Theistic Arguments Series: On Philosophical Reasoning
Deductive reasoning is a mechanical process. Logical processes consist of following a well-defined set of rules. It doesn't take human intelligence to perform a series of logical operations to arrive at some conclusion. There are machines that perform these processes without ever thinking about what they are doing. They simply start with some known propositional conditions (which may be regarded as premises), apply the rules of logic, and arrive at the inevitable result that is entailed by the starting conditions. For example,
(proposition) Socrates is a man.
(proposition) All men are mortal.
Then, by performing a series of operations that follow established rules of logic,
(conclusion) Socrates is a mortal.
A computer is quite capable of performing these logical operations. Once the conditions are established, the conclusion is a necessary consequence, regardless of the means used to perform those operations.
Mathematics is a form of purely deductive reasoning without the baggage of semantic interpretation of its propositions. In mathematics, we use symbols to represent values, and equations to state propositions that include those values. For example,
(proposition) y = 3x + 2;
(proposition) x = y/2 - 1;
Here, x and y are symbols that could represent many different kinds of values, including time, mass, money, etc. It doesn't matter what they actually stand for, but the propositions represent simultaneous constraints on what those values can be, and they are clearly stated in a manner that is not conducive to misinterpretation. If both propositions are taken to be true, there is one and only one conclusion that must result from the valid application of logical rules upon those starting propositions:
(conclusion) y = 2 and x = 0;
The conclusion is correct and indisputable because the logical process using symbolic propositions and operations is immune to any kind of misinterpretation or equivocation. This is in contrast to more general propositional logic typically seen in philosophical arguments that does not use symbolic representation, but relies on semantics and word definitions to fix the meaning of the propositions.
Any good logical argument should be stated in terms that are not subject to misinterpretation or equivocation. All the words used in the premises must be precisely defined so that there is no question about the validity of applying a sequence of logical rules or operations. When I hear an argument stated with "weasel-words" or phrasing that is semantically impenetrable, that is a glaring signal to me that I should be on the lookout for an attempt to evade cold, hard deductive reasoning. If you have a solid logical case to make, you should state your premises in the simplest terms possible, using words that are well-defined, and phrasing that is clearly understood to mean only one thing.
Deductive reasoning never yields information that isn't contained in the premises. In the example above, once the premises are provided, we have all the information we need to arrive at the conclusion, and no logical operation introduces new information - it merely manipulates the information we already have. The fact that x = 0 may be hidden from our awareness, but it is derived from premises, through a process of manipulating the available information with valid logical operations.
It is incumbent upon the one who makes a logical argument to demonstrate conclusively that the premises are true and valid, if he wants to prove something. If a premise is merely a hypothetical proposition that is assumed to be true, either as a bald assertion or for the sake of argument, then the conclusion is also hypothetical, and the case has not been proven. An argument that purports to prove the existence of supernatural entities must include premises that in some way assume the existence of those entities. That's perfectly fine, as long as you can prove independently that those assumptions are true. But if you can't, it's nothing more than a case of circular reasoning.
I'll have more to say about this as I continue with my series on theistic arguments.