#6 32.3 Aikin PubVers © Scott F. Aikin. Informal Logic, Vol. 32, No. 3 (2012), pp. 357-363. Discussion Note Pregnant Premise Arguments SCOTT F. AIKIN Senior Lecturer in Philosophy 111 Furman Hall Vanderbilt University Nashville, TN 37240 USA scott.f.aikin@vanderbilt.edu Enthymatic arguments are, roughly, arguments with at least one suppressed or unstated premise or conclusion. The classic ex- ample: Socrates is a man, therefore Socrates is mortal. The un- stated premise: All men are mortal. Enthymemes are manifesta- tions of our joint pragmatic objectives of efficient communica- tion and argumentative clarity. We leave out information that our listening audience can supply for themselves—sometimes for timeliness, and sometimes, as Aristotle noted (Rhetoric I.2, 1357a7–18), for rhetoric. And so: Enthymemes can be considered a special instance of Grice's Quantity Maxim: Be as informative as necessary for the purposes of agreement, but avoid being more in- formative than is necessary. (Jackson and Jacobs 1980: 263) It is more plausible (in cases of arguments with missing premises)—and certainly more constructive—to attribute to a speaker a statement that is more informative and does not violate the efficiency rule. (van Eemeren, Groo- tendorst and Snoeck Henkemans 2002: 58) The conditions for (i) distinguishing enthymemes from simple non sequiturs and (ii) identifying the content of the unexpressed premises are the objects of a good deal of theory.1 But another question hangs: can it also be the case that more than one propo- sition in a syllogism or multiple-premise argument is sup- 



























































 1 See, for example: Madden 1952; Hitchcock 1985; Govier 1987; Gilbert 1991; Levi 1995; Jacquette 1996; Johnson 2000; Malone 2003, and Walton and Reed 2005. Scott F. Aikin 358
 pressed? Can one express an argument with only one premise? The divisions of orders of enthymemes according to what, on the syllogistic model, has been suppressed has focused on single propositional suppression: 1st order has the major premise sup- pressed, 2nd order has the minor, and 3rd order has the conclusion suppressed.2 Here, I am interested in a sub-class of enthymemes with the conclusion and all but one of the premises suppressed. On the syllogistic model, we would see them as a cross between the 3rd and either 1st or 2nd order enthymemes. These are a kind of mirror image of the standard enthymeme in that only one premise is expressed, but the other premises and the conclusion are left unexpressed. But the form is not, as will be seen, limited to the syllogistic model. Call these pregnant premise arguments (or, 4th order enthymemes, if you must…actually, only if). In this brief note, I will show that stating a rule or generalization, given certain circumstances, functions as providing an argu- ment.3 This note, surely, is not the end of the discussion on the issue, but more an occasion to begin one. Take, for instance, the old standby example for an en- thymeme above. There are two stated claims, one a premise that Socrates is a man, the other the conclusion that Socrates is mor- tal, and there is one unstated claim, that All men are mortal. Now imagine their roles switched. Under the right conditions, perhaps uttered by Simmias after Socrates drinks the hemlock (and with the right emphasis), “All men are mortal” can function as the same incomplete syllogism as what we’d seen with the standard case of enthymeme. In this case, we don’t have to say that Socrates is mortal, but we, given the context, can see it. Conditionals and other forms of general statements can function as these pregnant premises: statements that are posed as arguments, but with suppressed coordinate premises and a suppressed coordinate conclusion. Interpreting arguments prof- fered as pregnant premises requires, then, that there be a fit be- tween what coordinate premises and conclusions we attribute to the argument, and determinations of which premises and conclu- sions fit are not purely logical or formal questions but also con- textual. Consider the following pregnant premise, one a profes- sor may pose to her students: (PP) If you study, you will pass the class. 



























































 2 For these divisions, see Copi and Cohen (2009: 289) and Cohen (2009: 50) 3 Arguments with singular expressed premises and suppressed coordinate premises and conclusions have been acknowledged in the literature, but they generally arise in the discussion of identifying and reconstructing the sup- pressed premises and conclusions. See, for example, Hurley (2000, 289) and Walton and Reed (2005, 347-8). Discussion Note: Pregnant Premise Arguments 359
 In one context, perhaps at the beginning of the semester, the as- sumed coordinate premise is that the students will want to pass and will take the means to their ends. So the following sup- pressed premise and conclusion for a practical inference are ap- propriate: (P1) You want to pass. (C1) Therefore, you should study (as a means to your end). The coordination of P1 and C1 with PP here works as an indi- rect communication of a complex of an operative principle of practical reasoning and background implication: You should take the best available means to your end. In stating PP, I am telling you what the best available means are. The key is that as the speaker identifies the ends a listener has with the consequent of the conditional (and thereby, the sup- pressed P1) and offers the suggested means to that end as the antecedent. And so, for example, if you diet and exercise, you’ll lose weight communicates that the speaker has identified that the listener wants to lose weight and that a combination of diet and exercise is the best option of the various means to that end. Con- sequently, this is what the listener should follow.4 However, let us change the context. Let it be the end of the semester, and some students are failing. Our professor utters PP, but she does not communicate P1 and C1. Rather, she com- municates that she knows something about these students: (P2) You are not passing. (C2) Therefore, you did not study (and should have!). Under these conditions, as a matter of face saving, the professor is communicating the counterfactual with PP, instead of stating it outright: If you had studied you would be passing the course (not failing it). 



























































