II. Basic insight -- what is logic all about?
A. The Principal of Non-Contradiction View Video
Written notes to summarize the video:
In arithmetic, if you start with zero,
add some number, e.g., 55, to what you started with, and then subtract
the same amount, then you will end up with zero.
In discourse, if you say something and
then say the contrary to it, you are left having said nothing. In a
way, being in such a situation is worse than having said nothing. Once
a contradiction has been discovered, a higher standard for verification
may be imposed on any replacement statements. There is
nothing really wrong with that condition since it probably
reflects a genuine difficulty in making the required empirical
In making contracts or other forms of
promises, a contradiction may mean that the entire document is invalid
because it does not state an airtight agreement between the involved
parties. In such a case the solution is simply to rewrite the contract
so that it does not produce unwanted consequences.
In computer programming, the formal
aparatus of mathematical logic is generally used to specify actions to
be taken under certain circumstances. For instance, "(T
> 250° F) → Initiate Shutdown Procedure" is a
direction, not a statement about promises or expectations. When T
> 250° F, the desired result is for shutdown to occur.
In a program suffering from a "bug," there might be another
statement such as, "(T≤ 250° F) →
Initiate Shutdown Procedure," and the result could be summarized in
ordinary English by saying that the instructions to the computer are to
initiate the shutdown procedure if the temperature is higher than
250° -- but also to initiate the shutdown procedure if the
temperature is not higher than 250°. The probably unintended
result would be that the shutdown procedure would probably be run as
soon as the computer program went into operation, and that the intended
heating procedure would never even get started. So giving
contradictory instructions can be as much a problem as making
contradictory statements about the real world or making contradictory
provisions in a legal contract or other such device.
In short, whenever a statement and its
negation are both put forth, there are likely to be severe