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 evaluations.

    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 complications.