Constructing Counter Dilemmas From Dilemmas

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Constructing Counter Dilemmas From Dilemmas
Rick Garlikov

Logical dilemmas have the form:

A implies B, and C implies D
A or C is true.
Therefore B or D is true.

Or to show this in a diagrammatic way:

A --> B, and C --> D
A or C
Therefore B or D

Sometimes B and D are the same thing, call it B, so that no matter what, B will be true.
Aristotle gave the following dilemma to show that logical determinism must be true -- that determinism must be a logical necessity because it followed from whether statements are true or whether they are false, so either way led to the same implication.

If it is true there will be a sea battle tomorrow, then nothing can prevent it; and if it is false there will be a sea battle tomorrow, then nothing can cause it.
It is true there will be a sea battle tomorrow or it is false there will be a sea battle tomorrow.
Therefore, nothing can prevent the sea battle or nothing can cause the sea battle.

General Conclusion : Since this argument can be given for every possible physical event there is nothing we can do to cause or prevent anything.

Typically, dilemmas are constructed that show no matter which option you take of those that are available, there will be a problem; we hardly ever call it a dilemma when the only available options lead to good results; but in terms logical format or form, those would still be dilemmas.

If we go to my mother's for Christmas, we will disappoint by spouse's mother. And if we go to my mother-in-law's for Christmas, we will disappoint my mother.
We will either go to my mother's or to my mother-in-law's.
Therefore we will disappoint either my mother or my mother-in-law.

There is a way to construct counter-dilemmas from any dilemma, and counter-dilemmas often show a way to get out of a dilemma that seems troublesome. They often show a way to resolve or avoid the dilemma.

For example, with regard to the dilemma Aristotle posed about logical determinism:

If it is true there will be a sea battle tomorrow, then something can cause it; and if it is false there will be a sea battle tomorrow, then something can prevent it.
It is true there will be a sea battle tomorrow or it is false there will be a sea battle tomorrow.
Therefore, something can cause the sea battle or something can prevent the sea battle.

And, since this argument can be given for every possible physical event, there is something that can cause them or something that can prevent them. So it would seem logical determinism is not true.

Since the dilemma and the counterdilemma are both sound arguments, the conclusion of both is true. Seeing that helps you see that the conclusion of Aristotle's is not what it psychologically implies. Psychologically it implies that there is nothing that can be done to cause the sea battle or to prevent it, which is the way I stated the "General Conclusion." But that is not actually what the general conclusion should be. It should be that "Either there is nothing we can do to prevent an event, or there is nothing we can do to cause it." That is different from saying that there is nothing we can do either way -- nothing we can do to cause or to prevent it.

For when there is nothing that can cause it, there is something that will prevent it; and when there is nothing that can prevent it, there is something that can cause it. So in those cases where the causes either way are within our control, there is something we can do, though, of course, we cannot both cause and prevent the sea battle, even if we can do either.

In the Christmas visit case, the good news is that no matter which visit you choose, you will please someone; your mother if you visit her; your mother-in-law if you visit her.

If we go to my mother's for Christmas, we will make her happy. And if we go to my mother-in-law's for Christmas, we will make her happy.
We will either go to my mother's or to my mother-in-law's.
Therefore we will either make my mother or my mother-in-law happy.

That, unfortunately, though it is sound, does not help one choose; nor does it mean you won't feel guilty about the one you disappoint. If there is a way out of this dilemma, it will have to be something other than just pure logic.

The way to construct any counter-dilemma is the following. When the dilemma is of the form first stated:

A implies B, and C implies D
A or C is true.
Therefore B or D is true.

The counter-dilemma can always be constructed as:

A implies the opposite of D, and C implies the opposite of B.
A or C is true.
Therefore either the opposite of D is true, or the opposite of B is true.

Or to show this in a diagrammatic way:

A --> opposite of D, and C --> opposite of B
A or C
Therefore, the opposite of D or the opposite of B

Unfortunately, sometimes the counter-dilemma will not be helpful, as in the mother/mother-in-law dilemma, or the first premise of it will not be true. Suppose, for example, there is a bomb about to go off and is constructed in such a way that if you tamper with it, that will also set it off, so that you have the following dilemma:

If we do nothing the bomb will go off, and if we do something to the bomb it will go off.
We must either do nothing or we must do something to the bomb.
Therefore the bomb will go off.

If all these statements are true, then it will make the first line of the counter-dilemma false:

If we do nothing, the bomb will not go off, and if we do something the bomb will not go off.
We must either do nothing or we must do something to the bomb.
Therefore the bomb will not go off.

Actually the first statement of the original bomb dilemma could be stated as:

If we do nothing the bomb will go off on its own, and if we do something to the bomb it will go off by booby trap.

Which would be countered by:

If we do nothing, the bomb will not go off by booby trap; and if we do something, the bomb will not go off on its own.

While that is more precise, and leads to a true premise, it is still not particularly helpful in such a situation because the bomb will still go off.

Nevertheless, the method of automatically constructing counter-dilemmas from dilemmas will sometimes be most helpful in seeing a way to solve or refute the dilemma, so it is a good attempt to make when you do not see any obvious way around a dilemma. It typically only takes a minute or so to construct a counter-dilemma from an original dilemma.