Logic, Proof, and Science

One of the easiest kinds of logic to follow is the Hypothetical Syllogism:

Most likely you won't find that directness here. Why? Because sometimes things just aren't spelled out that clearly. The problem of defining "belief in something" you can't just pull off the shelf, hold in one's hands, and show someone is a complex task.

Common Errors Made By People Using the Hypothetical Syllogism

Fallacies of Affirming the Consequence
Denying the Antecedent

    IF A, THEN B

      Therefore A

    Just because the consequence is true, does not mean that the antecedent is also true.

    For instance:

    If I am a dove, then I have feathers.
    I have feathers.

      Therefore, I am a dove.
      ...this would be incorrect if I was a feather-duster.

    IF A, THEN B
    NOT A

      Therefore NOT B

    Just because the antecedent if false, does not mean that the consequence is also false.

    For instance:

    If I am a glass of ice-tea, then I have ice.
    I have no ice-tea.

      Therefore, I have no ice.
      ...this would be incorrect if I was a full ice-tray in a freezer.

Suppose it was stated, from the above, that C was true. Many people would then deduce A from it. This would be an invalid conclusion (even if A was true by coincidence).

Furthermore, we can also see that NOT A does not necessarily cause NOT C either. Something else could be affecting C.

Sometimes in science we just can't prove A. But if we know something like IF-AND-ONLY-IF A, THEN B. Then we can tell A must be so because of B.

Testing a Hypothesis

Often the only rational explanation for B, is A... and that could be defined as faith. We may not be prove it, but the only way it would make sense is if that were the case. Furthermore we can look for examples based on A, and make statistically valid assumptions that A is true.

Alternate Forms of Proof

At some point we're going to have to make some assumptions one way or another and then put those assumptions, and the rules based on them, to the test. If everything works right, we assume that our assumptions are still valid, for the time being and move on.

If we find something the contradicts our original assumptions, we will toss our assumptions aside, postulate new ones or attempt to ascertain why our initial assumption was faulted and start anew.

To search for an unknown is an incredibly difficult task. We start at square one and work forwards. Sometimes we start at an assumed goal and work backwards. Sometimes we assume the end goal is false and work looking for a contradiction.

Sometimes we create a hypothesis, test the hypothesis, and form a theory. Once a single thing comes along that contradicts a theory, we need to restart.

Three bad practices when it comes to theories

  1. "What ever I learned of first, must be truth." (Up to that point there existed no data to refute -- so the thoery was accepted as fact; now the theory is used as fact to refute other theories.)
  2. "There's no good reason to abandon a perfectly good theory, just because it isn't true." ( believing for the sake of believing, or the time invested in it, or not wanting to abandon other people who believe in it too just because they are good people, which has nothing to do with truth )

  3. "Whatever invalidated our theory must in itself be the answer." ( if you are blind and believe the sky is green and I come by and tell you that the sky is red and leave, you may be inclined to ask someone who can see it "is the sky green" and they will correctly respond "no." This does not make the sky red, when, in fact, both parties were wrong. )

    We must be careful not to fall into any trap. A broken theory is a useless theory (unless it can be revamped to support the contradiction). And whatever evidence surfaced showing our theory was wrong did just that one thing: it showed the theory was wrong, nothing more.

    The latter is most likely the harder to accept. Something about being left with a void is disturbing, instead what we should do is look for other possible things that fit the criteria of the unknown. Or perhaps we can solve for the unknown based on the facts or testing assumptions. What we should be doing then is redefining the problem and expanding the scope of our self imposed limitation.

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