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Slovenian Lectures
trary to the laws of the French democracy, contrary at least to one of the great
acquisitions of the French democracy. Let us try to bring out the mechanism
underlying that debate. The first speaker says: “They pay taxes, so they have
the right to vote” (T, V). Now, in the French democratic tradition, withdraw-
ing the right to vote from people who do not pay taxes is unacceptable. That
explains the idea that to conclude that people have the right to vote from the
fact that they pay taxes is a ridiculous one. The second speaker has taken the
converse argument: he has shown that the converse argument of the first ar-
gument is unacceptable, and concludes that the first argument itself is unac-
ceptable. I wonder how one could rebut that second speaker’s statement, at
least in a way which, in the present state of society, would be effective.
Let us now try to explain that way of arguing with the idea of topical
form. Let us suppose that someone argues A C. If what I have said is true,
the argument relies on a topos, which connects two properties, P and Q; A
is related to P and C, to Q. To argue A C, he relies on the idea +P, +Q.
So, as A attributes a certain degree in property P to something, you have
to accept C, which attributes a certain degree in property Q to something
else (or the same thing). Now, let us suppose that you put forward the con-
verse argument: non-A, so non-C. On what principle do you rely? You rely
on the converse of the topical form which the first argument relied on. You
rely on something like -P, -Q. So the person who said: “When you pay tax-
es, you have the right to vote” (A C) relied on the topical form: The more
you pay taxes, the more you have the right to vote (+P, +Q). His opponent
identifies that argument A C and the argument non-A non-C (You
cannot pay your taxes, so you cannot vote), which relies on the topical form
-P, -Q (The less you pay taxes, the less you have the right to vote). What makes
that polemically very useful assimilation linguistically legitimate (I am not
saying logically legitimate, because for a logician, the assimilation is a culpa-
ble one) is the fact that +P, +Q and -P, -Q are two forms of the same topos:
the topos relating P and Q in a scalar way. It is the scalarity of a topos which
implies that it must have two forms: The more you go up P, the more you
go up Q; The more you go down P, the more you go down Q. Given that the
arguments A C and not-A not-C rely on those two forms, they tend to
be more or less confused: consequently, when you have made out the argu-
ment non-A non-C to seem unacceptable, you give the impression that
you have successfully destroyed the validity of argument A C.
I will now sum up everything I have said so far. A same topos in so much
as it establishes a scalar relationship between two properties can appear un-
der two forms: the more you go up one, the more you up the other; the more
trary to the laws of the French democracy, contrary at least to one of the great
acquisitions of the French democracy. Let us try to bring out the mechanism
underlying that debate. The first speaker says: “They pay taxes, so they have
the right to vote” (T, V). Now, in the French democratic tradition, withdraw-
ing the right to vote from people who do not pay taxes is unacceptable. That
explains the idea that to conclude that people have the right to vote from the
fact that they pay taxes is a ridiculous one. The second speaker has taken the
converse argument: he has shown that the converse argument of the first ar-
gument is unacceptable, and concludes that the first argument itself is unac-
ceptable. I wonder how one could rebut that second speaker’s statement, at
least in a way which, in the present state of society, would be effective.
Let us now try to explain that way of arguing with the idea of topical
form. Let us suppose that someone argues A C. If what I have said is true,
the argument relies on a topos, which connects two properties, P and Q; A
is related to P and C, to Q. To argue A C, he relies on the idea +P, +Q.
So, as A attributes a certain degree in property P to something, you have
to accept C, which attributes a certain degree in property Q to something
else (or the same thing). Now, let us suppose that you put forward the con-
verse argument: non-A, so non-C. On what principle do you rely? You rely
on the converse of the topical form which the first argument relied on. You
rely on something like -P, -Q. So the person who said: “When you pay tax-
es, you have the right to vote” (A C) relied on the topical form: The more
you pay taxes, the more you have the right to vote (+P, +Q). His opponent
identifies that argument A C and the argument non-A non-C (You
cannot pay your taxes, so you cannot vote), which relies on the topical form
-P, -Q (The less you pay taxes, the less you have the right to vote). What makes
that polemically very useful assimilation linguistically legitimate (I am not
saying logically legitimate, because for a logician, the assimilation is a culpa-
ble one) is the fact that +P, +Q and -P, -Q are two forms of the same topos:
the topos relating P and Q in a scalar way. It is the scalarity of a topos which
implies that it must have two forms: The more you go up P, the more you
go up Q; The more you go down P, the more you go down Q. Given that the
arguments A C and not-A not-C rely on those two forms, they tend to
be more or less confused: consequently, when you have made out the argu-
ment non-A non-C to seem unacceptable, you give the impression that
you have successfully destroyed the validity of argument A C.
I will now sum up everything I have said so far. A same topos in so much
as it establishes a scalar relationship between two properties can appear un-
der two forms: the more you go up one, the more you up the other; the more
