Augustine: De Dialectica

Around the year 387, Saint Augustine wrote this little text on logic, spanning only about 20 pages. According to his own account in Retractationes, the book was never finished, and he lost his only copy of the manuscript. However, the text we have genuinely seems to be written by him.

In spite of its opening statement, "Dialectic is the science of disputing well" (p. 5/82), De Dialectica does not contain much that we would now recognize as logic. It's a discussion of a number of topics related to language, most notably ambiguity and etymology.

Truth Values and Dispute

One notable feature of Augustine's discussion of 'dialectics' is that he seems to take dispute to be more fundamental than truth values. A meaningful statement has a truth value in virtue of being up for discussion – not the other way around.

In his words:

For either a statement is made in such a way that it is held to be subject to truth or falsity, such as 'every man is walking' or 'every man is not walking' and others of this kind. Or a statement is made in such a way that, although it fully expresses what one has in mind, it cannot be affirmed or denied, as when we command, wish, curse, or the like. For whoever says 'go into the house' or 'oh that he would go into the house' [utinam pergat ad villam] or 'may the gods destroy that man' cannot be thought to lie or to tell the truth, since he did not affirm or deny anything. Such statements do not, therefore, come into question so as to require anyone to dispute them. (p. 6/85)

He consequently adopts the term "statements that require disputation" as a name for what we would call truth-functional statements (p. 6/85).

Eloquence and Proloquence

He later introduces the distinction "expressing" / "asserting" (eloquendo / proloquendo) to indicate the difference between the statements that "require questioning and disputing" and those that do not (p. 7/87).

This leads him, in the Chapter XII on "the force of words," to make he following wonderful comment on the relation between logic and rhetoric:

For although disputation need not be inelegant [ineptam] and eloquence need not be deceptive [mendacem], still in the former the passion of learning often – indeed, nearly always – scorns the pleasures of hearing, while the in the latter the more ignorant multitude [imperitior multitudo] think that which is said elegant is said truly. Therefore, when it becomes apparent what is proper to each, it is clear that a disputer who has any concern to make his points appealing will sprinkle them with rhetorical color, and an orator who wishes to convince people of the truth will be strengthened by the sinews and bones, as it were, of dialectic, which are indispensable to the strength of the body but are not allowed to become visible to the eye. (p. 13–14/103)

So logic and rhetoric are inner and outer values – but logic is not inner as in the soul, but inner as in internal organs.

An Observation on Implication

Another interesting feature is that he takes implication to be inherently connected to argumentation:

Whoever says 'if he is walking, he is moving' wishes to prove something, so that when I concede that this combined statement is true he only needs to assert that he is walking and the conclusion that he is moving follows and cannot be denied, or he need only assert that he is not moving and the conclusion that he is not walking must be agreed to. (p. 6/85)

It seems fair to say that Augustine thus sees the meaning of the implication as  given by its use in argumentation.

Signification and Writing

In Chapter V, Augustine gives a definition of a sign followed by a slightly strange qualification:

A sign is something which is itself sensed and which indicates to the mind something beyond the sign itself. To speak is to give a sign by means of an articulate utterance. By an articulate utterance I mean one which can be expressed in letters. [Signum is quod et se ipsum sensui et praeter se aliquid animo ostendit. Loqui est articulata voce signum dare. Articulatum autem dico quae comprehendi litteris potest.] (p. 7/87)

The intuition behind this comment seems to be the following: If something is said clearly and intelligibly, it can be broken up into its component parts (letters, or phonemes). However, this does seem on he face of it to make verbal understanding dependent on literary understanding.

But maybe this is only because we read too much into the word "letter":

For we misuse the term 'letter' when we call what we see written down a letter, for it is completely silent and is no part of an utterance but appears as the sign of an articulate utterance. In the same way [we misuse the term 'word'] when we call what we see written down a word, for it appears as the sign of a word, that is, not as a word but as the sign of a significant utterance. Therefore, as I said above, every word is a sound [omne verbum sonat]. (p. 7/89)

The theory thus seems to be this: The written word or letter is a sign because it evokes the spoken word or letter to the mind; and the spoken word or letter is a sign because it evokes its referent.

