The main contention (pp. 15-6, p. 22, p. 49, pp. 64-5, p. 104, p. 139, p. 159, p. 166, p. 205, pp. 229ff.) is that, far from being necessarily fallacious, very often ssas are acceptable, if weak, (warning) arguments in a discussion, to the effect that taking a certain step may be fraught with indirect results which could eventually turn out disastrous -- not as an unavoidable outcome, but as a quite possible upshot (p. 102, p. 112, p. 156). Thus construed, ssas shift the burden of proof. A proponent is advocating a certain step. The critic advances a ssa by showing that, once that step has been taken, there is a presumption that some kind of pressure towards further steps may quite possibly be hard to resist, the thus triggered process yielding a bleak result. Once such an argument has been advanced, it is up to the proponent to show that it is reasonable to hope that the process will not go on, that there is some good stopping point at which a sharp line can be drawn. What alone is fallacious with some ssas is wording them as if they were conclusive, non-defeasible or deductively valid reasonings allowing a strong rejection of the proposal and thus closing the discussion.
The wealth of examples and cases is not parallelled with a comparable depth of approach. There are difficulties concerning the core idea just described which are not addressed. The discussion of alternative views is cursory and in some cases almost boils down to an off-hand dismissal with little in the way of serious consideration.
I think such a drawback is all the more regrettable as it leaves us not just with a deficient understanding of the logic of ssas, but more seriously with no practical proposal for solving at least a broad range of such cases. Some people blame philosophers for failing to put forward practical solutions to human dilemmas. This book contains only a few practical proposals (mainly in its 7th and final chapter, ``Practical Advice on Tactics'', pp. 242ff.), which are rules of thumb as to how to react to ssas in a discussion, not really constructive recommendations as to how the conflicts can be solved. Walton is noncommittal on almost every particular controversy he broaches in the book.
Let me elaborate. Many ssas are ensuant on the gap between a continuous underlying series of characteristics -- the input -- and a discontinuous and sometimes just two-valued output. Walton fails to emphasize such a gap, but I have gathered the impression that he would not strongly disagree with such a point. The cleavage under consideration gives rise to difficult dilemmas. Speeding is a continuous property, but as it is implemented in our societies fining is not: if you are caught exceeding the allowed speed, even by an exiguous fraction, you are fined, no less than if you had driven your car like mad; and if you dangerously verge on the allowed limit amidst a dense traffic but with no rule breaking, you are safe -- as far as fine imposition is concerned. Likewise, if you are 17 years of age, an energetic, intelligent, politically aware young man or woman, you cannot vote (even though you can be sent to prison), but if you have just attained your 18th birthday, then you are supposed to have ``come of age'' and you are entitled to vote, even if you know nothing of politics and care less. With euthanasia, abortion and many other subjects, such dilemmas are more serious. Law as usually conceived only seldom allows of middle courses, and is prone to all-or-nothing attitudes.
Any proposal about ssas which has no practical recommendation to offer towards reconciling those opposite poles of reality and law seems to me deficient. The deficiency in the present case is due to a lack of logical appraisal. Walton shares the classical logician's view of two-valuedness. He claims (pp. 207 ff.) that formal proposals about ssas have failed because they have resorted to many-valued logics advocating truth-value gaps, which does not help to improve our practical treatment of such dilemmas. Now, there are several confusions here. For one thing, although multiple-valued logics can be construed in such a way that the intermediary truth values are looked upon as truth-value gaps, this is not the most common interpretation. On the other hand truth value gaps do not need many-valuedness. They can be accounted for with a super-valuation semantics like van Fraassen's. For another thing, at least some multiple-valued approaches hinge upon the notion of degrees of truth, which ensue in a quite different treatment of ssas, one which does not relinquish the principle of excluded middle. And, last, a multiple-valued logic approach can do what Walton's account fails to do, offering a recommendation on practical solutions, namely: as far as possible, keep clear of two-valued outputs when the inputs are infinite-valued.
