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Logical explanation: Aristotle, Posterior Analytics

Background

With the presocratic natural philosophers we saw the use of logic in the search for causes. Aristotle not only produced original research in every area of natural science, but he also formalized the study of logic. Moreover, for Aristotle, it was necessary for scientific explanation to be cast in the form of logic. Otherwise one might have the appearance of persuasive argument, as with Plato's dialogues, but nevertheless fail to examine an argument rigorously. For Aristotle and for Aristotelians ever afterward, to produce a scientific explanation required one to produce a logical demonstration, a formal proof explicitly relying upon logical argument, making every premise explicit and specifying every step toward the conclusion. Anything less than rigorous logical demonstration leaves one with only opinion rather than knowledge.

Introduction to a logical syllogism

As you know from your previous logic courses, any logical argument, or syllogism, consists of two premises and a conclusion. The conclusion must follow from the premises. That is, if both premises are true, then the conclusion of a logically valid syllogism must necessarily be true.

In our study of Parmenides we have already encountered a syllogism form called Modus Tollens: If P, then Q. Q is false. Therefore, P is false. Can you identify the premises and the conclusion in this syllogism? "If P" is the major premise; "Q is false" is the minor premise; and "P is false" is the conclusion. Not every syllogism takes this modus tollens form, but all syllogisms have two premises and one conclusion.

If you want to review more about logic see Oxford University's Introduction to Logic website.

In the Posterior Analytics, book 1, chapter 13, Aristotle presented a logical analysis of two contrasting forms of causal reasoning. These two forms of syllogisms are often called by their Latin names quia and propter quid:

• quia, reasoning from known effects to a cause; and
• propter quid, demonstrating an effect from a known cause.

We will examine both of these in the next two sections.

1. Quia reasoning: "Knowledge of the Fact"

Aristotle explained the quia form of argument as follows (Posterior Analytics, Book 1, ch. 13):

Knowledge of the fact differs from knowledge of the reasoned fact.... Thus you might prove as follows that the planets are near because they do not twinkle: let C be the planets, B not twinkling, A proximity. Then B is predicable of C; for the planets do not twinkle. But A is also predicable of B, since that which does not twinkle is near -- we must take this truth as having been reached by induction or sense-perception. Therefore A is a necessary predicate of C; so that we have demonstrated that the planets are near. This syllogism, then, proves not the reasoned fact but only the fact; since they are not near because they do not twinkle, but, because they are near, do not twinkle.

If you are not used to logic, this short paragraph contains a mouthful! Let's go more slowly and unpack what Aristotle has just been talking about.

Let's analyze the quia form of syllogism (Table 1).

Major premise: In Aristotle's famous example of a quia argument, the major premise (“Planets do not twinkle”) is an effect rather than the cause of the conclusion (“Planets are near”). That is why this kind of syllogism begins with knowledge of the “fact” (quia), not of the reason why. The reason why will be found once the argument has reached its conclusion.

The minor premise (“What does not twinkle is near”) is a universal statement obtained by some means, whether induction, analogy, or intuition. Where does one obtain universals? The troublesome universal in the minor premise raises the question as to what extent quia reasoning produces knowledge. The quia argument is an example of formally valid causal reasoning, but in practice it often seems uncertain because the minor premise raises the great problem of induction. The weakness of induction in the middle step can be illustrated in a similar syllogism:

This bird is black.
Black birds are crows.
Therefore this bird is a crow.

Like Aristotle's quia syllogism, this syllogism has an effect for a major premise, a universal for a minor premise, and a cause for a conclusion. But unlike Aristotle's syllogism, this quia argument is not sound. The problem lies in the middle step, in the universal statement that "black birds are crows." A black swan is not a crow, but what if one has never seen a black swan? How is one to know if a universal is really true? In acknowledgment of this difficulty, the middle step may even be stated as a probability or qualified in other ways (“Black birds hereabouts are likely to be crows”; therefore “This bird is likely a crow”). It is not surprising, then, that in disputes over quia arguments the evidence for the universal in the minor premise is closely scrutinized and contested. The abundance of debates over the role of analogical reasoning and of polemical controversies over alleged mis-identifications of actual causes is therefore not surprising. Aristotle was well aware of this problem with quia syllogisms, which he explored in greater detail throughout the Posterior Analytics.