Ambiguity and Obscurity

In Chapter VIII, Augustine introduces a distinction between ambiguity and obscurity. This is not terribly important, but I find his explanation so nice that I wanted to quote it:

When little appears, obscurity is similar to ambiguity, as when someone who is walking on a road comes upon a junction with two, three, or even more forks of the road, but can see none of them on account of the thickness of a fog. Thus he is kept from proceeding by obscurity. […] When the sky clears enough for good visibility, the direction of all the roads is apparent, but which is to be taken is still in doubt, not because of any obscurity but solely because of ambiguity. (p. 14/105)

He goes on to complicate this distinction by distinguishing further between obscurity based on inaccessibility to the mind and to the senses, as in not recognizing a picture of and apple either because one has never seen an apple before, or because it is too dark (p. 14/105).

Problems with Category Membership

In his discussion of ambiguity, Augustine distinguishes between the vagueness of a word like man and more straightforward cases of homonomy. He calls these two phenomena univocal and equivocal meaning, respectively.

This would not in itself be particularly interesting if he didn't get himself into problems by suggesting that a univocal concept is characterized by having "a single definition" (p. 16/111). This of course raises some problems once we start looking for such a definition:

When we speak of a man we speak equally of a boy and of a young man and of an old man, equally of a fool and of a wise man [and a number of further examples]. Among all those expressions there is not one which does not accept the name 'man' in such a way as to be included by the definition of man. For the definition of 'man' is 'a rational, mortal animal' [animal rationale mortale]. Can anyone say that only a youth is rational, mortal animal and not also a boy or an old man, or that only a wise man is and not only a fool? (p. 16–17/111)

So in order to save his definition, Augustine has to assert that a fool is rational, something he seems to sense the problem with:

One may wonder how a boy who is small and stupid [parvo aut stulto], or at least silly [fatuo], or a man who is sleeping or drunk or in a rage, can be rational animals. This can certainly be defended, but it would take too long to do this because we must hasten on to other subjects. (p. 17/111)

This is approximately the same rhetorical strategy he used when defining a sign back in Ch. V:

Whether all these things that have been defined have been correctly defined and whether the words used in definition so far will have to be followed by other definitions, will be shown in the passage in which the discipline of defining is discussed. [This part was never written.] For the present, pay strict attention to the material at hand. (p. 7/87)

Criticism of the Stoic Theory of Etymology

In addition to being an interesting text in its own right, Augustine's tiny book is also one of our prime sources for the Stoic theory of where meaning comes from.

The upshot of this theory is apparently the following: Every word has a meaning which derived metonymically from another word, and ultimately, these chains of metonymies all point back towards an original sound iconicity. Thus, Augustine reports that in order to avoid infinite regress,

… they assert that you must search until you arrive at some similarity of the sound of the word to the thing, as when we say the 'the clang of bronze' [aeris tinnitum], 'the whinnying of horses' [equorum hinnitum], 'the bleating of sheep' [ovium balatum], 'the blare of trumpets' [tubarum clangorem], 'the rattle of chains' [stridorum catenarum]. For you clearly see that these words sound like the things themselves which are signified by these words. But since there are things which do not make sounds, in these touch is the basis for similarity. If the things touch the sense smoothly or roughly, the smoothness or roughness of letters in like manner touches the hearing and thus has produced the names for them. For example, 'lene' [smoothly] itself has a smooth sound. Likewise, who does not by the name itself judge 'asperitas' [roughness] to be rough? It is gentle to the ears when we say 'voluptas' (pleasure); it is harsh when we say 'crux' (cross). This the words are perceived in the way the things themselves affect is. Just as honey itself affects the taste pleasantly, so its name, 'mel,' affects the hearing smoothly. 'Acre' (bitter) is harsh in both ways. Just as the words 'lana' (wool) and 'verpres' (brambles) are heard, so the things themselves are felt. The Stoics believed that these cases where the impression made one the senses by the sounds are, as it were, the cradle of words. From this point they believed that the license for naming had proceeded to the similarity of things themselves to each other. (p. 10/95)

Augustine's main beef with this theory seems that it is too speculative:

Even though it is is a great help to explicate the origin of a word, it is useless to start on a task whose prosecution could go on indefinitely. For who is able to discover why anything is called what it is called? (p. 9/93)

As an example, he gives a couple of hypotheses about the origin of the word verbum, asking "But what difference does this make to us?" (p. 9/93).

Varieties of Metonymic Shifts

The avenues by which words can jump from meaning to meaning are quite diverse. Twice in the text, Augustine gives a list of relationships that can warrant metonymic slides, once in chapter on "the origin of words" (Ch. VI) and once in the chapter on "equivocation" (Ch. X).

