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Are Names Abbreviated Descriptions?

The use of names in language seems very natural indeed, and we use them all the time to talk about people, pets and in extreme cases 'inanimate' objects such as cars or ships, but the place that names actually hold in a language has actually been much debated, and recently rather than trying to explain other linguistic features in terms of being convenient replacements for names the questions are in terms of whether a name can be replaced by a description that picks out the individual referred to. I shall try to explain why I do not feel that the simplest form of this thesis as roughly held by Frege and Russell is acceptable, and discuss a number of alternatives, none of which seem entirely satisfactory.

Consider the example of Pythagoras. It might seem sensible to argue that Pythagoras was the man who discovered (/ formulated / explained - depending on your beliefs about mathematics and whether axioms are discovered or thought up) Pythagoras' Theorem, or if we think that this is treading dangerous ground, the man who discovered the theorem which states that the square on the longest side of a right-angled triangle is equal to the sum of the squares on the other two sides. If this is the case than a theory which stated that names were simply abbreviated descriptions might suggest that the name 'Pythagoras' means 'The man who discovered the theorem which states that the square on the longest side of a right-angled triangle is equal to the sum of the squares on the other two sides'. This fact seems to state the most important or at least salient truth about this mathematician and philosopher, and is probably the only fact that most people who have heard of Pythagoras know about him (except perhaps that he was Greek, male or lived a long time ago) and is certainly the most frequent response to the question 'Who was Pythagoras?'. After all, Pythagoras Theorem is supposedly named after him, so surely he must be the man who discovered it?

This example, however, was not picked at random. The reason I chose this particular name to discuss is that there is now a reasonably widely accepted claim that Pythagoras did not, in fact, discover this theorem, but that it was one of his pupils that did, and that he stole the idea for which he is now famous. We need not even be concerned with whether this is true or not, but simply with the question of whether the claim that Pythagoras did not discover Pythagoras' Theorem actually expresses a real possibility. According to the abbreviated description theory of names, this claim is simply not possible: if 'Pythagoras' means 'The man who discovered the theorem which states that the square on the longest side of a right-angled triangle is equal to the sum of the squares on the other two sides' then if an ancient Greek philosopher stole his pupil's work which concluded just this trigonometric claim then Pythagoras was the pupil, not the teacher, with the confusion being something like that which leads people to believe that Frankenstein was the monster, and not his creator.

We might retreat from this position to the claim that 'Pythagoras' means 'The man attributed with discovering the theorem which states that the square on the longest side of a right-angled triangle is equal to the sum of the squares on the other two sides', but I don't feel that this is a reasonable explanation for the way we use the name - instead I think this could only be a discovery about how we already use the name and not an explanation of the way we do, since it would seem somewhat counter-intuitive to suggest that every name is the translation of a weak description such as 'thought to be...' or 'with... attributed to', rather than the stronger claim that they actually did. This is probably what most people aware of the fact that the discover of Pythagoras' theorem stole the idea from his pupil would reply to our question of 'Who was Pythagoras?' - that Pythagoras was attributed as having made this discovery, or that he was the person who publicised the idea, but I think this must result from a previous conception of who Pythagoras was, and can't really result from an adjustment of our previous conception of names as abbreviated descriptions, which would seem to have to be like definitions, with the name tracking the holder of the description.

A more popular response seems to be to say that we don't change the focus of the name 'Pythagoras' from the teacher to the pupil because our description of Pythagoras is not exhausted by a claim about his discovery of a theorem about right-angled triangles, and we in fact know quite a few other things about him - the theories developed from this intuition are known as 'cluster theories of names' due to the way they claim that a name stands for an extended description involving a large number of things we know about the person referred to. (This should not be confused with another response which basically reasons that the reason we do not call the pupil 'Pythagoras' rather than the teacher is simply a matter of inertia, that we can't be bothered to change the way we talk. Such a response misses the discussion entirely, which is not about reassigning names when we discover something new about them, but how we use them in the first place. According to an abbreviated description theory when we were talking about Pythagoras (presuming this translated as 'The person who discovered such-and-such about right-angled triangles) we were always talking about the pupil, and never the teacher, since it was he who in fact made this discovery, and so according to this theory inertia would tell us to stick with the pupil, and not change to the teacher, who would never have been Pythagoras in the first place.) We do not simply know Pythagoras as the discoverer of Pythagoras' Theorem, but also as a philosopher (reasonably rarely discussed these days, but certainly not entirely overlooked) and as the man referred to in contemporary literature and historical accounts. This is, in my opinion, a somewhat more satisfactory explanation than the simpler abbreviated description theory, and appears to be what Wittgenstein believed about names. If a name denotes a composite description of a large number of independent facts about a person then so long as the majority of these facts refer to that person, we can call that person by the name being discussed, in much the way that philosophers of science tend to be happy to use certain terms, such as temperature or electron, in a fairly fluid way, whereby any single fact can be disqualified from the definition of the term if it fails to correlate correctly with the other parts of the conception. In the same way as something can frequently accompany another in science, yet beyond a certain point diverge (a sort of definitional Hooke's Law) it is perfectly possible that one fact about a named individual can seem to accompany the others, but be found not in fact to.

