Reformed Logic / A System Based on Berkeley's Philosophy with an Entirely New Method of Dialectic

by D. B. McLachlan

When two or more alternative data are presented, of which only one is valid or relevant to a proposed argument, but we know not at first which the valid datum is, we have the dilemma (trilemma, tetralemma, &c.) of logicians. In such conditions we have a double process to go through; we must first settle by observation or by an auxiliary argument which of the alternative data to select, and then work out the principal argument in the regular dogmatic form.

Suppose we have to determine dialectically the specific gravity of a piece of metal, but do not know whether it is gold or gun-metal. It is evident we must first somehow make up our mind as to its identity, and then proceed on the usual method of argumentation. The 'making up our mind' is probably itself an argument, and might be of this character—'A piece of yellow metal stamped with what appears to be a hall-mark, is more likely to be gold than gun-metal; this piece of metal has traces of such a stamp; so I conclude it is gold.' Then we proceed to the principal question—'The specific gravity of gold is 19·26; I have concluded that this object is gold; I conclude further that it has a specific gravity of 19·26.'

We may work out all the alternative conclusions first and fix on a datum afterwards, as in deciding how we shall invest our money. 'If I put my money in Consols I shall have a small return with good security; if I buy Patagonian bonds I may have a large interest for a time, but the security is bad.' The next thing to settle is whether in our experience or on accepted principles small profit with good security is, or is not, to be preferred to large profit and bad security: having decided in favour of the former alternative, we now choose our investment dogmatically—'A good security with small profit is to be preferred; Consols are of this character; they are a suitable investment for me.'

We may be unable to decide for any of the alternative data, but we work out all the possible arguments as hypotheses, and so are prepared in a degree for all the possible events. A person is seen approaching our residence, but we cannot discern whether it is A. B., who is a bore, or C. D., who is an entertaining companion. We argue rapidly—'If it is A. B. I shall have a bad half-hour, for he always wearies me; if it is C. D. I shall have an agreeable distraction, for he is very amusing.'

According to the syllogists, the dilemmatic premises are a statement of alternative data and the choice of one of them, and the inference is the rejection of the remainder: or the rejection may be given as matter of fact and the selection as conclusion. In neither case have we argument.

From the moment we select a datum the remaining data are of no import to us, and they need not be mentioned. The selection of one datum is logically identical with the rejection of the rest, and this is therefore not a conclusion from that.—'Do you take tea or coffee?'—'Tea, please.'—'Then I conclude you do not take coffee.'—A person who would 'conclude' in this fashion would be justly deemed irrational. The choice of the tea is a fact, and the rejection of the coffee is the same fact otherwise expressed, so that the rejection cannot be a rational conclusion.—'My doctor sends me off every winter to Nice, Algiers, or Egypt; but I never go to Algiers or Egypt.'—There is no occasion to say, 'therefore you go to Nice'; that has been already announced as a matter of fact and is not susceptible of inference. For the sake of verbal emphasis we might remark, 'So it is to Nice you go', but this is not logically requisite.

Whately's examples of this kind of theorem are exactly of the model just given.—'Either the earth is eternal, or the work of chance, or the work of an intelligent Being; it is not eternal, nor the work of chance, therefore it is the work of an intelligent Being.' This is put forward in all gravity as a specimen of reasoning. It is plain that if we know the premises as matters of fact, we also know the proposed conclusion as a matter of fact. There is no occasion to reason about it.

The Aristotelian hypothetical can be reduced to arithmetical subtraction. Suppose we put five balls into a bag and afterwards take out three without seeing the remainder: is the judgment that two balls remain in the bag a logical inference? No—it is matter of fact. Since we last perceived the objects they have undergone diminution, but that does not confer on what is left of them the imaginary character proper to a rational conclusion. What remains is as much fact—recollected but not imaginary fact—as before the subtraction.