2. Propter quid: Demonstration of the Reason Why

Aristotle continued in Posterior Analytics 1.13:

The major and middle of the proof, however, may be reversed, and then the demonstration will be of the reasoned fact. Thus: let C be the planets, B proximity, A not twinkling. Then B is an attribute of C, and A-not twinkling-of B. Consequently A is predicable of C, and the syllogism proves the reasoned fact, since its middle term is the proximate cause....

Let's take a closer look at a propter quid argument (Table 2). The propter quid argument is the reverse of the quia: it begins with a cause and concludes with an effect. The major premise states the cause of the conclusion. The syllogism explains the reason why the effect occurs.

Aristotle explained that although equally valid, a propter quid argument, or demonstration of the “reason why”, appears more desirable than a quia argument. This is because in some ways it sidesteps the problem of induction explained above. In twentieth-century terms, an argument propter quid has more to do with the justification of knowledge than with the context of discovery, for it begins with a known true cause (“Planets are near”) stated as the major premise.

A universal statement, usually an observed regularity, functions as the minor premise. Again one faces the problem of how one can know universals, such as "Near things do not twinkle." For Aristotle, universals are apprehended only through extensive engagement with experience. Aristotle discussed the soul's capacity to apprehend universals given sufficient sensory experience in the last chapter of Book 2:

So out of sense-perception comes to be what we call memory, and out of frequently repeated memories of the same thing develops experience; for a number of memories constitute a single experience. From experience again -- i.e. from the universal now stabilized in its entirety within the soul -- originate the skill of the craftsman and the knowledge of the man of science, skill in the sphere of coming to be and science in the sphere of being....

The effect (“Planets do not twinkle”) is explained in the conclusion when it is deduced from the cause ("Planets are near").

For Aristotle, scientific explanations should take the form of a logical demonstration of the reason why. This ideal of propter quid reasoning meant that true explanations in science will provide causal knowledge of that which necessarily follows from the premises and could not be otherwise.

Twentieth-century logical positivists substituted empirical regularities or laws for Aristotelian definitions, but for them the same form of argument is necessary for a scientific explanation. In the language of logical positivists, they illustrate a “covering law” model of scientific explanation. For Aristotle deductive, causal, propter quid knowledge was the aim of science, as is the covering law for logical positivists, yet in his Meteorology Aristotle often found it is necessary to settle for knowledge of the fact.

• William A. Wallace, “Dialectics, Experiments, and Mathematics in Galileo,” in Scientific Controversies: Philosophical and Historical Perspectives, ed. Peter Machamer, Marcello Pera and Aristides Baltas (Oxford: Oxford University Press, 2000), 100–124. This article surveys the the demonstrative regress advocated by Jacopo Zabarella and other Paduan Aristotelians and considers its relations to Aristotle and to Galileo.
• Roger French, William Harvey’s Natural Philosophy (Cambridge: Cambridge University Press, 1994), especially chapter 11, explores the equally interesting example of methodological reasoning in debates over William Harvey’s Aristotelian anatomical investigations.
• The late medieval state of methodological discussion is surveyed in Steven J. Livesey, Theology and Science in the Fourteenth Century: Three Questions on the Unity and Subalternation of the Sciences from John of Reading’s Commentary on the Sentences, Studien und Texte zur Geistesgeschichte des Mittelalters, vol. 25 (Leiden: E. J. Brill, 1989).
• A magisterial survey of methodologies of analysis and synthesis is Alistair C. Crombie, Styles of Scientific Thinking in the European Tradition, 3 vols. (London: Duckworth, 1994).

	HSCI 3013. History of Science to 17th century Kerry Magruder, 2004-08 Report typos or broken links Many thanks to Mythology and Folklore and other online courses developed by Laura Gibbs.	Search course websites:
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