As plausible as this refinement (or entirely new theory, depending on how kind we are being to the various proponents) may seem, I'm not convinced that it will prove much more useful. Few philosophers would suggest that we should take the description as a simple conjunction of facts, of which we need to know them all, since this would seem to require a far greater knowledge that the vast majority seem to have before using a name, and instead tend to opt for some sort of majority theory - where so long as most aspects of the description are kept intact we can accommodate additional information or reject compromised facts whilst maintaining the name pointing at the same person. Some do actually seem to propose a democratic system for deciding whether the integrity of the name's description is still intact, whereby every property has the same weight in deciding who holds the majority of the properties (or indeed if anyone does), but this seems to be a somewhat unwise move, not least for the difficulty we would have in deciding what would could as a single property (should the colour of each hair be a property, or simply the average colour of the overall head of hair?) and that out intuitions seem to be that certain properties are more important or essential to a person than others. Most, therefore, seek to weight different properties in some way, according to what are more important and essential parts of the name. Any formulation of this kind, however, still suffers from a lack of stability as to to whom the name refers, and it seems to me that however we might weight properties in the case of Pythagoras his discovery of the theorem seems very important indeed in our conception of him, and if we were simply having the name follow important features this would far outweigh any other single feature for the fact that it is the one that most people talking about Pythagoras will be thinking about - it is more likely that a claim about Pythagoras will be about the man featured in Ovid, for example, rather than about the man that discovered the theorem, especially since many facts will be somehow related to the discovery itself, since this is his achievement we are most interested in, and with the greatest longevity of interest. It is plausible that a better weighting could be found which will be more satisfactory, but if we are going to allow the loss of such an important part of the description it seems hard to see where we will draw the line, since there are no doubt countless claims that have been rejected already as claims about Pythagoras and possibly because they were not true of the discoverer of the theorem.

more important problem in my mind, however, is the question of what we allow into our original description in the first place. If our description is going to be in some way definitional (picking out the class of people that fit a certain set of properties, hopefully identifying only one) then it isn't clear how we are to keep out vacuous properties from our definition. It would be possible to suggest that Pythagoras was a terrible chauvinist, and place this into our description, for example, yet even if a majority formulation could reject this aspect of the description it would presumably add to the instability of the name if we were to reject it. Also, at the time he lived they would have had far more idea how to answer 'How was Pythagoras?', in which case it seems likely that we have hit a huge degradation in our description associated with the name. The problem with this is that it suggests that we have already very greatly adjusted our use of the name, and I suspect that we will have changed it so much that any philosopher arguing a cluster theory would have a very hard time indeed claiming that the greater part of the description associated with the name remains intact. The response to this is presumably that so long as the description changes only a very little at a time the name will retain its stability, but this seems a very large claim to concede, and one which places the theory quite far from what one might intuitively presume that 'Names are just abbreviated descriptions' would mean - a name doesn't actually seem to tie to any description, and it is unclear in what sense a description can change and still be abbreviated to a name, rather than just being associated in some way with one.

Kripke's response to the whole debate is to take a different tact entirely. He argues that names are what he calls 'rigid designators' - things that point to a single person, and continue to point to that particular person regardless of any changes to them, or discoveries about how they've been all along. So once we have decided who we mean by Pythagoras we can discover that he in fact didn't do anything we thought he did, looked entirely different, held an entirely different position in history, chronology, geography, etc. yet the term 'Pythagoras' would still refer to him. Effectively he is suggesting that everyone who was even born was given a number consecutively, and that these are what names are (or at least a name is later associated with this numbered person) - so we connect a name to the person, and this hooks into them whoever they might be. Effectively he is saying that names are 'blank' - that they start of meaning nothing, and can have predicates applied to them in order to tell you facts about them. This is why when writing formal logic we refer to a definite description, such as 'The King of France' with a whole sentence (including a predicate which means ' the king of France') rather than simply a letter which could be anyone and has things indicated about it by forming subject-predicate links. The empty, fresh letters seem to be what Kripke means by 'rigid designators' - simply labels with no associations which can have ideas added to them.

Whilst Kripke's theory sounds a plausible suggestion, and would seem to be how we use names in formal logic, I don't think this is anything like the way we use names in natural languages. The most important reason why this is not the case is that names are not simply introduced and then explained, but usually come with a whole host of associated properties. It does not seem clear how the name 'Pythagoras' could pick out a certain individual if we refuse to say anything to start with about the name 'Pythagoras' when we introduce it. Whilst nobody seems to have an entirely satisfactory explanation of the (very interesting) semiotic question of how names come to connect to a person (even if they are descriptions) Kripke seems to have an even greater problem than most, since he refuses to have the name having any essential meaning at all. If a name could pick out anybody, how can it pick out only one person? Kripke doesn't seem to answer this question - I think this is because he cannot; if there's nothing essential to a name, I can't see how it can avoid floating around forever never managing to associate with anything.

Overall, therefore, I cannot see how we can formulate a theory of names as abbreviated descriptions, and yet the only other major contender, Kripke's suggestion, seems to find problems in the other direction - in that whilst it can say exactly who we are talking about, it can never say anything about them, and thus cannot identify them. Perhaps instead we simply have to assert that names do not follow any logical pattern (there seems no reason why language should work systematically, any more than there is reason why it should work rationally) and suggest that at some point we simply say 'We believe that a philosopher called 'Pythagoras' by his peers discovered Pythagoras' Theorem, and let's call this man 'Pythagoras'', and never make any claim other than that, presuming that people will simply understand who we are talking about. Whilst a claim that we are not logical, however, entitles us to make any sort of suggestions about how names are used, even this doesn't seem to get us any further - we may just presume that people understand who we mean, but that just sets the issue one step further back, to one of how they could understand who we mean, without the names themselves having a particular place in a logical language - so this leaves us no better off!