Post by Eugene 2.0 on Oct 13, 2022 7:42:25 GMT
Unlike deduction, traduction prescripts for results (entailments) to have the same quantity (in a broad sense) as the given conditions (axioms, assumed things, etc).
It has two meanings: a) narrow:
Qp→Qq (i)
where 'Q' – is a quantity for certain propositions p and q. According to this, "if all the cleft-footed are fast, therefore all horses are fast" – is an example of traduction.
Another meaning: b) broad:
Cp→Cq (ii)
where 'C' – is a conceptual quantity, so if '1' means 'a whole set', or '∞' means 'infinity', then we can even assume that a certain conceptual quantity is just a form. This we're going to rewrite the previous formula into:
Fp→Fq (iii)
where 'F' is a form. (Notice: ii→i isn't a tradition implication.)
So, metaphysically it is impossible to violate the traduction. We cannot infer anything that has the different form. Our conceptual scheme is closed by those principle (i-iii). In general, if A is a certain concept, then any inferences from it (let's say B) such as:
C¹A→C²B (iv)
is just impossible, if C¹ and C² share the different conceptual quantity.
But what does it mean there's no way to think not according to traduction? This means that we cannot just go gack, and start thinking not assuming the previous assumptions. So, to correct the IV we have to write then:
(C¹+C²)A→(C²+C¹)B (v)
It has two meanings: a) narrow:
Qp→Qq (i)
where 'Q' – is a quantity for certain propositions p and q. According to this, "if all the cleft-footed are fast, therefore all horses are fast" – is an example of traduction.
Another meaning: b) broad:
Cp→Cq (ii)
where 'C' – is a conceptual quantity, so if '1' means 'a whole set', or '∞' means 'infinity', then we can even assume that a certain conceptual quantity is just a form. This we're going to rewrite the previous formula into:
Fp→Fq (iii)
where 'F' is a form. (Notice: ii→i isn't a tradition implication.)
So, metaphysically it is impossible to violate the traduction. We cannot infer anything that has the different form. Our conceptual scheme is closed by those principle (i-iii). In general, if A is a certain concept, then any inferences from it (let's say B) such as:
C¹A→C²B (iv)
is just impossible, if C¹ and C² share the different conceptual quantity.
But what does it mean there's no way to think not according to traduction? This means that we cannot just go gack, and start thinking not assuming the previous assumptions. So, to correct the IV we have to write then:
(C¹+C²)A→(C²+C¹)B (v)