We propose a nonclassical logical system to solve the sorites, since LEM is not preserved in this system. The main advantages of this system are: preservation of the classical logic truth-values and tables apart from when the subject speaks in a confusional way, when the truth-values will still be classical, but the table is going to change. Speaking in a confusional way means that they utter both A and not-A or utter nothing involving A, so neither A nor not-A. Yet another advantage is that, in it, contradictions are false, just like in classical logic. There is a clear explanation for the boundaries: it is only when the individual has confused speech that we have to intervene with the translation of their speech into logical entries. Each individual has their own assessment results and therefore is entitled to their own assignment of responses: does this predicate apply or not to this soritical sequence entity? If they answer yes and no at the same time or if they don’t answer, which means they are confused, we put a false (0) as the truth-value of the premise. If a person utters, with no confusion, A, then not-A may still be true or false. If the person says true and false, then we mark that as false and, if they say nothing, we also mark that as false.
Take A and B to be two consecutive soritical sequence premises. We
then have the classical logic table for speech that contains no confusion, so,
for instance, when the individual utters A but does not utter not-A.
|
A |
B |
A=>B |
AΛB |
AVB |
not-A |
not-B |
not-AVB |
|
1 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
|
1 |
1 |
1 |
1 |
1 |
0 |
0 |
1 |
|
0 |
1 |
1 |
0 |
1 |
1 |
0 |
1 |
|
0 |
0 |
1 |
0 |
0 |
1 |
1 |
1 |
When there is confusion, the table will change. Say the individual makes confusion when talking about A but not when talking about B, so they utter A and not-A but utter B only or they utter nothing involving A and utter B only. Because there is confusion when they refer to A, A is false (0). Not-A is also false (0) because there is confusion about A.
The table will then be:
|
A |
B |
A=>B |
AΛB |
AVB |
not-A |
not-B |
not-AVB |
|
0 |
1 |
1 |
0 |
1 |
0 |
0 |
1 |
|
0 |
0 |
1 |
0 |
0 |
0 |
1 |
0 |
Another possibility, in terms of confusional speech, is that they utter
A and not-A plus B and not-B or utter nothing about A and nothing about B or
utter nothing about A plus B and not-B or utter A and not-A plus nothing about
B. Because there is confusion when they refer to both A and B, A is false (0)
and so is B (0).
|
A |
B |
A=>B |
AΛB |
AVB |
not-A |
not-B |
not-AVB |
|
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
|
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
Yet another possibility, in terms of confusional speech, is that they
utter A and not-A plus not-B or they say nothing about A and utter not-B. In
this case, there is confusion when they refer to A, so that A is false (0) plus
not-A is false as well (0). Not-B was uttered, so that not-B is true (1) and B
is false (0).
|
A |
B |
A=>B |
AΛB |
AVB |
not-A |
not-B |
not-AVB |
|
0 |
0 |
1 |
0 |
0 |
0 |
1 |
0 |
