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The Form of Practical Inference

biridans-assIn her essay on Practical Inference, Anscombe argued that practical reasoning is not formally distinct from theoretical reasoning.

The argument is relatively straightforward — relative, that is, to the average Anscombe argument. Suppose we have the inference pattern:




Therefore: C.

This looks like a piece of theoretical reasoning. From A, and from the relevant entailments, we’re able to conclude C. Suppose that A is “the potatoes have been in the oven for 20 minutes”, B is “the potatoes are cooked”, and C is “the potatoes are ready to eat”. If we know that A, we know that A entails B, and we know that B entails C, then we know that C.

Suppose, on the other hand, that C is something we‘re aiming at bringing about (we’re cooking potatoes). We can use the same inference to decide to bring about A. Now the inference looks like this:

Aiming at: C.



Therefore: bring it about that A.

The formal inference is the same. What makes it practical is nothing about the logical form, but only what we’re using that inference for.

What prevents some logicians from seeing this, says Anscombe, is a misguided idea about necessity. In the theoretical case, there appears to be a logical compulsion that is absent in the practical case. No reasonable person can accept the premises without accepting the conclusion. In the practical case, by contrast, there does not appear to be the same necessity. There might, for all the inference shows, be a way to bring it about that C without bringing it about that A. Thus aiming at bringing about C does not compel bringing about A.

Anscombe argues that this is a false distinction. If “compulsion” means “compulsion according to the norms of inference”, then we can say that the norms of practical inference compel bringing it about that A when C is desired, just as the norms of theoretical inference compel believing C when A is believed. It might not represent the only way to bring about C, but then the theoretical inference might not represent the only way to conclude that C. Meanwhile if “compulsion” means “psychological compulsion”, then we must admit that neither the theoretical nor the practical inference is compelling: people reason badly both theoretically and practically.

There is much more to be said, and Anscombe deals with various objections. But the conclusion is that the form of the inference is the same in the practical and in the theoretical case. What makes the difference between practical and theoretical reasoning is what we use the inference for rather than its form.

Anscombe is discussing what Aristotle calls “practical syllogism” in the ‘common books’ of the Nichomachean and Eudemian Ethics. Aristotle uses “συλλογισμος” to mean simply “reasoning”; there is no strong compulsion to suppose him to be talking about the more specific syllogistic theory of inference found in the Prior Analytics. And yet the examples that Aristotle gives of practical syllogisms can be read in line with that theory.

Anscombe moves right away to a logic of propositions rather than to a logic of terms. But Aristotle’s examples can be analysed in terms of the logic of terms proposed in his syllogistic. Here is one of them (more or less):

Human beings benefit from dry food.

I am a human being.

This bread is dry food.

Therefore: I’ll eat this bread.

(Never mind what Anscombe calls Aristotle’s “curious dietary theory”. Replace “dry food” with “healthy food” if you like.)

As stated, the syllogism clearly isn’t valid under the rules of the Prior Analytics. But the obvious reason for this obscures the more interesting reason.

The obvious reason is that the conclusion mentions something that isn’t in any of the premises: my action of eating something. If the argument is a sorites, then the conclusion should be: “I benefit from dry food”. The moral philosopher can bring in all sorts of Humean quibbles about whether this is sufficient on its own to compel any action.

But the logician might be at least equally interested in the way the terms are divided up. Let me represent the inference, with the modified conclusion, putting subject-terms in round brackets and predicate-terms in square brackets. The copulas I leave out. Then we have:

(Human beings) [benefit from dry food].

(I) [human being].

(This bread) [dry food].

Therefore: (I) [benefit from dry food].

For the syllogism to be valid (as a sorites), we would need four terms, to match our four propositions. But what we have here is five terms. “Dry food” is not the same term as “benefit from dry food”. If we treat the two terms as equivalent, we can end up with one of the following valid but nonsensical soriteses:

Humans beings benefit from dry food.

I am a human being.

Benefit from dry food is this bread.

Therefore I am this bread.


Human beings are dry food.

I am a human being.

This bread is dry food.

Therefore I am this bread.

The conclusion is the same in each sorites. And it is decidedly not what we want from our practical reasoning.

What causes us the trouble is that “benefits” belongs to the matter and not the form of the syllogism. It goes into one of the terms, giving us one too many terms for our sorites.

One way of getting “benefits” out of the matter of the syllogism would be to treat it as syncategorematic. Thus in “humans benefit from dry food”, we could say, the subject is “humans” and the predicate is “dry food”, while “benefits” expresses the way in which the predicate belongs to the subject.

