Mind Matters Natural and Artificial Intelligence News and Analysis

Coming to the Defense of Classical Logic

Classical logic belongs to everyone and can be equally wielded by anyone
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It seems odd that classical logic would need defending, but, in modern times, this seems to indeed be the case. Many modern scholars see the need for demoting the place of classical logic and viewing it as an aspect of western cultural imperialism. In reality, classical logic is a gift to civilization. It was created in the classical west, but its benefit is that it belongs to everyone and can be equally wielded by anyone who chooses to do so.

Many critics of classical logic, like critics of mathematics, have both problematic and justifiable complaints. It is true that many people use classical logic incorrectly, and then use the authority of classical logic as the justification for problematic statements. In logic, all inferences flow from a set of assumptions, which logic itself does not justify. It is easy to create a logical inference from bad assumptions, and then claim that your results are just “logical deductions” from the truth. However, it is difficult to blame classical logic itself on this, as there is not any system of inference that is capable of preventing its misuse, and none have even been proposed as such.

The benefit that classical logic has, though, is that it has sufficient tools to evaluate its own usage. That is, if logic is being misapplied against you, better logic can be applied in your favor. Because the rules of logic are explicit, known, understandable, and agreed upon, this provides the means for someone who is having bad logic used against them to respond in their own defense.

Additionally, classical logic is very clear on the prerequisites for using classical logic. The premises must be both true and non-contradictory. Therefore, anyone attempting to use logic with problematic or contradictory premises can easily be shown to be misusing logic. Classical logic even has terminology for distinguishing between various situations:

• An argument is invalid if the premises contain contradictions or if the logical flow from premises to conclusions is faulty.
• An argument is valid if the reasoning is correct assuming the truth of the premises.
• An argument is unsound if the argument is valid but the premises are false.
• If the premises are not used in a consistent way, then that is known as equivocation, and also makes the argument unsound.
• An argument is sound if the argument is valid and the premises are indeed true.

What makes classical logic especially important is that the reasoning process is not dependent on the status of the person making the argument. It provides a playing field for which the rules are equal for any participant. It provides rules which objectively give peasants the tools and rules to override kings and queens. It provides a method by which the public can adjudicate against the powerful, and demonstrate to anyone that the emperor has no clothes.

If there is any problem in logic, it is this: The assumption that it is easy to formulate premises which are both correct and give themselves to logical deductions. We want to know what is logically entailed by various assumptions, but we fail to realize the real difficulty in this. This attitude can indeed lead to the abuse of logic where people regularly use equivocal phraseology to make unsound logical arguments, and believe themselves to be logical.

What is needed here, however, is not a lowering of respect for classical logic, but a raising of it. We need to recognize the limits of what can be inserted into logical statements, and realize just how high a bar it is for an argument to be demonstrated to be both valid and sound. We should recognize that there are a number of valid arguments whose soundness we may never know, or whose soundness is a question to be asked and not an assumption to be given. We should better recognize the rigor required in creating (and evaluating) a logical argument.

Losing logic means giving up the most consistent means for questioning powerful people. In a world where the rigor of classical logic cannot be applied, truth is determined by power, not reason. Classical logic provides the best means for ordinary individuals to question their leaders, and for the oppressed to oppose their oppressors.