But is it possible? Again, a classically minded logician -- such as Walton -- would think not. Age is continuous, whereas you cannot grant a continuously increasing right of vote. You cannot establish a continuous system of fines in virtue of which the amount due varies according to your speed excess. And so on. All that seems clear and reasonable. Is it? No, I do not think so. I am quite convinced that it is only laziness which prevents us from devising a subtler way of handling rights and wrongs. Again, this is no all-or-nothing issue. Our juridic practice cannot completely fit the continuous series of variations in reality, but the discrepancy can be decreased considerably, at least in many cases.
In fact, a juridical advance has been accomplished since the 18th century precisely by acknowledging degree variations where our ancestors failed to envisage them. Capital punishment was inflicted on many ``crimes'' which nowadays are minor offenses and receive moderate punishment. Yet in other respects the all-or-nothing attitude is still with us. Jurists spend a lot of time redrawing the boundaries, and only seldom recommending an abandonment of any sharp boundary.
Walton is quite convinced (p. 50, pp. 58-9, p. 209, p. 236), that the sorites type of ssa -- one of the four main types in his classification, along with the causal, the precedent and the full ssas -- ensues on the vagueness of key concepts or terms, i.e., on uncertainty as to where the line is to be drawn. He doesn't for a moment challenge the assumption that the line has to be drawn. Why?
In the first place, ``vagueness'' is not indisputably the root of the problem, for vagueness is not the same as graduality. A statement may be vague because of pragmatic considerations concerning the context of utterance: the utterer is expected to convey more specific information and instead he contents himself with general remarks; thus what he says is vague. Terms can be said to be vague in so far as they are used in vague statements. Yet on their own they are not vague. `Tall' is not vague. It is a term denoting a property which comes in degrees. The issue is not vagueness but graduality. (I shall return to this central issue at the end of this review.)
The discussion on euthanasia -- an issue Walton rightly emphasizes -- is not due to vagueness of such expressions as `letting die', `actively causing the death', `complying with the patient's willingness repeatedly expressed in a state of clear conscience and not in a moment of transitory despair', and so on. Such phrases can be used in a vague manner, but they can also be used with no vagueness. Yet all of them denote properties which admit of degrees. It seems to the present reviewer very likely that at most a generation hence euthanasia will be legal everywhere with provisos of this sort, the Dutch having been the pioneers. The irrational resistance comes most of all from the maximalistic attitude: since those provisos are matters of degree -- and of aspect too --, there is no way of drawing the line so as to put a stop to a conceivable deterioration leading to compulsory medical killing of socially undesirable people. Well, yes, if it comes to either whole guilt or absolute innocence, with nothing in between, then it is difficult, if not impossible, to draw any line at all -- not even the one that supposedly is now enacted, except that it is whatever may now be in operation. The difference between failing to give a medicament and providing one is relative: is providing serum with no nourishing qualities just non-action? (Is starving a cripple purely negative? Walton seems implicitly to accept such an Aristotelian radical distinction, but he does not go into the issue with any detail.) But if we think of ourselves as not completely innocent of misdeeds, and acknowledge that many actions can be both praiseworthy up to a point and yet also reprehensible to some extent, if we try to overcome the two-valuedness of our juridical systems, replacing it, in so far as it is feasible, with systems of scales, our attitudes can become more reasonable and less strained. A physician's action may be much more meritorious than blamable. A different action of another physician, very like the first one, may still be a little less meritorious and a little more blamable. And so on. Unless and until we adopt such a good common sense, unless and until we cease concocting hard and rigid patterns with heaven on the right, hell on the left, and nothing in-between, only a bad casuistry is possible. Walton defends casuistry and rightly so, since he correctly points to qualities in the jesuitic casuistry which Pascal grossly overlooked. Yet, the main flaw with casuistry was precisely its resorting to self-deception by fancying that with some proviso -- whose whole spelling-out may take hundreds of volumes of fine writing -- an action may be perfectly and absolutely blameless, whereas failing to comply with just a little detail of the conjunctive proviso may render the action a mortal sin.
