The Validity of Reasoning
The reliability of the syllogism and mediate inference as instruments for extending certain knowledge.
Reasoning is a roundabout way of reaching a judgment that cannot be reached directly: when two ideas are too obscure to be joined at once, the mind brings in a third idea known in relation to both, and so reaches its pronouncement. A syllogism is a form of expressed reasoning consisting of three propositions so connected that, the first two being given, the third follows of necessity; the first two are the premisses and the last the conclusion, which is latent in the premisses and drawn out explicitly. John Stuart Mill attacked the syllogism as useless, arguing that the conclusion must be known before the premisses can be stated, and that it adds nothing to knowledge. Both objections fail: the conclusion is contained implicitly, not explicitly, and to make knowledge explicit, definite, and usable is a real service to science.
Article 3. The Validity of Reasoning
Reasoning
Reasoning is neither more nor less than a roundabout way of reaching a judgment that cannot be reached directly. It is a process by which the mind, unable to pronounce upon the agreement or disagreement of two ideas, resolves the difficulty and reaches pronouncement by bringing in a third idea which it knows in relation to the first two. If, for example, my ideas of “oak” and “plant” are obscure; if “oak” suggests rugged strength; if “plant” suggests tender greenness in a living thing; then my ideas are not clear enough for me to bring them together in judgment. Something (intrinsic to the ideas or extrinsic) may give me my first suspicion that the ideas belong together, that the judgment, “The oak is a plant,” ought to be enunciated. But I doubt; I am unable, by reason of obscurity in my ideas, to make the judgment. On the other hand, I am not able to make the opposed judgment, “The oak is not a plant.” Now, I call in the third idea, “tree.” I do know “tree” in relation to “oak”: I know that the oak is a tree. I also know “tree” in relation to “plant”: I do know that trees are plants. Thus, through the idea “tree” I am able to reach judgment on the ideas, “oak” and “plant.” This process is called reasoning. I may express it thus:
All trees are plants
The oak is a tree
Therefore, the oak is a plant.
Thus, by reasoning, I have reached the judgment; I have obtained the evidence to enable me to enunciate the judgment, “The oak is a plant.”
The example of reasoning here given is deductive. There is also a form of reasoning called inductive. Deductive and inductive reasoning are, as we have seen, not opposed methods of reaching a conclusion, but supplementary methods. The student is referred to Chapter III, Art. 2, a, of Book First.
Valid Reasoning
We speak here of the validity of deductive reasoning. Induction needs no argument for validity, once the validity of sensation and of ideas and judgments is admitted. But some philosophers, notably John Stuart Mill (1806-1873), have attacked deductive reasoning and its instrument, the syllogism, as futile. Against this attack we need a short word of defense; we require a proof that the attack is itself futile and unwarranted.
A syllogism is a form of argumentation (that is, of expressed reasoning) which consists of three propositions so connected that, when the first two are given, the third follows of necessity. We have given an example of the syllogism in the last section. We offer another here:
All circles are plane figures
This figure is a circle
Therefore, this figure is a plane figure.
The first two propositions are the premisses, and the last is the conclusion of the syllogism. The conclusion is drawn out of the premisses. Therefore, the conclusion must exist in the premisses. The conclusion is latent or implicit in the premisses, and it is drawn out explicitly by the reasoning expressed in the syllogism.
Mill says that the syllogism is useless. His reasons are two. (a) He says that the conclusion must actually be known before the premisses can be enunciated. (b) He says further that the conclusion gives no new knowledge, adds nothing to science, and leaves the mind informed to precisely the same extent as it was before the syllogism was formulated.
His first reason is not valid. In a true syllogism, the conclusion is not known explicitly before the premisses are formulated, but is implicitly contained in the premisses, and is explicitly deduced from them.
His second reason is without value. The syllogism does not give entirely new knowledge, but it gives more explicit knowledge. The syllogism clarifies knowledge, makes it more definite, precise, usable. Hence, the syllogism does serve science, and it leaves the mind in a much more effective state of information than it was before the syllogism was formulated.
Thus, the syllogism serves a notable purpose. It is far from useless to bring knowledge to explicit and definite form. It is far from futile to work out the implications of premisses. One who possessed a treasure wrapped tightly in a parcel, would not consider it futile or useless to unwrap the parcel and render the treasure visible and available for use.
Summary of the Article
This brief article on the validity of reasoning completes what we learned about the reasoning process in Book First, Chapter III, Art. 2. We have reviewed our definition of reasoning, and have shown that deduction and its instrument, the syllogism, are valid and useful. In special we have shown the fallacy of the argument directed against the syllogism by John Stuart Mill.