Here's the list from Chapter VI, page 11/97:

Proximity [vicinitas] is a broad notion which can be divided into many aspects:

1. from influence, as in the present instance in which an alliance [foedus] is caused by the filthiness of the pig [foeditate porci];
2. from effects, as puteus [a well] is named, it is believed, from its effect, potatio [drinking];
3. from that which contains, as urbs [city] is named from the orbis [circle] which was by ancient custom plowed around the area […];
4. from that which is contained as it is affirmed that by changing a letter horreum [granary] is named after hordeum [barley];
5. or by transference [abusionem], as when we say horreum, and yet it is wheat that is preserved here;
6. or the whole from the part, as when we call a sword by the name 'mucro' [point], which is the terminating part of the sword;
7. or the part from the whole as when capillus [hair] is named from capitis pilus [hair of the head].

Here's the list from Chapter X, page 19/117–119:

I call it transference [translatione]

1. when by similarity [similitudine] one name is used of many things, as both the man, renowned for his great eloquence, and his statue can be called 'Tillius.'
2. Or when the part is named from the whole, as when his corpus can be said to be Tillius;
3. or the whole from the part, as when we call whole houses 'tecta' [roofs].
4. Or the species from the genus, for 'verba' is used chiefly of all the wors by which we speak, although the words which we decline by mood and tense are named 'verba' in a special sense.
5. Or the genus from the species as 'scholastici' [scholars] were originally and properly those who were still in school, though now all who pursue a literary career [litteris vivunt] use this name.
6. Or the effect from the cause, as 'Cicero' is a book of Cicero's.
7. Or the cause from the effect, as something is a terror [terror] which causes terror.
8. Or what is contained from the container, as those who are in a house are called a household.
9. Or vice versa, as a tree is called a 'chestnut.'
10. Or if any other manner is discovered in which something is named by a transfer, as it were, from the same source.

You see, I believe, what makes for ambiguity in a word.

The itemization is not in the original. It is interesting that many of these examples are slightly strange or would be analyzed differently (but equally speculatively) today; the relationship of a chestnut tree and a chestnut would, e.g., probably be seen as producer–product relation rather than container–contained.

Word, Thing, Concept, and Word-Thing

One last thing that I want to mention is the rather complicated four-part distinction that Augustine introduces in chapter VI between verbum, dicibile, dicto, and res.

The last tree can roughly be glossed as concept, word, and thing:

Now that which the mind not the ears perceives from the word and which is held within the mind itself is called a dicibile. When a word is spoken not for its own sake but for the sake of signifying something else, it is called a dictio. The thing itself which is neither a word nor the conception of a word in the mind [verbi in mente conceptio], whether or not it has a word by which it can be signified, is called nothing but a res in the proper sense of the name. (p. 8/89)

The verbum, however, is a word considered as a thing one can refer to:

Words are signs of things whenever they refer to them, even though those [words] by which we dispute about [things] are [signs] of words. […] When, therefore, a word is uttered for its own sake, that is, so that something is being asked or argued about the word itself, clearly it is the thing which is the subject of disputation and inquiry; but the thing in this case is called a verbum. (p. 8/89)

We thus have here a kind of use/mention distinction, although put in a slightly different vocabulary.

Barbara Dancygier: "Mental space embeddings, counterfactuality, and the use of unless" (2002)

According to many native English speakers, the word unless has a tendency to work less well in hypothetical contexts:

• You're not clinically depressed unless you're tired.
• ?You wouldn't be clinically depressed unless you were tired.

In Barbara Dancygier's paper on the use of unless, she tries to explain this fact by means of some rather extravagant cognitive assumptions about people's use of hypothetical mental spaces. This explanation mainly amounts to describing the different distributions of unless and except if.

Unacceptability: Counterexamples

Although unless is indeed not appropriate in many hypothetical constructions, there are couterexamples. Dancygier gives a number of quite nice corpus examples, including

• 'Unless I was naked, you'd still worry I was wearing a gun or a wire.' (p. 365)
• 'I have pulled my tail off,' replied the younger Mouse, 'but as I should still be on the sorcerer's table unless I had, I do not regret it.' (p. 368)
• [I]f Miss Catherine had the misfortune to marry him, he would not be beyond her control, unless she were extremely and foolishly indulgent (p. 369)

So apparently, some hypothetical uses are OK, whatever the reason is.

Some Acceptability Judgments

Zooming a bit out from this observation, we have, according to Dancygier's intuitions, the following pattern (p. 369; I've abbreviated the sentences a bit):

• If she married him, he would be under control unless she were extremely indulgent.
• If she married him, he would be under control except if she were extremely indulgent.