As for abortion -- another highly emphasized case in Walton's book (pp. 45 ff., 140 ff., etc) -- more or less the same can be said. If we have only the two opposite terms of `person' and `an entity which is no person at all', i.e., if failing to completely be a person amounts to completely failing to be one, and killing the former entirely deserves punishment whereas putting an end to the life of the latter is of no consequence whatsoever, then of course we are left with the unsavoury choice of either saying that personhood begins at birth (what of the emerging baby, when only a hand is outside the womb?), or at the joining of the gametes (what about the spermatozoid having just touched the ovule?) or with some profoundly inspired maxim, to the effect that personhood begins at the 259201 minute after conception. All that is absurd, isn't it? But the absurdity is brought about by legal enforcement of two-valuedness. I agree that legal practice cannot be as subtle, fluid and fuzzy as life and truth are, but they can be a little less rigid, less absurdly crisp than they are commonly supposed and expected to be.
All this is down to earth. What is its connection with logic? Quite simply, if truth doesn't admit of degree, and if applications of words are either completely all right or else absolute misnomers, then we are bound to champ at the bit and resign ourselves to juridic casuistry, drawing arbitrary lines on the ground of devious, lengthy and disingenuous provisos which the lawyer alone can master.
When discussing the logical structure of ssas, Walton takes for granted, with no critical canvassing at all, that modus ponens is involved. Under CL (Classical Logic) `r if p' is of course equivalent to `r or not-p', i.e. to `Not both p and not-r'. But in many non-classical logics things are not like that. The sorites-engendering principle can be formulated like this (SEP):
(SEP) If B differs from A, in having F, only by a small margin, and A has property F to a certain degree, d, then, if, on this account, A has (or is bound to have) also property G, B has property G, too.
(SEP) is rejected by many a nonclassical logical approach. What is accepted is what I shall be calling -- in accordance with Walton's line -- the principle of consistency, PC for short, namely:
(PC) If B differs from A, in having F, only by a small margin, and A has property F to a certain degree, d, then it is not the case that, on this account, A has (or is bound to have) also property G, but B does not have property G.
But modus ponens does not allow to infer `r' from the premises `p' and `Not both p and not-r'. For suppose `p' is only partly true. Then it can be safely asserted with [partial] truth that p, but also that not p. Since not-p, it is not the case that p (heed the difference between its just not being the case that p and its completely failing to be the case that p). Since it is not the case that p, not both p and s -- for any `s', including `not-r'. But from such a [partial] truth you cannot conclude `r', which for all we know may be an utter falsity. Likewise, the claim (which can be regarded as a particular case of PC -- see below) that it isn't the case that the 259200 minutes foetus is a non-human-being and the 259201 minutes foetus is not a non-human-being, together with the claim that the former is [at least to some extent] a non-human-being, does not entail the conclusion that the 259201 minutes foetus is a non-human-being. Probably it is not (altogether) a human being, but you cannot draw such a conclusion only on the strength of the premises. At most we have here a defeasible presumption -- using a notion Walton makes much of. Yet Walton has no doubt that what is involved here is a quite unobjectionable modus ponens.
Furthermore, even if we accept the claim that, if the 259200 minutes foetus is a non-human, then the 259201 foetus is also a non-human, even then all is not logically as straightforward as Walton imagines. For he then applies to this sort of case both modus ponens and modus tollens (p. 215, p. 226). Now, several non-classical logics do not admit modus tollens for the couple of connectives formed by mere (simple, natural) negation and mere conditional, `if'. They admit modus tollens for the couple formed by the mere conditional and strong negation (`not■at all'), and also for the couple formed by implication (`to the extent that■') and mere negation. Thus, according to such logics the two following reasonings are valid:
To the extent [at least] that p, q; not-q ├ Not-p.
