1. For a sense of the issues involved in this problem and some of its possible solutions, cf. Jonathan Barnes, "Proof and the Syllogism," in Aristotle on Science: The Posterior Analytics, ed. Enrico Berti (Padua: Editrice Antenore, 1981), 17-59; M. F. Burnyeat, "Aristotle on Understanding Knowledge," in Aristotle on Science: The Posterior Analytics, ed. Enrico Berti (Padua: Editrice Antenore, 1981), 97-139; J. G. Lennox, "Divide and Explain: The Posterior Analytics in Practice," in Philosophical Issues in Aristotle's Biology, ed. A. Gotthelf and J. Lennox (Cambridge: Cambridge University Press, 1987) 90-119.
2. On the other hand, one does find such syllogisms in William of Ockham. What is interesting about the syllogisms he offers is that they are almost entirely lacking in any meaningful content. This should have been a warning to theologians about just how little is gained from a demonstrative syllogism. For an example, cf. William of Ockham, Scriptum in Librum Primum Sententiarum Ordinatio, ed. Gedeon Gál, O.F.M. and Stephen Brown, O.F.M., Guillelmi de Ockham Opera Philosophica et Theologica, vol. OT I (St. Bonaventure: Franciscan Institute Publications, 1967) 115.
3. The issue here is not that a syllogism with a necessary conclusion must have necessary premises, for contingent premises can produce a necessary conclusion just as false premises can produce a true conclusion. Rather, the issue is that if the premises are to exhibit the cause of a state of affairs which is itself necessary, then the cause must also be necessary. No contingent cause can produce a necessary effect.
4. Beginning with John Duns Scotus, this question will come to be asked using the term notitia intuitiva. Thus, in prologues to Sentences commentaries from Ockham on, one finds a variation of the question, "Whether intuitive knowledge of some theological truth is possible in this life."
6. The terms "superior" and "inferior" should not be taken in the sense of "better" and "worse" but rather in the sense that an "inferior" science depends upon its "superior" for its premises. Both sciences are equally "scientific."
7. Ibid., emphasis added. In both these passages, I have allowed principia to be translated as principle because a syllogism has principles just as a natural object does. I have added "premise" in brackets to indicate that in the case of a syllogism, the principles are premises.
16. The second argument concludes in much the same way as the first: "ergo habitus theolgicus ex articulus fidei tamquam ex principiis non procedit, sed magis ipsos declarare intendit." The five arguments, then, show either in different ways or from different authorities that theology cannot have the articles of faith as its principles, but rather has them as its conclusions.