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INFINITE REGRESSARGUMENTSTimothy Joseph Day aa University of Missouri , ColumbiaPublished online: 20 Jan 2010.

To cite this article: Timothy Joseph Day (1987) INFINITE REGRESSARGUMENTS, Philosophical Papers, 16:2, 155-164

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Philosophical Papers Vol. X VI (1987). N0.2

INFINITE REGRESS ARGUMENTS

Timothy Joseph Day University of Missouri, Columbia

An infinite regress argument has two parts. The first shows that certain premises lead to an infinite regress. The second attempts to show that this regress is‘vicious’. I shall refer to the second part of an infinite regress argument as the ‘viciousness part’. George Schlesinger, in discussing the question of when a regress is objectionable, observes that ‘There is nothing wrong with an infinite chain of something as such. No problem arises unless it is shown that to admit such a chain leads to some specifiable trouble.’ (Schlesinger (1 983), p. 2 19) Regresses can be good, bad or indifferent. The viciousness part of an infinite regress argument must show which of these properties applies to the component regress.

In this paper I offer a taxonomy of infinite regress arguments. This involves looking (somewhat superficially) at the question of when an infinite regress is vicious. I suggest that there are certain coherent themes that we can find in the viciousness parts of typical infinite regress arguments. It is this suggestion that I develop in this paper. I begin by surveying some examples of infinite regress arguments to get a general view of what has been said about the viciousness of infinite regresses. After this I consider a classification that David Sanford proposes in his article ‘Infinite Regress Arguments’ (Sanford (1984)). Finally, I make a proposal of my own and argue that it gives us some insight into what these arguments are about and how they can go wrong or right.

I

In this section I briefly survey four examples of infinite regress arguments with special reference to their viciousness parts.

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Example I: Gilbert Ryle criticizes Plato’s theory of Forms in Ryle (1932). He objects to the claim that there is an exemplification relation that holds between universals (Forms) and particulars. The various instances of the supposed exemplification relation would be instances of a Form. The relation between these instances and the Form of exemplification itself would be a higher order relation of exemplification. We thus generate an infinite regress of exemplification relations. According to Ryle ‘This conclusion is impossible. So there is no such relation as being-an-instance- of (Ryle (1932), p. 107)

Ryle does not tell us why he thinks the regress is impossible. Clearly, though, if some set of premises leads to an impossible result, something must be rejected. Ryle rejects the realist claim that there is a relation of exemplification.

Charles Landesman, in contrast, finds nothing logically impossible in Ryle’s regress. He rejects it rather on the grounds that it violates Occam’s Razor (Landesman (1972)). Schlesinger follows Landesman here, claiming that a regress of physical or metaphysical entities is vicious because we should ‘. . . avoid the ontological extravagence involved in admitting the chain of entities, for whose existence there is no independent evidence.’ (Schlesinger (1983), p. 221)

Example 2: John Passmore (1961) treats the theory of Forms as an attempt to explain predication, and gives the following infinite regress argument against this attempted explanation: Each time we explain a predication by appeal to a Form we introduce a new instance of predication, for in explaining how x is P we say that x is related to the Form P. If we try to explain this new predication we will introduce another predication, and so on ad infinitum.

For Passmore, this regress is vicious because it shows that the theory of Forms does not explain predication in a way that makes our understanding of predication intelligible. It is Passmore’s view that a philosophical explanation must be completely general in its scope. A philosophical explanation of predication must, if it is to be successful, explain all instances of predication. The theory of Forms fails to do this. Every time it explains a predication it introduces another instance of

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INFINITE REGRESS ARGUMENTS 157

predication, and this new instance is not included in the scope of the proposed explanation. The argument purports to show that no matter how often you reiterate the explanation in order to include the predication just introduced, you will always introduce a new, unexplained predication.