If p, q; It isn't the case that q at all ├ It isn't the case that p at all.
Whereas the following one is invalid:
If p, q; not-q ├ Not-p.
So, even were it true that, if the 259200 minutes foetus is not a human being, then neither is the 259201 minutes foetus, it wouldn't necessarily follow from that premise plus the claim that the latter is a human being that the former is one. Again we may have here only a defeasible nondeductive reasoning to that effect -- just where Walton thinks he is treading on firm soil.
Walton admits of course that many terms involved in ssas are vague, as he puts it (see p. 227). What he means (see pp. 227-8) is that those words have a clear zone of ``definite'' application, a clear zone of ``definite'' non-application, and a grey zone of (non-definite?) uncertainty. But definiteness and uncertainty have nothing to do with our present concern. We are uncertain about the extension of many mathematical properties, which are none the more vague for such a reason. On the other hand, typically fuzzy words do not involve uncertainty. It is not that I am uncertain about whether or not the three months foetus is a living person; what happens is that it is one [to some extent], but less so than your one year old girl. Not that the issue is not a yes/no question, but only that it is not just such a question; it is also a how much question. (According to some people it is senseless to say that it is 37.472 % true, because purportedly issues of that kind do not admit of such precision; the claim seems to me as reasonable as saying that temperature does not admit of precise measure, because you do not feel that it is now 31.237 degrees hot, but just that it is hot.)
There are a number of separate difficulties for Walton's approach. For instance, he does not broach the question of why he thinks that trenchant or strong claims close a discussion, whereas weak, cautious half claims keep it going (see p. 104, p. 164, p. 203 and passim). It seems obvious to the reviewer that this is not necessarily so, but Walton takes it for granted. Also, he contends that a ssa is fallacious only when it is advanced so as to shut off the flow of questioning, to hinder or even block the sequence of the dialogue. Is there any formal mark to be found in virtue of which we can say that such is the case? In other words, can two debate-behaviours be exactly alike in their perceivable manifestations, only one of them being fallacious, in the sense Walton uses the term? If so, have we to scan the arguer's mind -- or rely on some mysterious ``intuition'' -- in order to say he is committing a fallacy? (Walton rejects such a psychologistic approach -- p. 34. I am not sure, though, his whole account really keeps clear of it.)
I do not deny Walton's pragmatic account has real merit. I accept his two dichotomies -- duly fuzzified and only partly overlapping: that between tranchant claims and hedged considerations; and that between pronouncments aimed at closing a discussion and those which tend to keep it going. However it seems clear to me that, in such matters, a fallacy is committed only when a sharp line is claimed to be needed where in fact none can be reasonably drawn -- the very nature of the properties involved asking for a gradualistic approach.
There is also a problem concerning the logic underlying Walton's own approach. He adheres to CL and dismisses many-valued logics. Yet he uses expressions like `to the extent that' (p. 94), `not fully', comparatives -- e.g. he speaks (p. 121) of a precedent being more binding that another on a court --, and so on. What can be a plausible treatment of the denotations of such expressions compatible with CL?
A different problem which Walton fails to raise is whether the norms of obligation concerning the furtherance of discussion -- non compliance with which amounts to fallacy -- are prudential rules, or moral duties. The moralistic undertones seem to me noticeable, and Walton's choice of words can hardly be ascribed to coincidence (`it would be unfair' and so on). But is a strongly normative approach required in such a context? Is not a merely instrumental view to be preferred on account of its greater simplicity?
Walton defends a relaxation of the standards of strict consistency (p. 67), but he doesn't define what `consistency' means here. It seems clear to me that he means what I have called above the principle of consistency. Yet, he firmly adheres to CL. Why is such a relaxation permissible? How can an utterly illogical procedure be tolerated? (If you are a CL adherent you cannot accept degrees of logicality; hence such stances as are not entirely logical are totally and downright illogical.)