 4 See Walton and Reed (2005: 350) for a version of the thought that such suggestions have other practicability desiderata. This thought is an extension of the requirement that all suppressed components of enthymemes must meet audience-acceptability requirements, outlined by Perelman and Olbrechts- Tyteca (1971: 458). Scott F. Aikin 360
 To be sure, to get the conclusion You did not study from the as- sumption You are not passing, the counterfactual must be true. But, again, the transition to the counterfactual commitment from PP should be clear, as stating the rule or lawlike connection also commits one to the correlate counterfactuals. The logic of PP and what background assumptions are acceptable in the context determine what the argument given by the pregnant premise is. That is to say, the logic of PP (licensing a practical series of in- ferences leading to modus ponens or a modus tollens on a coun- terfactual) determines that P1 and C1 are coordinate, and P2 with C2. But the context determines which of these two interpre- tive options is preferable for the stated conditional. And, follow- ing the same pragmatic objectives as those for enthymemes, those coordinate premises, when supplied by the context and the audience’s awareness of the context, may be left unstated for the sake of efficiency. Consider an example of a pregnant premise argument from the history of philosophy. The PreSocratic philosopher Xeno- phanes of Colophon posed a famous conditional widely taken as the core of an argument for religious reform: If horses had hands and could draw, they would draw their gods as horses. (B15)5 The counterfactual here functions as a kind of ad ridiculum, and its ridiculum qualities were taken to extend to depictions of the gods as looking in a way similar to any of their depictors. The conditional is posed as an occasion for a kind of critical reflec- tion on depicting god (or the gods), a premise of an argument that isn’t given, but is clearly implied. Now, what exactly that argument is, itself, isn’t clear, but that there is one implied and that it’s critical, that’s clear from the fact that the Xenophanes conditional is invoked by critics of many traditional forms of religious practice portraying the divine in anthropomorphic terms.6 



























































 5 This is Diehls-Kranz’s numbering system for the fragments, so B15 is a fragment that DK assess the source (in this case, Clement of Alexandria) as quoting Xenophanes accurately. Xenophanes’s critical line in the fragment is noted by Zeller (1980 [1882]: 41), Scoon (1928: 49), Kirk and Raven (1962: 169), Ring (1987: 38), Lesher (1992: 99) and Robinson (2008: 487). 6 Here, it may be objected that because it is not entirely clear what the argu- ment is that is implied here, it is problematic to say that there’s an argument. But, again, this is a point that has motivated all the theory of interpreting en- thymemes. That we haven’t lighted on an interpretation of the argument isn’t a reason to think there isn’t one at all. In fact, that there are ones that are less good interpretations than others (for example, taking Xenophanes to be en- dorsing anthropomorphism in B15) shows that there must be an argumenta- tive core to be extracted. Discussion Note: Pregnant Premise Arguments 361
 A further case of pregnant premises will demonstrate an additional feature of the form as occasionally audience- dependent. Abraham Lincoln, the 16th American President, de- livered the following pregnant premise in a letter to Albert G. Hodges, editor of the Frankfort, Kentucky, Commonwealth: If slavery is not wrong, nothing is wrong.7 Lincoln’s line was a favorite of John Rawls’ (Freeman 2002), and perhaps for obvious reasons. One need not have any sub- stantive view of what constitutes wrongness generally or what else specific wrongs there might be, but one need only have the view that there are wrongs in order to infer that slavery is wrong. It is a pregnant premise that, because of the contexts its suppressed coordinate premise may obtain in, yields overlapping consensus. With pregnant premises, context matters, and in this case, the premise is posed to apply similarly in a variety of con- texts. That pregnant premise arguments can be deployed is one thing, but that they are a regular occurrence is another. Here are a few that come to mind: (A) Nobody on his death bead wishes he spent more time at work. (B) You can graduate only if you take a logic class. (C) You can find salvation only through Christ. (D) No parking without a permit. (E) Drive hammered, get nailed. (F) If that’s an A paper, I’m a monkey’s uncle! These are all, as my aunt Dottie used to say, “You do the math” statements. They are either uttered at times when or posted in places where it is clear how they bear on their audiences. The contexts for successfully communicating the arguments would be, perhaps: (A) A friend offering advice to a workaholic. (B) A faculty advisor to a rising senior. (C) An evangelist to sinners. (D) A sign next to a parking space. (E) A billboard in the midst of the town’s bar district. (F) A grader for introduction to philosophy, to other grad- ers. And the correlately suppressed premises are: 



























































