Page 70 - Oswald Ducrot, Slovenian Lectures, Digitalna knjižnica/Digital Library, Dissertationes 6
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Slovenian Lectures
point that I am going to defend myself. When I say that the topos is scalar,
I am saying two things.
First, properties P and Q themselves are scalar. That is to say, that they
are properties which you can have more or less of. In the example I took, it
is quite obviously so. There the topos, which was the basis of the argument,
was the one according to which warmth makes a walk pleasant. Now, ob-
viously, there are different degrees of warmth and there are also degrees of
pleasantness. I will formulate that scalarity of a topos by saying that predi-
cates P and Q, which a topos connects, must be considered as scales. There
are different degrees of intensity in the possession of characteristic P and
in the possession of characteristic Q. That does not at all mean (I would
like to avoid a misunderstanding on this point) that the arguments and the
conclusions are scalar. The properties within the topos are scalar but not the
propositions used in discourse as arguments or conclusions. I take an ex-
ample. Consider the following argument: “It’s less than ten degrees, take a
coat with you”. Well, there is no doubt that neither A nor C are scalar: it
cannot be more or less ten degrees, and you cannot more or less take a coat.
So, the indications contained in A and in C are not scalar ones. But that
does not prevent the topos, which is the warrant for that string, from being
describable in scalar terms. The topos here is that when it is cold, you must
dress warm: it relates one property P, which is the cold, and another prop-
erty Q, which is, say, garment warmth. The indications contained in dis-
course-segments A and C, “It’s less than ten degrees” and “Take a coat with
you” represent degrees within those general properties P and Q. Minus ten
(-10°C) is a degree of cold: there are lesser degrees of cold and greater de-
grees of cold. A coat is a type of warm garment, and there are still warm-
er ones (say, the outfits skiers put on) and also less warm ones, for example
a jacket. So, when I am speaking about the scalarity of predicates, I am not
speaking about the scalarity of A and of C but, I stress, I am speaking about
the scalarity of properties P and Q connected to A and C. Such is the first
idea contained in my contention that a topos is scalar: the two propositions
P and Q are scalar.
Now, there is a second idea, an even more difficult one to accept, and
I will certainly have difficulties in getting you to accept it. The idea is that
the relationship which a topos establishes between P and Q is itself scalar.
We have seen that P and Q are scales: a topos indicates (I hope to have ar-
guments to justify this thesis) that there is a scalar relationship between the
degrees of property P and the degrees of property Q. That is to say, that go-
ing along the scale of property P in a certain direction also means going
point that I am going to defend myself. When I say that the topos is scalar,
I am saying two things.
First, properties P and Q themselves are scalar. That is to say, that they
are properties which you can have more or less of. In the example I took, it
is quite obviously so. There the topos, which was the basis of the argument,
was the one according to which warmth makes a walk pleasant. Now, ob-
viously, there are different degrees of warmth and there are also degrees of
pleasantness. I will formulate that scalarity of a topos by saying that predi-
cates P and Q, which a topos connects, must be considered as scales. There
are different degrees of intensity in the possession of characteristic P and
in the possession of characteristic Q. That does not at all mean (I would
like to avoid a misunderstanding on this point) that the arguments and the
conclusions are scalar. The properties within the topos are scalar but not the
propositions used in discourse as arguments or conclusions. I take an ex-
ample. Consider the following argument: “It’s less than ten degrees, take a
coat with you”. Well, there is no doubt that neither A nor C are scalar: it
cannot be more or less ten degrees, and you cannot more or less take a coat.
So, the indications contained in A and in C are not scalar ones. But that
does not prevent the topos, which is the warrant for that string, from being
describable in scalar terms. The topos here is that when it is cold, you must
dress warm: it relates one property P, which is the cold, and another prop-
erty Q, which is, say, garment warmth. The indications contained in dis-
course-segments A and C, “It’s less than ten degrees” and “Take a coat with
you” represent degrees within those general properties P and Q. Minus ten
(-10°C) is a degree of cold: there are lesser degrees of cold and greater de-
grees of cold. A coat is a type of warm garment, and there are still warm-
er ones (say, the outfits skiers put on) and also less warm ones, for example
a jacket. So, when I am speaking about the scalarity of predicates, I am not
speaking about the scalarity of A and of C but, I stress, I am speaking about
the scalarity of properties P and Q connected to A and C. Such is the first
idea contained in my contention that a topos is scalar: the two propositions
P and Q are scalar.
Now, there is a second idea, an even more difficult one to accept, and
I will certainly have difficulties in getting you to accept it. The idea is that
the relationship which a topos establishes between P and Q is itself scalar.
We have seen that P and Q are scales: a topos indicates (I hope to have ar-
guments to justify this thesis) that there is a scalar relationship between the
degrees of property P and the degrees of property Q. That is to say, that go-
ing along the scale of property P in a certain direction also means going
