(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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Inevitable Brexit Post

I am a citizen of Portugal. My mother is from Macau and was born there when it was still under Portuguese control. She went through the long and difficult process of claiming her Portuguese citizenship so that I could have it through legacy. This allows me to live and work in the UK without having to apply for visas every few years (my other passport is Australian).

The process of gaining Portuguese citizenship was long, arduous, and expensive. But the Portuguese government treated us ex-colonials with respect and dignity. It was worlds apart from the way I was treated by the UK Border Agency when I tried to apply for visas as an Australian.

The UKBA treats applicants like criminals. It makes it impossible to speak with anyone in the system. The forms warn that any attempts to contact the agency will not be successful but will result in delays to the processing of your application. The agency is fortified within a labyrinth of Kafkaesque runarounds. It charges outrageous fees. The process of bringing in dependents or applying for spousal visas requires submission to humiliating and invasive examinations.

The UKBA also rejects every application it possibly can by creative interpretation of the laws. A friend of mine had his application rejected because his pen mark went too far outside one of the boxes he ticked. One of mine was rejected because I included the wrong page on one of twenty bank statements I had to send with the application. When your application is rejected, you are told that you have 28 days to leave the country. You are not told that you are allowed to appeal the decision and provide the right documentation (or send another form with all the ticks exactly the correct size). I had to ring a lawyer to find this out. The UKBA also warns that the appeal process can take months. You are not informed that you cannot be deported while the appeal is pending – again, I needed a lawyer to tell me this.

When I had sent in the correct page on my bank statement, my application was eventually accepted after appeal. But from that point onwards, I could never cross the UK border without being made to wait while an agent investigated my sordid past of illegal immigration. I must say that every agent apologised to me after finding out the truth but told me that they are obliged to investigate any visa that has a ‘flag’ on it.

Strangely enough, I still have this problem when entering the UK on my Portuguese passport, since the UKBA has linked together my EU passport with my Australian one. I am told this is (was!) in direct contravention of its treaty obligations to the EU, but that is a different story.

My immigration story is incredibly benign compared with others I have heard. I have heard of people being detained, deported, and fined for the most absurd imaginable reasons. I have heard of children being separated from their families. I have heard worse than that.

Immigration was a core issue in the EU Referendum, possibly the deciding issue. Intelligent people have argued that one advantage of leaving the EU is that Britain will be able to pick and choose its immigrants rather than having them forced upon it. My friend Neil Wilson has made this argument eloquently.

Neil claims that “every other advanced civilised nation on earth, outside the EU” runs a points-based system of selective immigration. I respectfully disagree. Face down the Australian Department of Immigration or the US Department of Homeland Security and tell me if you see evidence of civilisation.

I see a process that is deliberately made as expensive and dehumanising as possible. At times I barely managed it, and I am well off and a native speaker of English, with friends in high places. I cannot imagine what it would be like for somebody less privileged.

Do I believe in open borders? No. I believe, as Michael Dummett argued (please read his book), that just as anyone prosecuted for a crime should be treated as innocent until proven guilty, anyone seeking to migrate to a nation should be treated as legitimate until proven otherwise. We should not be treated as criminals trying to prove our innocence.

Now let me explain one reason why I voted for Britain to remain in the EU. The inhumanity of the UKBA and its counterparts in other nations did not emerge out of nothing. Such procedures are brought in on a wave of popular support, among native populations that always will harbour resentment against immigrants – including the ‘good’ (high point-scoring) sort of immigrants: fancypantses like me with higher degrees, often mixed ethnicity, middle-class jobs, and the requisite impressive bank balance. This popular resentment will always be a rich seam from which votes can be mined. The television stations make documentaries about heavily armed border guards chasing foreigners around, and the native populations squeal with delight. When one nation does it to the immigrants of another nation, that nation retaliates in kind. An accelerating arms race of nastiness between the UKBA and the Australian Department of Immigration has got us to where we are today. Immigrants become cannon fodder in a battle of national egos.

There is one and only one way to escape this vicious cycle. It is for nations to give up their sovereignty over immigration and enter into mutually binding international agreements, overseen by transnational bodies not subject to the ugly identity politics from which no national government can escape on its own. Nations must compromise on core principles of immigration to which they can all agree. The EU’s Free Movement of People might not have been the right principle, and I personally disagreed with its approach to non-EU migrants. But that is a matter that should have been argued within the EU Parliament or, in the ideal case, a Parliament of all the stakeholder nations.

Neil argues that: “People want nations for the same reason they want family and not just friends. People like their friends but want to live with their family – behind their own front door. Demonising nations is like demonising family, and needs to stop.

I strongly repudiate the analogy. We all struggle to get on with our families at times, but if you’re lucky enough to have a good family you know they’ll always be there for you when you need them most. Nations are not like this. The ex-industrial regions of England needed the more affluent regions to support them during the 1980s. Instead they got Thatcher telling them they weren’t getting their grubby hands anywhere near the family jewels, to wild popular acclaim. The resentment builds to boiling point, and the only escape valve for it blows straight through the hearts of immigrants and their families. That is what we have just seen. I’m sorry for being unoriginal, but it is true.

Thoughts on Direct Democracy

I don’t like bureaucrats in Brussels making decisions that affect my life.

For that matter, I don’t like Westminster MPs making decisions that affect my life.

But you know who I really, REALLY don’t want making decisions that affect my life?

The general public of Britain and the Commonwealth nations.