Searching for appropriate fatalism candidate of Lazy argument

Sophism and parallel argument

Let us look for a moment at what the sophism is and what the parallel argument is? Historical comments, including that of Cicero, usually used to list this argument among sophisms. Ammonius presents this type of argument as an aporia [in de int. 131,20]. What did ancient commentators have in mind when they marked LA as a sophism? What is the sophism? Bobzien [1998:193] thinks that, in a sophism, there must be some bug in inference. But what kind of bug it is? In his Topics, Aristotle wrote the following on the sophism:

“When the argument stated is a demonstration of something, but it is something irrelevant which has nothing to do with the conclusion, no inference will be drawn from it about the latter; if there appears to be such an inference, it will be a sophism not a demonstration... a sophism is a contentious inference...” [162a15-16].

About character of such ‘inference bugs’, we could learn something further from Sextus [PH ii, 229 ff.]. There, he gives us some of features of the sophism and also claims that the discipline of dialectic is a tool capable of unmasking the sophism’s apparent plausibility and thus of solving it. He said: “They [dialectics] say that a sophism is a plausible and treacherous argument leading one to accept the consequence which is

1. 
   either false, or
   
2. 
   similar to something false, or
   
3. 
   unclear, or
   
4. 
   in some other way unacceptable.”
   

To these four types of sophism Sextus gives corresponding examples. In the chapter devoted exclusively to sophisms, however, he doesn’t forgot to remind us that “other say about sophism other things” [ibid., 235]. We don’t know the real meaning of this last reflection – is it connected with his division or maybe some could defend the same argument as invalid or valid from other grounds, metaphysical or just logical. Several passages latter [ibid., 247], Sextus informs us why the study of sophisms was especially important for training in dialectics – because dialectics is the science concerned with “what is true, false and indifferent”. This discipline enables us to recognize and analyze an argument, in an appropriate and precise way, to identify it as either valid or invalid, or indifferent (in the cases of ambiguities and insolubilia). This training goal was a part of the educational tradition of the Stoics through the ages. We know that Chrysippus wrote twenty-one treatises (in forty-eight books) on sophisms and other puzzling arguments [Diog. Laert. vii, 195-198]. Dialectics is not just about forming valid arguments but also about resolving bad arguments. We will leave aside some extensive details here, but what Sextus notices as necessary to be said about sophisms concerns the structure of an argument. An argument, in general, is ‘true’ if a true conclusion follows from true assumptions. He continues further by proceeding from a (true or untrue) argument (as a whole) in respect to the relations among (true or untrue) assumptions to the conclusion and to valid or invalid procedures of inference. The characterization of the sophism is not exhausted just by invoking the elemental mechanics of inference for the elements of an argument. He continues, saying that a sophism “leads not only to falsity but also to other absurdities” [atopias, Sextus, ibid., 251; cf. iii, 240] and that such an argument could compel us to agree with something that is absurd. This is the moment where we are not able to find what is wrong with an argument only according to the mechanical procedure of analyzing it, for it seems to be well formed and “a plausible but treacherous argument”. To sum up, Sextus’ position is that if something in the argument is wrong then it should be considered a sophism and can be classified according to the division given above (even “others say other things”).

Origen and Cicero are our prime sources for the argument and it seems that they were following a common source, as Turnebus [1556] first made out. Barnes [1988] makes a successful comparison between these two sources. The text seems to be almost the same: either their source was the same or Origen translates Cicero’s text (which is highly improbable, since we have no testimonies indicating he knew Latin). Cicero does not tell us why the argument could be a sophism (captio). However, he tries, as it seems, to find an adequate Latin term for the Greek sophisma when he states that such arguments, like LA, are ‘generis captiones’. This meaning for the expression, in the sense of ‘sophism’, can be found in more places in Cicero [ac. 2. 15. 46; div. 2, 17, 41; etc.]. Since the qualifications of both authors are almost the same, the more probable solution is that either the source was common for both authors or that it comes from the same line of sources (directly from Chrysippus himself as Barnes supposes). Cicero informs us that all these arguments of a ‘captious kind’ (so, there were more of them) can be rejected in the same way, by introducing the difference between simple and co-fated events. Actually, Cicero’s suggestion is very likely taken over from Chrysippus, whom he quotes in preceding lines. So, Cicero’s source probably contained some kind of answer to our question.

The clearest characterization of the sophism in Galen [De animi cuiuslibet peccatorum dignotione et curatione 3,14-17, p. 49sq. De Boer, transl. Harkins, 1963] largely corresponds to Sextus, not only in methodology, but also in his purpose, namely, to learn dialectical skills by solving sophisms. Sophisms “bear a similarity to arguments which are true” and for this reason they “are hardly recognizable to those who are inexperienced in dealing with arguments.” “Since ... the solution lies in showing the similarity of the false argument to the true, one must first have understood the nature of arguments which are true. For if a man has become so experienced in true arguments that he accurately and quickly recognizes their nature, he would still have no difficulty in recognizing those which are false.” What is of interest for us is that Galen emphasizes that it is necessity to analyze two similar arguments as a pair or a parallel – i.e. a sophism beside a corresponding correct argument. But what is a parallel argument?

Origen also compares two arguments, LA and a parallel or mirror argument that contains the example of Laius and Oedipus as taken from Euripides [Phoenissae, 18-20]. We know that Chrysippus’ answer, given in a parallel argument, is this:

“If it is decreed that you should beget children, you will beget them, whether you have intercourse with a woman or not. But if it is decreed that you should not beget children, you will not do so, whether you have intercourse with a woman or no. Now, certainly, it is decreed either that you should beget children or not; therefore it is in vain that you have intercourse with a woman” [Cels. 2. 20.].

Chrysippus’ interpretation is, according to Cicero, that ‘to have intercourse with a woman’ is co-fated (confatalia) with ‘to beget children’. This means that it is fated “both that Laius will sleep with his wife and that he will beget Oedipus by her” [fat. 30]. In other words, the necessary condition cannot be omitted in capturing the outcome.

Origen as a source seems to be sometimes more informative than Cicero because he tries to explicitly develop the answer by using a classic Stoic device – rebuttal by the construction of “parallels” (comparison, parabolé [Sextus, M, IX 109; cf. 97, 134] Cf. Shofield [1983]). The so-called “parallel argument” employs the same or very similar premises as the argument it counters (ti antiparaballetai), but aims to produce an absurd conclusion. Origen [ibid.] compares two lines of parallel arguments and tries to explicate why the parental argument is invalid:

“For, as in the latter instance, intercourse with a woman is not employed in vain, seeing it is an utter impossibility for him who does not use it to beget children; so, in the former, if recovery from disease is to be accomplished by means of the healing art, of necessity the physician is summoned, and it is therefore false to say that ‘in vain do you call in a physician’.”

If Barnes is right about the authenticity of the Origen passage (as taken over from Chrysippus’ source, where the case is analyzed as a sophism), then the parental part of the parabolé there is to be treated as a kind of sophism. In a parallel argument here – the pattern argument is a sophism while the other is a mirror argument given for the purpose of unmasking the first. The argument is a sophism as well as a part of a parallel argument at the same time. There is nothing conflicting in that claim. Moreover, the parallel argument could vividly indicate that the former argument is a sophism.