But does “benefits” then express the quantity or the quality of the proposition? Since the proposition appears straightforwardly affirmative, “benefits” does not seem to express a new quality. It might, then, express quantity. But how? In addition to saying dry food belongs to all humans and dry food belongs to some humans, can we also say that dry food belongs tobenefit humans?

This seems bizarre on the face of it, but there might be something in it. Michael Thompson’s Life and Action proposes that in order to understand practical reasoning, we need a new “logical form”. From the way he describes it, what he seems to want is a new quantifier. To use Geach’s example, “acorns grow into trees” is a true proposition meaning neither thatall acorns grow into trees nor merely that some acorns grow into trees. The first is false; the second is not quite what is meant, since “grow into oaks” isn’t just something that happens to belong to acorns; it belongs to themessentially: it is part of the ‘life-form’ of acorns that they grow into oaks.

Most philosophers would say that the reference to ‘life-form’ here is categorematic; it expresses a non-logical relation between acorns and the activity of growing into oaks. But Thompson’s Hegelian proposal is that when we begin talking about living things, we introduce at least one newlogical form. There is a distinct logical relation between subject and predicate, when we predicate an activity that belongs to the ‘life-form’ of a living thing.

This works, I have proposed, like a quantifier. It is not that all acorns grow into oaks, nor merely that some acorns grow into oaks, nor even that mostacorns grow into oaks (they don’t). Rather, acorns grow into oaks ‘life-form-wise’, where the latter expression introduces a distinct quantifier not recognised in standard predicate or plurative logic.

In Aristotelian terms, it expresses a way in which the predicate belongs to the subject, a way that is neither universal nor particular.

This can, I think, be used to make sense of the Aristotelian practical syllogism. If we rush to the solution, here is what we might do. First, take “b” as a strange sort of belonging that a predicate can have to a subject, expressed by the word “benefits”. Now we can assign the terms of the sorites in this way:

A: humans

B: dry food

C: me

D: this bread

The form of the sorites will then be (taking the quantity of singular propositions to be universal): AbB, CaA, ∴CbB, DaB, ∴CbD. I represent the sorites again putting subjects in round brackets, predicates in square, and now syncategorematic terms in italics:

Benefit (human beings) [dry food]

All (I) [human being]

All (This bread) [dry food]

Benefit (I) [dry food]

Note that the form is the same as what it would be if the ‘quantity’-term “benefit” were replaced with “all”. But then we’d get the absurd conclusion that dry food belongs to me in the standard way that a predicate belongs to a subject — that “dry food” is either a class to which I belong or a property of me.

But since we have taken “benefit” out of the matter of the syllogism and placed it into the form, it can modify the copula. It modifies it by causing it to express a relation of benefiting rather than a relation of class-membership, identity, or predication.

This is extremely radical. It makes the relation of benefiting into a logical relation! And it is much more radical than what Thompson proposes. He wants activities to be predicated of subjects in the normal way, but subject to a strange quantifier.

We can get to something more like what he is after by going a bit more slowly. First, we replace “dry food” and “this bread” by “eating dry food” and “eating this bread”. We still need the extra quantifier, since what we want to say is that those activities belong to the subject in a very particular way, as pertaining to its ‘life-form’ and not just to some or all or most of its extension. But now it looks much more like a quantity-term than “benefits”, which seemed to change the relation of predication into something else entirely.

Suppose we use the adverb “ideally” to express this special sort of quantity (as we might say that “ideally” acorns grow into oak trees). The resulting sorites is:

Ideally (human beings) [eat dry food]

All (I) [human being]

All (Eat this bread) [eat dry food]

Ideally (I) [eat dry food]

The sorites would be equally valid if “ideally” were replaced by “all”, but then it wouldn’t look like a practical syllogism at all. The conclusion would be an assertion about what I do, whereas here the conclusion looks like a recommendation. And it would anyway be bad practical reasoning to move from what everyone does to what I ought to do: e.g., everyone screws up sometimes.

I do not mean to disagree with Anscombe, however (I rarely do). It is stillnot the case that it is the form that makes this syllogism practical. Having certain propositions in the form, “P belongs to S ideally” is a necessary but not a sufficient condition for a syllogism to be practical. Take, for instance, the syllogism:

Ideally swallows migrate for winter.

These birds are sparrows.

Therefore: Ideally they migrate for winter.

I might be using this inference to decide what to do, but I am more likely to be making a prediction about what the birds will do. It is still the case that what makes an inference practical is what we want to do with it and not its form as such. But now it is the case that practical inferences have to be of a certain form; they have to contain propositions of the right quantity.

Another question is whether an inference of the right form, of which I am the subject of the conclusion, is necessarily practical. Does a conclusion about what I ideally do have to involve some recommendation that I do something? Here moral philosophy begins, and I run away.

