Monday, January 10, 2011

Foundation for Logic

Many people want a universal standard of truth. There are a few people who are content with relativism where personal ideology leads to personal truth for every individual. But most people want some standard of morals that everyone in society should abide by. Religion provides a basis for morality for many people. However, there are others who are unsatisfied with religion: they see belief in a deity as arbitrary, which means that there is no real universal standard found in religion, only personal beliefs. These people may be atheists or agnostics, or they may even be religious but feel uncomfortable with holding other people to their standards. As such, they must appeal to a different universal source of truth: reason and logic.

What is reason? There are two types: deductive reasoning and inductive reasoning. Deductive reasoning starts with two premises and reaches a conclusion following laws of logic. For example:

All dogs have three legs. (Premise 1)
Henry is a dog. (Premise 2)
Therefore, Henry has three legs. (Conclusion)

Notice that deductive reasoning is only as good as its premises. In the example, the reasoning is valid (the conclusion follows the premises) but the conclusion is false because one of the premises is false (since most dogs have four legs). To be assured that a conclusion is true, it must be established that the premises are true. Sometimes, a premise can be shown to be true by deductive reasoning. But that only results in two more premises which will have to be verified in turn. Ultimately, there will have to be at least two premises whose truth is verified by some other means otherwise deductive reasoning will be based on unverified premises.

The other type of reasoning is inductive. With this type of reasoning, a conclusion drawn from one or multiple objects or events is extrapolated to all objects and events. Inductive reasoning is frequently used in science where observations are made in the laboratory and the results are extrapolated to events that take place outside the laboratory in the real world. Inductive reasoning must follow rules of logic, but its greatest weakness is that it relies on an assumption of uniformity. Uniformity means that the rules that apply to one event (for example, in the laboratory) also apply to other events (in the real world). Can it be shown that uniformity is true? Inductive reasoning can not verify uniformity for it assumes uniformity to be true to begin with. Deductive reasoning can not verify it until at least two premises are verified by some other means. What about observation? Don’t we see uniformity all around us? After all, pure water evaporates at 100 oC everywhere it is tried, therefore the same rules for the evaporation of water apply everywhere. But that is using inductive reasoning: yes, water has always evaporated at 100 oC every time it is tried, but it has not been tried in every possible location or event. Therefore, conclusions from a group (every time it has been tried) are extrapolated to all objects and events. In the end, uniformity can not be verified by logic, reason, or observation, leaving uniformity as an assumption.

Lastly, consider logic itself. How can the rules of logic be verified? Take the law of non-contradiction, for example. The law says one object can not exist in two mutually exclusive categories at the same time. For example, something can not be dead and alive at the same time, since those two states of being are mutually exclusive. How can we know that this law is true? Inductive reasoning can not be used unless uniformity is verified. Observation can not since it will use inductive reasoning to extrapolate from a group of events to all possible events. Deductive reasoning can not unless at least two premises whose truth is known by some other means are found. In conclusion, logic and reason can not be shown to reach truth unless multiple assumptions (at least two foundational premises, uniformity, and the rules of logic) can be shown to be true. Unless these assumptions are verified, using logic to reach universal truth is an arbitrary assumption.

Since logic by itself is an assumption, what can be used to validate it? A God who created everything (Gen. 1:1, John 1:3), who never changes (James 1:17, Num. 23:19), and who uses reasoning Himself (Isa. 1:18) would be a good start. Seeing that the God of the Bible makes these claims, it is no wonder that He would say that knowledge comes from Him (Prov. 1:7, 9:10). So if someone wants to use logic and reason to determine truth, he must first accept the existence of God. Otherwise, his use of logic and reason is nothing more than an arbitrary assumption.

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