Page:Mind (New Series) Volume 15.djvu/270

 256 CRITICAL NOTICES : source of much confusion. " All men are trees, some men write books, therefore some trees write books " asserts two false propo- sitions ; but " If all men were trees, and some men wrote books, some trees would write books " asserts one true proposition. "Nearly all fallacies," Mr. MacColl says, "are due to the neglect of the little conjunction if. Mere hypotheses are accepted as if they were certainties " (p. 49). And, we may add, hypotheticals whoss hypotheses are seen 10 be false are unduly disregarded, because they are considered as inferences, and as such would be erroneous. Mr. MacColl differs from most symbolic logicians on certain points of considerable philosophical importance. These are all connected with each other ; and his views seem to me to spring from the fa^t that he deals rather w r ith verbal expressions than with what is meant by them. In this respect I cannot but think that two relevant and connected distinctions have been overlooked, namely (1) that between a verbal or symbolic expression and what it means, (2) that between a proposition and a prepositional function. A good deal of Mr. MacColl's reasoning appears to me to fail if these two distinctions are borne in mind. He distinguishes five classes of statements : true, false, certain, impossible, and variable. (These are not mutually exclusive : what is true may be certain, what is false may be impossible, and what is variable may be true or may be false, though it cannot be certain or impos- sible.) A certainty is something which follows from the laws of logic or from the data of the question concerned ; an impossibility is something of which the contradictory is a certainty. A variable is defined as follows (p. 19) : " When I say ' A is sometimes true and sometimes false,' or ' A is variable,' I merely mean that the symbol, word, or collection of words, denoted by A, sometimes represents a truth and sometimes an untruth ". As an instance he gives ' Mrs. Brown is not at home ". Here it is plain that what is variable primarily is the meaning of the form of words. What is expressed by the form of words at any given instant is not itself variable ; but at another instant something else, itself equally invariable, is expressed by the same form of words. Similarly in other cases. The statement " He is a barrister" expresses a truth in some contexts and a falsehood in others. Thus the variability involved is primarily in the meaning of the form of w r ords. Or- dinary language employs, for the sake of convenience, many words whose meaning varies with the context or with the time when they are employed ; thus statements using such words must be supplemented by further data added before they become unam- biguous. It is such forms of words that constitute Mr. MacColl's " variables ". But is not this importing into logic the defects of common speech? One of the objects to be aimed at in using symbols is that they should be free from the ambiguities of ordinary language. When we are told " Mrs. Brown is not at home," we know the time at which this is said, and therefore we know what