Further, we have the following distribution in the mouse example, again according to Dancygier's intuitions (p. 372):

• As I should be on the table unless I had pulled my tail off, I do not regret it.
• *As I should be on the table *except if I had pulled my tail off, I do not regret it.

I suppose it's fair to assume the following acceptability judgments as well, even though Dancygier does not explicitly say so:

• *I wouldn't have finished unless you had helped me.
• *I wouldn't have finished except if you had helped me.

If these three cases are representative, then unless is more lax than except if: Whenever except if fits in a frame, unless does, too. Whatever story we tell about these distributions, it thus better be one in which except if requires some kind of higher standard of well-formedness.

Acceptability Patterns: A Possible Explanation

Dancygier's theory has something to do with contrast.

She proposes that except if needs to introduce a condition that stands in contrast with the whole hypothetical context (I think?) all the way up to the actual situation. Unless, on the other hand, only needs to introduce a condition that stands in a contrastive relationship with the immediate intensional context.

What this means is not quite clear, and it requires some further (and quite strong) assumptions about the introduction of new layers of intensional context. Such layers are introduced quite often in Dancygier's theory; not only modal verbs like would and should trigger them, but also future tenses and conditional items like if.

Beyond Control

So, and example: Let's look at the marriage example and show how this example allegedly builds up layers of context according to Dancygier's analysis. The relevant embeddings are:

This should be read as follows: In the base layer, Miss Christine and the male character are not married. However, in the first conditional scenario (if…), they are imagined to be, and from this hypothetical situation (would…), it is judged that "he would not be beyond her control."

This imaginary situation is then equipped with an exceptional condition (unless…), namely that "she were extremely and foolishly indulgent." This condition is taken to imply to lack of control in a future scenario (not lexically expressed). (Cf. pp. 369–70.)

Pancake Upon Pancake

Another way to visualize the same thing is by keeping track of when different assumptions are introduced, inherited, and negated in the embedded structure:

Not marriage (assumed)
(No assumption about control)
(No assumption about indulgence)
Hypothetical scenario:
        Marriage (overridden)
        (No assumption about control)
        (No assumption about indulgence)
        Future scenario:
                Marriage (inherited)
                Control (assumed)
                (No assumption about indulgence)
                Exceptional scenario:
                        Marriage (inherited)
                        Control (inherited)
                        Indulgence (assumed)
                        Future scenario:
                                Indulgent (inherited)
                                No control (overridden)
                                Marriage (inherited)

The important grammatical fact is here which of its ancestor layers the exceptional condition (indulgence) is inconsistent with. The ancestor layers are here the base layer, the hypothetical scenario, and the future scenario.

Since the indulgence is neither assumed nor denied in any of these layers, the exceptional assumption stands in a relationship of contrasts with all of them. Both unless and except if are thus grammatical in this context.

Note that this conclusion crucially depends on the fact that the base layer assumed to be undecided about control. If we suppose that Miss Christine has no control over the male character in the base layer, except if should be ungrammatical

Tailless Escapes Captivity

This analysis should be compared to the example I should be on the table unless I had pulled my tail off (cf. p. 371):

Pulled tail (assumed)
Not on table (assumed)
Hypothetical scenario:
        (Assumptions about the tail deleted)
        On table (overridden)
        Exceptional scenario:
                Pulled tail (assumed)
                On table (inherited)
                Future consequence:
                        Pulled tail (inherited)
                        Not on table (overridden)

In this case, the exceptional condition (I pulled my tail off) is in contrast with the immediately preceding scenario, which has no assumptions about the tail. The exception is, however, not in contrast with the base layer. Consequently, except if is ungrammatical, and unless is grammatical.

But note again the assumptions going into this conclusion: Without the assumption of "forgetfulness" in the hypothetical scenario, the conclusion would not follow. It is thus crucial that the hypothetical If I were still on the table… "deletes" a particular one of our assumptions in a seemingly rather arbitrarily fashion.

And All the Other Cases…?

Let's look at the case I wouldn't have finished, which I assumed above was ungrammatical with both unless and except if. This sentence should presumably be analyzed as follows:

I have finished (assumed)
You helped me (assumed)
Hypothetical scenario:
        I have not finished (overridden)
        You helped me (inherited)
        Exceptional scenario:
                I have not finished (inherited)
                You did not help me (overridden)
                Future consequence:
                        I have not finished (inherited)
                        You did not help me (inherited?)