Example 3: For our third example we turn to the epistemological regress argument. Suppose that justified beliefs must be inferentially justified on the basis of some further justified beliefs. Allowing certain assumptions about non-circularity of justification, this leads to an infinite regress. Bonjour provides one way to fill out the viciousness part of the argument. The regress causes at least one problem for anyone wfio accepts the suppositions giving rise to it, for it commits one to ‘. . . the seemingly dubious thesis that an ordinary knower holds a literally infinite number of beliefs.’ (Bonjour ( 1 9 7 0 p. 3)

Example 4: My final example I take from St. Thomas. In the ‘Second Way of proving the existence of God’, Aquinas argues ‘from the nature of efficient causes.’ He first establishes that nothing can be the efficient cause of itself. ‘For it would be prior to itself, which is impossible.’ (Aquinas Summa Theologiae 1, 2 , 3 ) He then argues that there must be a first efficient cause on the grounds that everything that is caused has a cause, and that infinite causal regression is incapable of producing a final effect. Since we obviously see final effects all the time, there cannot be any infinite causal regressions behind those effects.

Let us take these four arguments as our paradigms. A first striking fact about them is that their viciousness parts are not interchangeable. It is also not at all obvious that there are any formal features which are common to the viciousness parts of all the arguments, or to more than one of them. I will argue, though, that there is some common ground in these arguments. As a way of approaching it I would like to consider the taxonomy of regress arguments proposed by David

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Sanford. Sanford’s classification is motivated, as is my own, by what philosophers have said about what makes a regress vicious.

Sanford begins by discussing the view that the regresses in infinite regress arguments are superfluous. This view is held by G. E. Moore and John Passmore, both of whom reduce viciousness to some form of circularity (see Moore (1962), p. 109 and Passmore (1961), chap. 2). P.T. Geach, paraphrasing Wittgenstein, endorses a version of this view: ‘. . . often when philosophers think the trouble is a vicious regress, the real trouble arises already at the first step: if it is rightly diagnosed there, we can forget about the regress.’ (Geach (1979), p. 100) Geach gives a version of Plato’s Third Man Argument as an example: The Theory of Forms says that there is only one form of large, but the first step of the regress shows that there are two. This is a contradiction and so we need not worry about the rest of the regress.

According to this view regress arguments oppose circularity, or contradiction, or ‘making no real progress towards an explanation.’ (Passmore (1961), p. 37) All these problems should, as Sanford points out, show up in the first step of any regress. Sanford also claims that what the above philosophers say about infinite regresses ‘. . . applies to negative [regress] arguments that attempt to show that a definition, explanation, or theory is inadequate’, but denies that they apply to ‘positive regress arguments.’ (Sanford (1984), p. 93, italics added)

Sanford’s distinction between positive and negative regress arguments depends primarily upon two things; the content of an argument and the form of its conclusion. His ‘content criteria’ are as follows: Negative regress arguments are those ‘. . . with wholly negative conclusions: a certain philosophical account, definition, theory, or explanation will not do because it leads to an infinite regress.’ (Sanford (1984), p. 100) On the other hand, positive regress arguments are‘. . . positive because they conclude that something of a special sort must exist. If something of this special sort did not exist, there would be an infinite regress.’ (Ibid.) I call these the content criteria because they appeal to what the argument is about.

Next we get the form criteria. Sanford admits that ‘The negative-positive distinction is difficult to account for

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INFINITE REGRESS ARGUMENTS 159

generally, since any assertion is equivalent to the denial of its contradictory.’(Ibid.) However, he thinks that ‘The distinction between positive and negative existential statements . . . is nevertheless clear enough.’ (Ibid.) Unfortunately, Sanford does not clarify the connection between existential statements and regress arguments. I take it that whenever a regress argument concludes with a positive existential statement, we have a positive argument, and when it concludes with a negative existential statement, we have a negative argument. (Note that these form criteria may not always yield the same result as the content criteria.)

In terms of Sanford’s criteria it appears that, of our four paradigm arguments the first two are negative and the last two positive.

Ryle’s argument (Example 1) concludes that there is no exemplification relation, and an immediate corollary to this conclusion is that any philosophical theory that depends on there being such a regress is wrong. The regress is therefore negative.

Passmore’s argument (Example 2) reaches a negative conclusion about a certain philosophical explanation. The content criteria, therefore, require us to put this argument in the negative class. Sanford’s form criteria, however, do not apply directly to the argument, which concludes that the Theory of Forms does not explain predication. This conclusion, however, could perhaps be stated as a negative existential statement. So with a bit of fussing Passmore’s argument satisfies both the form and content criteria for negative regress arguments.