 7 A. Lincoln to A.G. Hodges: April 4, 1864. In Basler (1953: 282–283). Scott F. Aikin 362
 (A) You won’t regret, in the end, missing out on work. (B) You want to graduate. (C) You want salvation. (D) You don’t want whatever punishments await those who park without a permit. (E) You don’t want to get nailed (arrested). (F) I’m not a monkey’s uncle. And the conclusions they impel us to consider are clear: (A) Spend less time at work, more time on things that really matter. (B) Take the logic class. (C) Get right with Jesus. (D) Either don’t park here or make sure your permit is up to date. (F) Don’t drive hammered. (G) That’s not an A paper. But, again, given our familiarity with these usages, stating the coordinate suppressed conclusions and premises (when the sen- tences are posed appropriately) is overkill, at least for the sake of communication. Culturally competent listeners should be able to see the force of those statements as arguments and where they lead without explicitly stating them as arguments. These prem- ises are pregnant, and our competently hearing them is mid- wifery. References Basler, Roy (Ed.). (1953). Collected Works of Abraham Lincoln, Volume 7, Ann Arbor, MI: The Abraham Lincoln Associa- tion. Cohen, Elliot. (2009). Critical Thinking Unleashed. New York: Rowman and Littlefield. Copi, Irving and Cohen, Carl. (2009). Introduction to Logic. Upper Saddle River, NJ: Pearson-Prentice Hall. Eemeren, Frans H. van, Grootendorst, Rob, and Snoeck Henke- mans, Francisca A. (2002). Argumentation: Analysis, Evalua- tion, Presentation. Mahwah, NJ: Lawrence Erlbaum. Freeman, Sam. (2002). John Rawls: Friend and Teacher. The Chronicle of Higher Education: The Chronicle Review, 49(16): B12. Gilbert, Michael. (1991). The Enthymeme Buster. Informal Logic, 13(3): 159-166. Discussion Note: Pregnant Premise Arguments 363
 Govier, Trudy. (1987). Problems in Argument Anaysis and Ev- luation. Dordrecht: Foris. Hitchcock, David. (1985). Enthymatic Arguments. Informal Logic, 7(2&3): 83-97. Hurley, Patrick. (2000). A Concise Introduction to Logic. Belmont, CA: Wadsworth. Jackson, Sally and Jacobs, Scott. (1980). Structure of Conversa- tional Argument: Pragmatic Bases for the Enthymeme. The Quarterly Journal of Speech, 66: 251-65. Jacquette, Dale. (1996). Charity and the Reiteration Problem for Enthymemes. Informal Logic, 18(1): 1-15 Johnson, Ralph H. (2000). Manifest Rationality. Mahwah, NJ: Erlbaum. Kirk, G.S. and Raven, J.E. (1962). The Presocratic Philoso- phers. Cambridge: Cambridge University Press. Lesher, James. (1992). Xenophanes of Colophon. Toronto: Uni- versity of Toronto Press. Levi, Don S. (1995). The Case of the Missing Premise. Informal Logic, 17(1): 67-88. Madden, Edward H. (1952). The Enthymeme: Crossroads of Logic, Rhetoric, and Metaphysics. Philosophical Review, 61(3): 368-376. Malone, Michael E. (2003). Three Recalcitrant Problems of Ar- gument Evaluation. Informal Logic, 23(3): 237-261. Perelman, C. and Olbrechts-Tyteca, L. (1971). The New Rheto- ric. Notre Dame, IN: Notre Dame University Press. Ring, Merrill. (1987). Beginning with the Pre-Socratics. Palo- Alto, CA: Mayfield Publishing. Robinson, T.M. (2008). Presocratic Theology. In P. Curd and D. Graham (Eds.), The Oxford Handbook of Presocratic Phi- losophy, pp. 485-500. New York: Oxford University Press. Scoon, Robert. (1928). Greek Philosophy Before Plato. Prince- ton: Princeton University Press. Walton, D. and Reed, C.A. (2005). Argumentation Schemes and Enthymemes. Synthese, 145: 339-70. Zeller, Eduard. (1980 [1883]). Outlines of the History of Greek Philosophy. Trans. L.R. Palmer. New York: Dover.