Original writings by Avi Sion on the theory and practice of inductive and deductive LOGIC  

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© Avi Sion, 2005. All rights reserved.



R. Ishmael’s Rule No. 11 – “…lidon badavar hechadash– can also to some extent be represented graphically. Do not refer in the present case to the earlier common premises and conclusions (for Rules 8-10) – this is an entirely different situation. Here, we are initially given the premises:


All S1 are P1 and All S2 are P2


And we are told that an individual, say ‘x’, changes over time from membership in the class S1 to membership in the class S2. Whence, incidentally, by singular syllogism, x is initially P1 and later P2. Later still, x leaves S2 and returns to S1. Formally speaking, granting the given premises constant, there is no doubt as to the outcome of such return: x must again be P1. As to x’s relation to P2, it depends on further conditions; for we are not told in the way of a general premise whether P1 and P2 overlap or not.

These formal considerations are illustrated in the following diagram (assuming here, for the sake of argument, that P1 and P2 are mutually exclusive):


Diagram 9a


However, R. Ishmael conceives the possibility that when x returns from S2 to S1, the relation of S1 to P1 may in the meantime have changed to “Only some S1 are P1”, so that we can no longer syllogistically infer from x being S1 that x is P1.

Alternatively, the original premise “All S1 are P1” may have from the start been less general than apparent; that is, it may have more specifically been intended to refer to “All first-time members of S1”, so that we cannot be sure whether P1 applies “returnees to S1” like x.

Thus, the preceding diagram might conceivably be revised as follows:


Diagram 9b


Anyhow, R. Ishmael considers the issue open, and recommends the matter be verified in the Biblical text.



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