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A Kripkean Argument For Goatism

Bill Capra demonstrates that the fact that everything is a goat can be shown by a simple argument which draws on elementary modal principles.

Saul Kripke showed us that identity statements, when true, are necessarily true, assuming that what flanks the identity sign are both rigid designators [names]. But the opposite principle is no less true. Statements of non-identity, when true, are also necessarily true, assuming that what flanks the identity sign are both rigid designators. What could be more intuitive than the principle that if two things are distinct, then they could not have failed to have been distinct? Two things, surely, could not have been one.

‘Goat’ and ‘cat’ are both rigid designators. So if goats and cats are distinct, then they are necessarily distinct. Now surely Hilary Putnam was right to argue that cats might have turned out to be robots from Mars. We can tell a story according to which this is coherent and quite possible. Similarly, cats might have been goats. We can imagine that goats know how to make themselves quite small and fit themselves into cat suits, although we have not noticed this before. We have a strong intuition of possibility here, and it is not as if it is some illusory intuition of possibility that can be explained away. How could someone argue that goats could not have put on cat suits and learned to purr, chase mice, and engage in other cat-like activities? No, cats themselves (those very things) might have been goats. This is not a mere ‘epistemic’ possibility that is not really possible. It is really metaphysically possible that we might have examined cats carefully and found that they were goats in cat suits. Cats might have been goats.

Now, as we know from Kripke, if an identity fails, it fails of necessity. So if cats are not goats, then necessarily cats are not goats. The trouble is that we have an intuition of contingency – that cats might have been goats – which we have no reason to disrespect. It follows that it cannot be the case that cats are distinct from goats. Therefore cats are goats.

The same argument carries over to birds, cars, pencil sharpeners, and all other material things. They all might have been goats, and thus they all are goats. For if they are not goats then they could not have possibly been goats. But what could be plainer than the fact that they could be goats? (Who here is the philosopher and who the plain, commonsensical person?) Indeed, you, dear reader, might have been a goat. Therefore you are not necessarily distinct from a goat. And since non-identities are necessary, you are not non-identical with a goat. Therefore you, dear reader, are a goat.

This sort of argument generalizes, to show that all material things are goats. But what about parts of goats? Surely a goat’s leg is not itself a goat, and thus goatism is false? One reply would be that modern philosophy of language has shown that there is no determinate difference between referring to a goat and referring to an undetached goat leg. But we need not rely on that possibly contentious doctrine, because it is obvious that a goat’s leg might itself be a goat, just as a cat might be a goat. It follows that goat’s legs are goats. And the same goes for other goat parts. Hence all goats are composed of smaller goats. So the world is goats all the way down! Furthermore, like many Mediaeval philosophers, we should accept that mereological fusions of goats [whereby many things compose another thing] are themselves goats. These fusions are many-headed goats. There is even the ‘All-goat’, which is the mereological fusion of all goats – even of all actual and possible goats. The All-goat is itself a goat, even if it is admittedly a rather exceptional goat in view of how many heads, legs and tails it has in contrast with the goats we are more familiar with. The All-goat has many heads.

Abstract Goatism

Although we have thus shown that all material things are goats, the thesis is not yet fully general. We have not yet shown that absolutely everything is a goat, for the argument does not obviously extend to abstract objects such as numbers. We need to demonstrate that numbers are one and all goats; and for that we need the premise that any number might have been a goat.

We set considerable store by ordinary modal intuitions in the above argument concerning material things; yet it seems that some people have intuitions to the effect that numbers are necessarily abstract and do not exist in space and time, whereas goats are necessarily concrete and do exist in space and time. The surprising conclusion which would seem to follow from this, is that numbers could not be goats, and thus are not goats.

One response would be to deny the existence of abstract objects such as numbers. This strategy would certainly fit with one aspect of goatism, whereby it strives to be a simple and economical view. If goats turn out to be the one underlying substance which takes a variety of forms, then empirical science can investigate the combinations and permutations of the goat-substance which gives rise to the manifold of diverse appearances which suggest to the na ïve that some things are not goats.