(Part 2) Collingwood’s Revolution in Logic

In my last post I looked at Collingwood’s attempted revolution in logic and its anti-realist implications. Sam Lebens raised the interesting question of how the proposed revolution in the Autobiography connects with the more radical line pushed in the Essay on Metaphysics.

The theory in the Autobiography is, if I interpreted it rightly, relatively simple. Truth-bearers become question-answer complexes rather than propositions. Their truth-values depend on the answer’s being the right answer to the question, defined in terms of justifiability. The Essay on Metaphysics presents a much more complex structure, involving propositions, questions to which propositions are answers, and presuppositions giving rise to questions. “Logicians”, Collingwood opines, “have paid a great deal of attention to some kinds of connexion between thoughts, but to other kinds not so much.” (23)

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Collingwood’s Revolution in Logic

“In logic”, writes R.G. Collingwood in his autobiography, “I am a revolutionary; and like other revolutionaries I can thank God for the reactionaries. They clarify the issue.” (52)

The revolution in logic he hoped to bring about does not seem to have come about. The matter is not helped by Collingwood’s vague and confusing way of presenting his alternative logic.

The reactionaries in his story are those who subscribe to what he calls “propositional logic”. His use of this name is apt to be somewhat confusing, since he does not mean, as most people mean by that term, the study of true and false propositions and sentential connectives. Rather, “propositional logic”, for Collingwood, is any logic that holds that propositions are truth-bearers:

According to propositional logic (under which denomination I include the so-called ‘traditional’ logic, the ‘idealistic’ logic of the eighteenth and nineteenth centuries, and the ‘symbolic’ logic of the nineteenth and twentieth), truth or falsehood, which are what logic is chiefly concerned with, belongs to propositions as such. This doctrine was often expressed by calling the proposition the ‘unit of thought’, meaning that if you divide it up into parts such as subject, copula, predicate, any of these parts taken singly is not a complete thought, that is, not capable of being true or false. (34)

Collingwood’s objection to this doctrine is not that the components of a proposition are units of thought (or what Frege simply called “Thoughts” – those items for which the question of truth arises). Rather propositions themselves have the status that the “reactionary” logicians would ascribe to subjects, predicates, etc.: they can be parts of a larger whole to which truth and falsity can be ascribed, but truth and falsity cannot be ascribed to them directly. Truth-bearers, for Collingwood, are complexes of which propositions form only a part:

It seemed to me that truth, if that meant the kind of thing which I was accustomed to pursue in my ordinary work as a philosopher or historian – truth in the sense in which a philosophical theory or an historical narrative is called true, which seemed to me the proper sense of the word – was something that belonged not to any single proposition, nor even, as the coherence-theorists maintained, to a complex of propositions taken together; but to a complex consisting of questions and answers. (37)

Collingwood implies that propositions in his logic have the same status as subject- or predicate-terms in standard logic. They can thus be presented as arguments in truth-functions, the questions being the truth-functions. For instance, the question “Who ate the eggs?” can be treated as a function that yields the value true if the proposition “Ms. Jones ate the eggs” is taken as an argument. In this way any proposition will be part of both true and false complexes. Who-ate-the-eggs?(Ms.-Jones-ate-the-eggs) will come out true, as will What-did-Ms.Jones-eat?(Ms.-Jones-ate-the-eggs), whereas Why-is-the-sky-blue?(Ms.-Jones-ate-the-eggs) will come out false. The form “Q?(x)” is meant to represent a question-function, where “Q?” specifies the question and “x” represents the argument-place into which various propositions can be inserted to yield truth or falsity to the whole complex.

To retain various benefits regarding quantification, etc., Collingwood’s logic could be made to include Frege’s functional analysis of names and predicates. Thus “x ate the eggs” can be taken as a function that yields different values when different names are given as arguments for x. Unlike in the Fregean analysis, however, the values yielded will not be true and false; rather, they will be items of a logically intermediate status that yield truth and falsity when taken as the arguments in question-functions.

It is interesting to consider the anti-realist implications of this. Collingwood is hard on what he calls “realism” and connects with propositional logic in the Autobiography; in Essay on Metaphysics he claims that realism “has the grandest foundation a philosophy can have, namely, human stupidity” (34). Here, however, I mean “realism” in Michael Dummett’s sense: one is a realist about a class of propositions, roughly, if one believes that classical logic, especially bivalence, holds for them. It is not entirely clear how close realism in Dummett’s sense is to realism in Collingwood’s sense, but certainly there is a connection.

Is Collingwood’s logic anti-realist in Dummett’s sense?