Our last two examples are both clearly positive regress arguments. The epistemological regress argument (Example 3) purports to show that there are foundational beliefs. The conclusion of Aquinas’s argument (Example 4) is that there exists an uncaused cause. Both these arguments claim to show that if you follow the relevant regress back far enough you will reach a special entity. Thus both are positive regress arguments in terms of Sanford’s form and content criteria.

The above classification of our paradigm infinite regress arguments is not, I hold, the most helpful one, for the arguments it groups together are notably different in their

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viciousness parts. Consider Examples 1 and 2, which in Sanford’s terms are classified as negative regress arguments. The viciousness parts of these arguments are, however, based on very different kinds of considerations. The viciousness part of Example 1 depends primarily upon ontological concerns- specifically, the view that a certain infinite regress of entities is either impossible or incompatible with Occam’s Razor. The viciousness part of Example 2, on the other hand, depends mainly upon epistemological concerns-specifically, the view that no explanation is adequate if it generates an infinite regress of new unexplained cases of what it is meant to explain. This difference between Examples 1 and 2 is crucial to their evaluation. A good classification should reflect that.

In the cases of Examples 3 and 4, which in Sanford’s terms are classified together as positive regress arguments, we find similar problems. Here too, widely different reasons are given for the viciousness of the regresses concerned. And we again see a distinction between primarily ontological concerns, which are operative in Example 4, and concerns which are mainly epistemological, as in Example 3.

I11

These considerations strongly suggest that we divide infinite regress arguments into two categories: those that are primarily epistemological, such as Examples 2 and 3, and those that are primarily ontological, such as Examples 1 and 4. This epistemological-ontological division (hereafter E-0 division) is quite general yet non-trivial, and it is evident that it respects much of what has been said about why certain regresses are vicious.

I conclude by examining one last argument to show how the E-0 division can help isolate difficulties that arise in infinite regress arguments. The argument in question is D.H. Mellor’s version of McTaggart’s argument against the reality of the temporal A-series.

Mellor says that McTaggart’s argument claims that ‘. . . past, present and future tenses are mutually incompatible properties of things and events.’ (Mellor (1981), p. 92) However, since these tenses are always changing (future becoming present

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INFINITE REGRESS ARGUMENTS 161

becoming past) everything must possess all of them. This is contradictory, hence ‘. . . nothing in reality has tenses. The A- series is a myth.’ (Mellor (1981), p. 93) This argument for the unreality of tense is the first step of McTaggart’s regress.

The next step of the regress consists of a reply to this argument: While it is true that things and events must have all the tenses, they need not have them at the same time. ‘Things and events only have these properties successively: first they are future, then present, then past.’ (Ibid.)

Finally, we get the critical step in the regress, another argument. The reply given in step two refers to things and events having tenses at different times. We can, and McTaggart does, ask when these things have the tenses which they do. The answer to this question will be stated in terms of complex tenses: the event was future, is now present and will be past. Among these complex tenses are some that are incompatible; what will be future cannot also have been past. So, we again see that the supposition that tense is real leads to contradiction.

The reply given at step two may be repeated here, but it is no more effective. This dialectical interchange therefore leads to ‘. . . a regress that is vicious because at no stage in it can all the supposed tensed facts be consistently stated.’ (Mellor (198 I ) , p. 94)

Sanford treats this as a negative regress argument which argues against a philosophical theory of tensed expressions. It is more natural, however, to treat it as an argument for the ontological claim that there can be no tensed facts. If there were, then events would have contradictory properties. Of course the contradictions at level n can be explained away by referring to tenses at level n+l but doing so only introduces a new impossibility, a contradiction at level n+l . Contradictory things do not exist, hence there can be no tensed facts.

Sanford does not view Mellor’s argument in this way because, although he sees that it is obviously negative, his own categories have no place for an argument that has a negative conclusion and yet does not criticize an explanation, theory or definition. He thinks his content and form criteria are equivalent. This leads him to interpret the argument as an attack on an attempt to consistently explain tensed facts rather

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162 TIMOTHY J DAY

than a challenge to the reality of tense. Sanford‘s classification allows regress arguments in favour of the existence of certain entities, but does not directly accommodate arguments against the existence of certain entities that are not tied to particular theories. Mellor’s point is that tensed facts do not exist. McTaggart’s point was that the A-series does not exist. The regress argument is supposed to show that tensed facts must, at any level of complexity, display contradictory properties. There is no appropriate level at which to escape the contradiction. Neither philosopher is in any direct sense criticizing a theory of tense.