In this case, the conditional exception (you did not help me) contrasts with both of the two layers above. So why not a grammatical use of unless and except if?

I think questions like these point to the fact that the cognitive assumptions behind Dancygier's theory are pretty vague and very, very speculative. It is by no means clear when assumptions are "forgotten," or exactly which or how many assumption that have to contrast with the intensional context.

In fact, it is not even quite clear to me whether except if requires contrast to all ancestor levels, and whether it requires contrast on a particular, high-focus parameter, or just any single parameter. Without an answer to these questions, it will be very difficult to assess the theory to any interesting degree.

Literature on the meaning of "only if"

I've been looking for some empirical studies of A only if B constructions. In the theoretical literature on natural language semantics, there is a number of models, but I want to know more about how they are actually understood. Fortunately, there seem to be some facts about that out there, too.

What Does It Mean, Allegedly?

The problematic issue with the only if construction is that it is supposed to be logically equivalent to a number of related constructions, even though non-logicians sometimes disagree with this. According to the classical convention, the following sentences thus all mean the same:

• It only thunders if it rains.
• If it thunders, it rains.
• If it doesn't rain, it doesn't thunder.

On the other hand, if we reverse the implication, we change the truth conditions:

• It only rains if it thunders.
• If it rains, it thunders.
• It it doesn't thunder, it doesn't rain.

If this was just a mere convention about logical language, all would be fine. The problem is, however, that these sentence forms are not used in the same situations, and they do not integrate equally well into all reasoning patterns in spite of their (alleged) equivalence.

The Performance Problem

One difference between the If A, then B and A only if B forms is that if form is generally more difficult to use in a modus tollens inference than the only if. At least, this is what Carlos Santamaría and Orlando Espino say (Santamaría and Espino 2002, p. 42). They're referring to three studies, including one by Jonathan Evans and M. A. Beck (Evans and Beck 1981).

The problematic case is thus the following inference:

If it thunders, it rains.
It doesn't rain.
–––––––––––––––––
It doesn't thunder.

This (clasically valid) inference should be performed more readily when served in this alternative, and supposedly equivalent formulation:

It only thunders if it rains.

I doesn't rain.

–––––––––––––––––––––

It doesn't thunder.

Cognitively, or perhaps in terms of actual natrual language semantics, this seems to indicate that A only if B works more like the contrapositive If not B, then not A than like its positive translation, If A, then B. Or at least, it seems to issue a conversational warrant closer to it.

It would be interesting to know if this alternative formulation comes with a corresponding decrease—are we trading of willingness to perform the straightforward modus ponens inference for higher rates of modus tollens? This would imply that the following inference generally is less accepted:

It only thunders if it rains.
It thunders.
–––––––––––––––––––––
It rains.

If the only if formulation really does works like a contrapositive, then this inference should appear to us like a modus tollens inference in terms of plausibility and difficulty. I do not know right now whether such an effect can actually be measured or not.

The Issue of Time

Another interesting proposal that Santamaría and Espino cite, also coming from Evans and Beck, is that there is a systematic interaction between our conception of temporal order and the choice of form.

Thus, even though If A, then B, and A only if B are supposedly logically equivalent, we get different patterns of acceptability or naturalness depending on whether A or B happened first. For A preceding B, we then (perhaps) have:

• If you bought on Tuesday, you're paying on Wednesday.
• (?) You bought on Tuesday only if you paying on Wednesday.

And for B preceding A:

• (?) If you're paying on Wednesday, you bought on Tuesday.
• You're only paying on Wednesday if you bought on Tuesday.

Of course, much clearer intuitions can be produced if we ruffle up the tenses a bit. But this, I think, relatively fair example to start the discussion from.

So, Causality?

Note that the issue of before/after interfaces with the concept of causality, which is notoriously bound up with implication, even if logicians and statisticians hate to admit this fact.

Possibly, the the only way we can really justify an inference from a later effect to a prior cause in the form of If EFFECT, then CAUSE is to objectify the cause and the effect by thinking about the observation of the effect and the deduction of the cause. In this way, we would straighten out the temporal sequence so that EFFECT could in fact precede CAUSE.

If this is true, it has a quite important consequence for the psychology of reasoning: We would then only be able to understand abductive inference by effectivly embedding a cause/effect relationship in a different and larger cause/effect relationship—namely the only in which a real or imagined person reasons from fire (the logical "cause") to smoke (the logical "effect").