One failure of classical logic for propositions is suggested by Collingwood when he implies that his logic is paraconsistent. But his choice of example to illustrate this, “The contents of this box are both one thing and many things”, is extremely unfortunate, since the contradiction turns out to be only apparent; context reveals that the first part of the statement counts sets of chessmen as things whereas the second counts individual chessmen as things. The resolution of the contradiction does not require the adoption of a non-classical logic; it requires one to recognise a point that Frege often made: a number assignment attaches to a concept or kind of thing (a Begriff, in Frege’s terminology), not to a thing directly. Collingwood provides no other examples to show that his logic can permit true contradictions in a way that classical logic cannot.

On the other hand, it is clear that one and the same proposition can contribute to both true and false question-answer complexes. Who-is-Caesar?(Caesar-is-Emperor-of-Rome) could be a true complex while Why-is-there-something-rather-than-nothing?(Caesar-is-Emperor-of-Rome) is obviously a false complex. Since the answer part of the complex is usually the only part that is explicitly articulated – according to Collingwood we need to pay attention to wider context to work out the question part – this can give the appearance of allowing for a single proposition to be both true and false at the same time. But it is only an appearance; no proposition is either true or false, and the fact that a proposition can yield both truth and falsity when taken as the argument for different functions entails no more a rejection of classical rules than the fact that a single name can have both true and false predications made of it.

There is a similar appearance of a failure of bivalence. For instance, the proposition “I have exactly 10,003 hairs on my head” would usually be thought to be either true or false. Collingwood’s logic of question and answer entails that the proposition independently of its being offered as the answer to any question has no truth-value at all. In this sense, Collingwood could be said to be an anti-realist concerning a large class of ordinary propositions.

We need to remember, however, that in ordinary usage, according to Collingwood, the utterance, “I have exactly 10,003 hairs on my head”, expresses not a proposition on its own but rather a question-answer complex (with the question expressed through the context of utterance). And then it might well be, for all Collingwood says, that the complex How-many-hairs-do-I-have-on-my-head?(I-have-exactly-10,003-hairs-on-my-head) is decisively either true or false; it may be true or false even if nobody actually asks the question. Once we accept that thoughts, in the Fregean sense, are now question-answer complexes rather than propositions, classical logic can continue to apply to thoughts, though not to propositions.

Anti-realist implications begin to creep in, however, where Collingwood’s account requires an explanation of how a proposition yields truth or falsity in a question-function. It seems that a question-and-answer complex is true or false depending on whether the answer to the question is right or wrong. But this leaves rightness and wrongness unexplained. They can’t be explained in terms of the truth or falsity of the answer, since truth and falsity only belong to the question-and-answer complexes.

One possible explanation of rightness might be as follows: a right answer is a justifiable answer. We need no recourse to the concept of truth to explain justifiability: an answer is justifiable if it meets with certain standards embodied in our social and linguistic practices. Thus for Collingwood a proposition can contribute truth to a question-function by being a justifiable answer to the question; it can be (though it may not in fact be) shown to be worthy of acceptance according to some standard. Meanwhile wrongness can be explained in terms of an answer’s being capable of being shown worthy of rejection. This is not said explicitly by Collingwood, so far as I know, but it seems a plausible option; at least I can’t think of a better explanation of rightness and wrongness in answers to questions.

If this is right, then Collingwood’s theory of meaning is a justificationist theory – the classic recipe for anti-realism in Dummett’s sense. Question-answer complexes will be true in virtue of the answer’s being right, meaning (roughly) it can be shown to be worthy of acceptance; they will be false in virtue of the answer’s being wrong, meaning (roughly) it can be shown to be worthy of rejection. A truth-value gap will appear if an answer cannot be decidedly shown worthy of either acceptance or rejection. Negation will function non-classically where there is a difference between being able to show that an answer is not worthy of rejection (~~Q?(a)) and being able to show that it is worthy of acceptance (Q?(a)). Obviously this all needs a lot more working out.

On Money and Defining Things

There is a technical point that I left out of my last post.

Smit et al seek to identify the feature of money that makes it money. They reject its function as a unit of account and a store of value as being “important empirical facts about money, but not constitutive or individuating.” (330)

What does “constitutive or individuating” mean here? When Smit et al rule out a certain function as being constitutive of money, they show either that something could function in that way and still not be money or that something could be money and yet not function in that way. And when they settle on a definition, it is of the form: “x is money if and only if Fx”. It appears, then, they they regard the form of that definition to ensure that the property F is constitutive or individuating. They rule out candidates for F on the grounds that they cannot be placed in such a statement yielding truth.