I shall bring this review to a close by focusing on the relationship between Walton's book and patterns of thought and linguistic behaviour. If truth admits of degree, if designation (denotation) admits of degrees, if a reasonable approach to our moral and legal judgments and practices would entail a step-by-step departure from rigid dichotomies, favouring a more gradualistic approach -- nothing of which is to be found in Walton's book --, can we be confident that the gradualistic approach which is then required in both logic and juridical doctrine is compatible with the inner patterns of our thought process?
A very simple hypothesis springs to the mind -- and has been put forward by some authors -- namely that our thought process is bound by innate dichotomist constraints. Were such a hypothesis true, we could have an explanation of the widespread adherence to two-valuedness, viz. some species-specific leaning towards a discrete pattern even where in reality there is none. Such an explanation is attractive and ambitious. It explains why so often people adhere du stiff dichotomies -- whereas reality displays a continuum -- and try to proceed by jumps -- while only step by step advances are practicable or reasonable. What the explanation does not account for is why so often those attitudes result in failure, and have to be patched up towards a less drastic departure from continuism. Neither does it explain why continuist attitudes are not infrequent among humans, at many stages of our species's development. If humans are that dichotomist, how can we explain the existence of comparatives and related expressions in all known languages of our planet (and even constructions which allow nouns to be terms of comparison, as happens in English through the phrase `more of ■ than', and in other languages in a more straightforward manner)? How can we account for the fact that very often the so-called primitive religions see a full scale of transitions whereas only purportedly superior religious doctrines introduce cut-offs and in fact abysmal chasms? And how do you explain that in turn such dualistic doctrines are superseded by more sophisticated views which revert to a continuistic look at the world?
I regard the dichotomist constraint with extreme cautiousness. There is at least as much evidence against the hypothesis as there is in its support. Moreover, if dichotomism is wrong, such explanations are of little help. They provide a consolation of sorts for our shortcomings by persuading us that we are like that, that we cannot free ourselves of them. But we can, of course. And, after all, humans have also had non-dichotomist attitudes for thousands upon thousands of years. So perhaps a different hypothesis can be advanced: it is not that human thought in general is that two-valuedness ridden. You cannot blame every bad feature of many men and women on human nature ``as such''. It is just that sluggishness often gets the better of us. A principle of economy is all right, of course. But there must be an economic way of applying the principle, by comparing the costs and the returns. A dichotomist outlook may impose an excessive economy, skimping at the high price of divorcing ourselves from reality.
In fact gradualism is not alien to ordinary human views and ways of speaking, far from it. Indeed the overwhelming majority of our words admit of degrees in their application and lend themselves to some sort of qualification by hedges, comparisons, and degree expressions. Usually the context implicitly makes it clear which threshold has to be attained for an expression to be suitable enough. When that does not happen, the phrase is used in a vague manner. Thus `human' admits of degrees -- if modern palaeontology is right. But in ordinary contexts there is no doubt about the threshold, since among the animals which now exist the line between humans and non-humans is sharp. In a number of contexts, the threshold is not clearly provided, and in those contexts saying `It (or he or she) is (or was or will be) a human' is to make a vague statement. The question is automatically invited: `How much human?' -- in the same way as in some contexts to say that someone is tall is vague, the question arising of how tall he or she is.
Walton discusses none of those issues (I think he should have done). After all he tries to implement a pragmatic approach to the treatment of slippery slope arguments, which seems to me right. But a good account of such arguments cannot be only pragmatic -- a logical assessment of the validity of the arguments is also called for as we have seen. On the other hand, a satisfactory pragmatic approach has to explain that vagueness is a matter of use, not of meaning, as I have argued in the foregoing paragraph.
Lorenzo Peña (Spanish Institute for Advanced Study, Madrid)