number) as fundamental when he announces Frege's
achievement in "The Foundations of Arithmetic" (this is the "semantic
problem" [see Steiner]). In contrast, when one reads Husserl's "Prolegomena
to Pure Logic," a different perspective emerges. Husserl warns the
philosophical community against placing too much emphasis on the concept of
number. Rather, he claims that it is the theory of manifolds that is
emerging as foundational and that one should look to advances in the theory
of probability for insight into the foundations of mathematics.
Actually, there is a connection between these disputed positions that is
found in the subject of measure theory. If you look at Paul Halmos' book,
one finds that the definition of a measurable function depends on zero as a
"distinguished member" (?) of the real number system. This is significant
because of how both Frege and Kant use the notion of contradiction as a
ground within their theses. Frege uses contradiction to describe a class
with no members. He interprets this object as the number zero. That is, he
is grounding the (Kantian?) category of existence with an objectification
strategy.
Kant also uses contradiction significantly to address the completeness of
his system. The actual construction is to be found in the section entitled
"Amphiboly of Concepts of Reflection" from "Critique of Pure Reason." Here
Kant is grounding the category of possibility. The alleged connnection is
seen to hold by looking at Halmos' discussion of probability where he
translates the measure-theoretic terms into the usual terms from probability
theory. The role of measurable functions are not trivial.
One can also see the manifestation of K | | | | |