But this is far from adequate. Many expressions, describing features of money, could be substituted for F in that statement. Are they all “constitutive or individuating” features of money?

Suppose it happened, as a matter of historical contingency, that everything we rightly call “money” traced its history back to some original institution (this is highly doubtful, but suppose it were true). Then “traces its history back to the original institution” could be substituted for F in Smit et al’s definition of money. But it does not seem constitutive or individuating; history could have worked out differently so that money was invented independently in different places and at different times.

We could avoid this problem by attaching a modal operator to Smit et al’s definition. Then we have: [](Mx <-> Fx). Is that enough?

I don’t believe so. What Smit et al are (sans phrase) enquiring after, I believe, is the essence of money. And I agree with Kit Fine, that “the notion of essence which is of central importance to the metaphysics of identity is not to be understood in modal terms or even to be regarded as extensionally equivalent to a modal notion.”

Assuming that what we are looking for is a constitutive property, and that “constitutive” is not just a synonym for “coextensive”, then on the modalised account we still get false positives. Something is money if and only if Midas would love it. Or perhaps something is money if and only if it is easy to confuse with near-money substitutes. Or if and only if it is the root of all evil, or it and a fool are soon parted, etc. These properties, perhaps, can be substituted for F, preserving the truth of the definition. But they are coextensive with the property of being money, not constitutive of it.

If I were to locate the flaw of Smit et al’s test, it would be in its symmetry: [](Mx <-> Fx) trivially entails [](Fx <-> Mx). To me there is something wrong with saying that while being a medium of exchange is constitutive of being money, being money is also constitutive of being a medium of exchange. I have no argument for this, but maybe I can provoke agreement with the following consideration. The sense of “constitute” in use here seems to match D in the Lewis and Short entry for “constituere“: “to fix, appoint something (for or to something), to settle, agree upon, define, determine.” This suggests asymmetry: x’s possession or non-possession of F decides the case about whether x qualifies as M; x’s possession or non-possession of F cannot then hang on whether x qualifies as M.

To say what constitutes something’s being money, I propose, is to give the essence of money. If the essence of M consists in being F, then the converse does not hold, even though it might well be that anything that is M must also be F and vice-versa. Essence is thus hyperintentional (no, not “hyperintensional” – see Geach, Reference and Generality, 157n.)

But this means we can’t decide on essence by the tried-and-true analytic method of looking for obviously false counterexamples. There are many functions associated with being money, perhaps exclusively associated with it. These are merely coextensive not essential or constitutive. What makes an institution money is a purpose, not necessarily represented in the minds of agents (few purposes are), but embodied in the institution. I gloss “embodied” as: coinciding as both the formal and the final cause of the institution – acting as its “primary cause” (Arist. Metaphys. 983a26). Looking for this is something that would have come naturally to most philosophers before the twentieth century. We postlapsarians will have to do our best.

But Is It Money?

chrismartenson_chapter6_whatismoneyThanks to Mike Otsuka for pointing me towards a new article by Smit, Buekens, and Du Plessis in the Journal of Institutional Economics, which addresses the vexed question what is money?

Here is the first part of the abstract:

What does being money consist in? We argue that something is money if, and only if, it is typically acquired in order to realise the reduction in transaction costs that accrues in virtue of agents coordinating on acquiring the same thing when deciding what thing to acquire in order to exchange.

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Descartes on the Syllogism

2000px-square_of_opposition_set_diagrams-svgDescartes made several criticisms of the syllogism. In the Discourse on Method, he remarks that “syllogisms … are of less use for learning things than for explaining to others the things one already knows”. This might lead us to think that Descartes’s main criticism is that syllogisms are non-ampliative. This is the general line pushed by Stephen Gaukroger in his Cartesian Logic. But arguably it presents Descartes as falling into ignoratio elenchi (“of all the fallacies, that which has the widest range”, as De Morgan claimed – Formal Logic, p.260).

No doubt the role of the syllogism was conceived variously by philosophers of Descartes’s time. Many regarded it as a purely didactic device. But it does not follow from the fact that it is non-ampliative that it must be constrained to that role. The power of non-ampliative knowledge can also be harnessed in a decision method. And Descartes, after all, was happy to use such knowledge for such a purpose. His own method of drawing out the consequences of innate ideas by intellectual intuition, in order to decide what is known for certain, seems a paradigm case of such an application. Nothing appears in the consequent that is not contained in the innate idea serving as antecedent. We might try to soften the non-ampliativity by saying that the consequent is only implicitly contained in the antecedent, but I don’t see why we can’t place the same qualification onto the claim that the consequent of a syllogism is contained in its antecedent.

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