However, I believe in being metaphysically cautious, and this crude dismissal of abstract objects seems metaphysically extravagant. It seems metaphysically safer to say that some goats are abstract objects. But does not the intuition that goats are concrete get in the way of this idea?

Well, I think it is true that numbers are necessarily abstract. But we have conceded that pencil sharpeners might have been goats, and thus cannot be said to be necessarily distinct from goats, and thus are identical with them. But it is also true that superficially, pencil sharpeners seem to have essential properties incompatible with their being goats. However, once we know that they are in fact goats, our view of their essence should change; and we know that the essential properties that we associate with our conception of pencil sharpeners do not in fact exclude their being a goat. So pencil sharpeners do not in fact have properties that exclude a goaty essence; and the same is true of numbers. It might be part of the nominal essence of a number to be, say, even, or prime, or an abstract object. But in addition to such nominal essences, things may have hidden or real essences, which are not available by mere conceptual reflection. We may come to believe that a thing has essential properties that we did not know it had merely by conceiving it. Being a goat is just such a property of numbers.

Since there is no conceptual bar to numbers being goats, it appears that it is possible that numbers are goats. But is this really possible? What we need here is something parallel to the story of goats putting on cat-suits, so as to give us positive reasons for thinking that there is a possibility open here, rather than the mere appearance of a possibility. Yet it is difficult to see how goats could have dressed up as numbers so that numbers (those very things) could turn out to be goats.

However, perhaps this is making things too hard for ourselves. What we need to do is to tell a story according to which goats could have numerical properties. Now, on the structuralist view of mathematics, it is essential to numbers that they have relational properties but not essential for them to have intrinsic properties. Some such views insist that numbers only have relational properties, and have no intrinsic properties at all, but that seems over strong. The weakest structuralist view – and hence the most plausible – restricts itself to claiming that insofar as we conceive of numbers as numbers, we conceive of them as having relational essences, not as having intrinsic essences. These relational properties are their nominal essences, leaving open whether numbers have intrinsic essences. Structuralism only says that in thinking of numbers we do not think of them as having intrinsic essences. This means it is a quite open question what the intrinsic nature of numbers is. Numbers as we conceive of them are roles. It is a conceptual truth that numbers have certain roles with respect to other numbers; but what fills those roles is not a conceptual question. It is perfectly possible that goats are the role-fillers. What fills the roles are vast ranks of immaterial goats standing in numerical relations to each other. It is true that we will need an infinite number of such goats. But even in the material world we have seen reason to believe that there are an infinite number of goats, if goats are always composed of other goats. So we need not shrink from postulating infinitely large numbers of goats. Hence numbers can be goats, since goats may fill the roles that are the nominal essences of numbers. And thus, by the elementary principles of modal reasoning we rehearsed in the case of cats, numbers are goats.

Goats take a variety of forms, and the ones that we are most familiar with are those whose essence is most immediately manifest to us. These are the ‘classic’ goats – those with beards, which try to butt people, and which can be perceived by the five ordinary senses. But other goats are shy. They conceal their goaty essence. In particular, numbers are shy goats. Numbers are shy goats whose goaty essence is not as immediately available as the goaty essence of the more brash material goats that we can perceive. Deep down though, the world is of one underlying goaty nature.


The assertion that everything is a goat is something that we should embrace on the broad grounds of its coherence with other things that we believe, and because of its unifying explanatory power. Faced with this kind of argument, some philosophers respond with an incredulous blank stare. But if the goatist thesis has the virtues of economy and explanatory power, these must weigh more highly than nebulous feelings of metaphysical discomfort. Furthermore, in many respects, the goatist thesis is an entirely commonsensical theory in its accordance with our ordinary modal intuitions.

© Bill Capra 2010

Bill Capra ruminates at the CHVR Institute.


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