FUTURE LOGIC

We will now present these 37 valuable new forms in full, for the record.

a.         First Figure.  Form: M-P, S-M, S-P.

b.         Second Figure.          Form: P-M, S-M, S-P.

c.         Third Figure. Form: M-P, M-S, S-P.

d.         Fourth Figure.           Form: P-M, M-S, S-P.

            A similar listing would be obtained for temporal syllogism. Secondary modes, valid derivatively and of lesser significance, will discussed later. Mixed syllogism will also be dealt with separately.

3.      Validations.

            We have seen that each figure has a method of validation most appropriate to it. Aristotelean syllogism being identical with our nonmodal (actual or momentary) forms, the task of validation of modal syllogisms is much facilitated. Similar approaches can be used with regard to modal syllogism; and moreover we can appeal, if we need to, to correct nonmodal argument, in the process. The following description of validation and rejection processes for natural modal syllogism, can all be repeated for temporal modes.

            a.         First figure.

            We previously defended Aristotle's valid moods in the first figure, on the basis of the principle that one must mean what one says. Some phenomena have been observed, perceptually and/or conceptually; within a complex of appearances, certain aspects have been distinguished; names have been assigned to their various components; thereby, a framework is established which we are logically required to adhere to; such recognition guarantees the accord between thought and reality (that is, long-term, overall, appearance.)

            Now, granting the six valid actual moods of this figure, the corresponding moods in the modes nnn and npp, are to be demonstrated valid.

            A necessary proposition 'X must be Y' may be viewed as merely a collection of actual propositions 'In circumstance 1, X is Y', 'in circumstance 2, X is Y', 'in circumstance 3, X is Y', and so on; it says 'Whatever the surrounding circumstances, X is Y'. Likewise, a potential proposition may be viewed as a partial enumeration of circumstances in which the stated relationship of X and Y is actualized. An actual proposition indicates a specific single circumstance in which the event occurs.

            Now, let us consider a group of three propositions which, in the actual mode aaa, constitute a valid syllogism, e.g. AAA. In the case of AnAnAn, the nnn equivalent, we can predict that in each and any circumstance we may select, we will find the two premises AA actual, and yielding the conclusion A. It follows that, given the premises AnAn, we can say, 'Whatever the circumstances, the conclusion A occurs'; which means that the An conclusion is valid. Thus, any mood valid in aaa mode is equally valid in nnn mode. With similar reasoning, we can demonstrate the validity of npp, since the 'all circumstances' in the major premise includes the 'some circumstances' in the minor premise, which are in turn posited as framing the conclusion, too.

            With regard to invalidation of invalid modal modes. Although the onus of proof is on anyone who wants to defend them, as it were, it is important to give special attention to the mode pnp, which might at first sight seem reasonable. We might think that the 'in all circumstances' of the minor premise, includes the 'some circumstances' of the major premise, so that a potential conclusion can be drawn. However, in any modal proposition, the circumstances under consideration apply primarily to the subject of the proposition. When we refer to all the circumstances surrounding the subject's existence, we do not claim these to be the only circumstances which can coincide with the predicate's existence, or any other subject's existence.

            In the case of npp, the 'some circumstances' under consideration, are implied for the middle term since the minor premise is affirmative, and concern the same subject in minor premise and conclusion. But in the case of pnp, the specific conditions under which the middle term is addressed in the major premise do not necessarily coincide with any condition concerning the minor term in the minor premise, and so cannot be transferred to it in the conclusion. The change of subject being qualified makes the process illicit. The invalidity of ppp is all the more obvious, since it has no misleading unconditional premise. Thus the analogy of valid modal modes to valid quantitative modes is complete.

            What of aaa, which is posited as valid, although we reject sss? Here too, one could argue that the unitary circumstance referred to by each of the two premises may not coincide, since their subjects differ. In truth, this argument against aaa is justified, and serves to warn us that the aaa mode is valid only on the condition that we know the unitary circumstance involved in the two premises to be one and the same. However, actual propositions by definition concern an ostensible circumstance (which though left tacit is understood). So aaa is a valid mode, when we know the sous-entendu circumstance to be common.

            Although we might attach a similar proviso for the validity of sss, we in fact cannot, because of a structural difference between actuality and singularity. The 'this' in a singular proposition is more firmly attached to the subject; it identifies the subject itself, and not a circumstance surrounding it. Comparing one subject's 'this' to another's is nonsensical, as is the idea of moving our mental finger from one to the other; because all they have in common is 'this-ness', not this one 'this-ness'. In actuals, on the other hand, the focus of the 'this' is a circumstance standing outside the subject of the proposition, though bounded by its existence; it is not the subject as such which is focused on by that 'this'. It follows that, here, the two 'this' occurrences in the premises may be compared, and the specification transferred to their conclusion.

            b.         Other figures.

            The valid moods of the second figure are established by reduction ad absurdum through the first figure. We attach the denial of the conclusion to the major premise, and see that the result would be denial of our original minor premise. Thus, 2/nnn is reduced through 1/npp, and 2/npp follows from 1/nnn; always of course provided the underlying actual mood has valid polarity and quantity properties. Invalid modes in the second figure are dealt with similarly, by showing that the combination of the major premise with the suggested conclusion results in a contradiction or a non-sequitur, through the first figure.

            The third figure modes could be reduced ad absurdum to the first figure for systematic validation; the denial of the conclusion would be combined with the minor premise and result in denial of the original major premise. Rejection of invalid modes could be achieved similarly. However, exposition reflects more accurately the way we deal with this figure in practise. We can reproduce our arguments for the first figure, showing that the circumstances in the premises intersect, and are passed on to the conclusion. This is facilitated by the fact that, in this figure, the two premises have the same subject (the middle term).

            For the fourth figure, direct reduction is the appropriate approach. There is, furthermore, only one primary valid mood to consider. The premises EnIp are both converted, allowing us to process them in the first figure, and obtain the desired Op conclusion. Other validations, and invalidations, are likewise easy to deal with.