Reasoning Itself
The third mental operation: reasoning described as mediate inference, defined in terms of both ideas and judgments, and divided into its two methods — induction (from particular to universal) and deduction (from universal to particular).
Reasoning is the third mental operation: mediate inference — the derivation of a conclusion that is not immediately evident by connecting two ideas through a mediating third idea (the middle term). It is called mediate because a medium is required between the two extreme ideas to disclose their relation. Reasoning divides into Induction (moving from particular instances to a universal conclusion — perfect induction exhausts all cases; imperfect induction samples a representative range) and Deduction (moving from a universal principle to a particular conclusion — the canonical form being the syllogism). The distinction between induction and deduction maps onto the two forms of the Dictum (de omni and de nullo) on which the validity of the syllogism rests.
a) Description of Reasoning
The relative properties of propositions studied in the last Article allow us to infer one proposition directly from another. Such immediate inference is, indeed, a kind of reasoning — it is “thinking things out.” But reasoning ordinarily means mediate inference, and it is in that sense that we understand it here.
When two ideas are compared, their relation of agreement or disagreement is enunciated in a judgment. But sometimes the mind, because of obscurity in the ideas, cannot tell whether they agree or disagree. Direct judgment is then impossible; judgment must be reached in an indirect, roundabout, mediate way. This roundabout process is reasoning.
The mediate process may be illustrated thus: the mind compares ideas A and B but finds direct judgment impossible. However, the mind sees that A agrees with idea C, and that C agrees with idea B. Thus, by using C as the medium, it arrives at the judgment “A agrees with B.” This is mediate inference; this is reasoning.
Concrete illustration: Suppose the mind compares the ideas oak and plant, but these are vague — oak associated chiefly with rugged sturdiness, plant with green and tender growth. Direct judgment is baulked. However, the mind knows clearly that the oak is a tree, and understands that all trees are plants. Using the idea tree as medium:
All trees are plants. The oak is a tree. Therefore, the oak is a plant.
The two judgments from which the sought judgment is worked out are called premisses. The judgment worked out is the conclusion (or consequent). The conclusion is nothing more than an explicit enunciation of what is implicitly contained in the premisses.
Analysing the premisses, we find three ideas:
- The idea to be predicated of another is the major idea.
- The idea about which predication is to be made is the minor idea.
- The idea used as medium is the middle idea.
The major idea will always be the predicate of the conclusion; the minor idea will always be the subject of the conclusion. In the illustration above, plant is the major idea, oak is the minor idea, and tree is the middle idea.
The reasoning process therefore involves three judgments (two premisses and a conclusion) and three ideas (major, middle, and minor). In the next Chapter we shall see that these elements find expression in three propositions and three terms.
b) Definition of Reasoning
Reasoning may be defined on the basis of either its ideas or its judgments:
1. Reasoning is an operation of the mind by which the agreement or disagreement of two ideas is inferred from their known relation to a common third idea.
2. Reasoning is an operation of the mind by which a judgment is explicitly inferred from two other judgments in which it is implicitly contained.
Both definitions are identical in meaning. The first describes what is sought (agreement or disagreement of two ideas = judgment); the second simply names judgment as what is sought.
c) Methods of Reasoning
The two methods of reasoning are Induction and Deduction.
1. Induction
Induction reasons from individual and particular data to a general or universal conclusion.
If one experiments with each of the known metals and finds every one of them heavier than water in equal bulk, one must conclude: “All the known metals are heavier than water.” This is complete induction.
If one observes that various bodies, in all circumstances of time, place, and temperature, tend to fall towards the centre of the earth, one may assert: “All earthly bodies tend towards the centre of the earth.” This is incomplete but sufficient induction — experiment has not been made with each and every existing body, but the data are representative and thoroughly investigated.
Induction is invalid when incomplete and insufficient — drawing a universal conclusion from data that are not representative. If one experiment showed that a fly could pull seventy times its own weight, it would be insufficient induction to conclude: “All flies can pull seventy times their own weight.”
Induction is the only method available to the experimental sciences. Its conclusions are valid when complete, or when incomplete but sufficient (drawn from representative data, exhaustively investigated). Dialectics, however, is concerned with deduction, not induction. The two methods are not opposed but supplementary: deduction starts with a general datum; induction seeks to establish a universal truth so that particular truths can be deduced from it.
2. Deduction
Deduction reasons from the universal to the particular and individual:
All trees are plants. (universal datum) The oak is a tree. Therefore the oak is a plant. (a particular datum)
Deduction proceeds from two important principles:
i. Dictum de Omni: Whatever is affirmed of a class as a whole, is thereby affirmed of each and every member of that class.
All trees are plants (plant affirmed of the whole class tree) The oak is a tree (member of the class) The oak is a plant (plant affirmed of that member)
ii. Dictum de Nullo: Whatever is denied of a class as a whole, is thereby denied of each and every member of that class.
No tree is a spirit (spirit denied of the whole class tree) The oak is a tree (member of the class) The oak is not a spirit (spirit denied of that member)
Deduction is the perfect method of reasoning. Its conclusions, when rightly drawn, are inevitable in view of the premisses.
Summary of the Chapter
In this Chapter we have learned what is meant by reasoning, and have marked a line of distinction between immediate inference (from the relative properties of propositions) and reasoning proper (mediate inference). We have noted the elements of the reasoning process as three ideas and three judgments, have learned to name these elements accurately, have defined reasoning, and have discussed its two methods — Induction and Deduction, and their respective principles (Dictum de Omni and Dictum de Nullo).