We conclude that Sanford’s classification and his reliance on the content criteria in negative regress arguments leads him to misrepresent Mellor’s argument. By contrast, we can say that since Mellor’s argument concerns the reality of tense, it is an ontological argument. We expect its regress to be vicious (if it is) for ontological reasons. Such reasons Mellor seems to have been trying to give. The point is not that ‘. . . contradictions compound faster than they can be explained away’ as Sanford seems to think. (Sanford (1984), p. 99) The problem lies rather in the supposed contradictory properties of tense and tensed facts.

By giving up the view that Mellor is criticizing a theory we can also more easily understand the difference between Sanford’s and Mellor’s views about the viciousness of the component regress. Sanford does not think that the regress is vicious. Why he does not depends on a sort of use-mention confusion that he finds in Mellor. At the purely syntactical level Mellor constructs an infinite regress of expressions which, given his intended interpretation, are not all compatible. Sanford accuses Mellor of putting the wrong interpretation on his hierarchy of expressions, and argues that, of the expressions constructed, some do not refer to new tensed facts, but are reducible to something given earlier in the hierarchy. Any expressions that do refer to new tensed facts are not contradictory but simply relative. This relativity can, Sanford argues, be consistently stated by appealing to complex tenses.

Tense, so construed, is not any entity the existence of which would require events to have contradictory properties.

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INFINITE REGRESS ARGUMENTS 163

Interpreting Sanford's criticism of Mellor in this way requires us to suppose that some of the expressions in the hierarchy actually refer to tensed facts and that we are actually arguing about that to which the expressions refer. Mellor claims, following McTaggart, that the tensed facts require contradic- tions. Sanford says that they do not require contradictions, but that they do need to be relativised in the correct way. We must, Sanford points out, recognize when we are using two syntactically distinct expressions to refer to one and the same fact. 'The argument gains its apparent force by failing to distinguish a series of distinct expressions from a series of supposed tensed facts.' (Sanford (1984), p. 100)

I think that Sanford may well by right in this assessment of Mellor's argument. I do not think that treating it as a negative regress argument is very helpful. Mellor wants to give an ontological argument. He wants to talk about tensed facts, but ends up talking about the language he has constructed. So, treating his argument as an ontological argument about the reality of tensed facts, it is a useful criticism to say that his regress is constructed out of the wrong sort of thing.

In conclusion, then, I do not think it helpful to use the negative-positive distinction. Infinite regress arguments and infinite regresses divide more naturally along different lines. There are those that are thought to arise from the nature (or possible nature) of the world. Others arise from our efforts to understand the world. In trying to determine viciousness, it will help to know first with what sort of regress we are dealing.'

NOTES

I . I would like to thank Romane Clark for helpful comments on earlier drafts of this paper. I would also like to thank the editors of Philosophicol Papers for help in matters of presentation.

REFERENCES

Bonjour, Laurence( 1978)'Can Empirical Knowledge Havea Foundation?, Americon Philosophical Quorter1.v 15, 1-13. Geach. P.T. (1979) Truth Love ond Immortali/~c on Introduction to McToggort's Philosophv. Los Angeles: University of California Press. Mellor, D.H. (1981) Real Time. Cambridge: Cambridge University Press.

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Moore, G.E. (1962) Commonpluce Book. New York: The Macmillan Company. Passmore, John (1961) Philosophical Reusoning, New York: Charles Scribner. Ryle, Gilbert (1932) ‘Plato’s Purmenides’, in R. E. Allen (ed.) Studies in Pluto’s Meiuph-vsics, London: Routledge and Kegan Paul (1969, pp. 231-263. Sanford, David H. (1984) ‘Infinite Regress Arguments’, in James H. Fetzer (ed.) Principles of Philosophical Reusoning. Totowa: Rowman and Allenheld, pp. 97-1 17. Schlesinger, George (1983) Meiuphysicsr 1ssues.und Techniques, Totowa: Barnes and Noble Books. St. Thomas Aquinas (1945) Summa Theologiue selections in Anton C. Pegis (ed.) Iniroduction to St. Thomas Aquinus. New York: Random House.

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