Category: Circularity Arguments

Circular Definitions, Arguments, and Explanations

In the course of our discursive operations we often encounter circularity.  Clarity will be served if we distinguish different types of circularity.  I count three types.  We could label them definitional, argumentative, and explanatory.

A.  The life of the mind often includes the framing of definitions.  Now one constraint on a good definition is that it not be circular.  A circular definition is one in which the term to be defined (the definiendum) or a cognate thereof occurs in the defining phrase (the definiens).  'A triangle is a plane figure having a triangular shape,' though plainly true, is circular.  'The extension of a term is the set of items to which the term applies' is an example of a non-circular definition. 

Ibram X. Kendi, the race 'theorist' currently much-loved by the 'woke,' was recently asked to define 'racism.' He came out with this brilliancy:  “A collection of racist policies that lead to racial inequity that are substantiated by racist ideas." Video here.

B.  Sometimes we argue.  We attempt to support a proposition p by adducing other propositions as reasons for accepting p.  Now one constraint on a good argument is that it not be circular.  A circular argument in is one in which the conclusion appears among the premises, sometimes nakedly, other times clothed for decency's sake  in different verbal dress.  Supply your own examples.

C.  Sometimes we explain.  What is it for an individual x to exist?  Suppose you say that for x to exist is for some property to be instantiated.  One variation on this theme is to say that for Socrates to exist is for the haecceity property Socrateity to be instantiated.  This counts as a metaphysical explanation, and a circular one to boot.  For if Socrateity is instantiated, then it is is instantiated by Socrates who must exist to stand in the instantiation relation.  The account moves in a circle, an explanatory circle of embarrassingly short diameter.

Suppose someone says that for x to exist is for x to be identical to something or other.  They could mean this merely as an equivalence, in which case I have no objection.  But if they are shooting for a explanation of existence in terms of identity-with-something-or-other, then they move in an explanatory circle. For if x exists in virtue of its identity with some y, then y must exist, and you have moved in an explanatory circle.

Some philosophers argue that philosophers ought not be in the business of explanation.  I beg to differ.  But that is a large metaphilosophical topic unto itself.

Stanislav Sousedik and the Circularity Objection to the Thin Theory

Daniel Novotny writes,

I have discovered (something like) the circularity objection in Sousedik's translation of Frege's "Dialog with Punjer on Existence" into Czech. It's about two pages; here are some snippets (very rough translation):

First we might find difficulties with the assertion that existence is a property of the second order, i.e. the property of "falling under a concept". This is not incorrect but we need to take notice of something that — as far as I know — has gone unnoticed, namely that this "property" is under closer scrutiny a relation. "To fall under" is evidently a two-place predicate expressing not the relation of the concept to the thing (as it seems from Frege's exposition) but rather of the thing to the concept.  …"

. . . If we accept that "falling under" (or more precisely: "to have under") is a name of the relation, a sentence [e.g., "Men exist"] speaks not only of the concept of "men" but also of something that falls under this concept. . . . .

In order to say truthfully that the concept  F has under itself the individual x, the condition of x's existence needs to be satisfied. This seems obvious but the question arises what does this word "exist" express in this case? … it cannot be the second-order property, since it is, as we have seen a relation; we ask here about existence which is presupposed by this second-order relational propery as its necessary condition.

Now I have never read anything by Professor Sousedik, and I would be very surprised if he has ever read anything by me.  So it is particularly gratifying to find that he is making points that are almost exactly the same as points I have made in published papers, my existence book, earlier posts and in a forthcoming manuscript, copies of which I sent to London Ed, Peter L., and a few others.  I will couch the points in my own preferred jargon.

1. The second-level property of being instantiated is a relational property, one logically  parasitic upon the  two-place relation  *___ instantiates —* or *___ falls under —*.  Being instantiated is like being married.  Necessarily, if a first-level concept is instantiated, then it is instantiated by an individual, just as, necessarily, if a person is married, then he is married to someone (distinct from himself), the Fargo, North Dakota woman who 'married' herself notwithstanding. (We won't speculate on the question how such a self-marriage is consummated.)

2. It follows from #1 that the grammatical form of a sentence like 'Men exist' is not the same as its logical form.  Grammatically, it has a subject-predicate form.  Logically, however, it is relational: the concept man is instantiated by one or more individuals.  So not only is the sentence not about men, but about a concept; it is also refers — with "studied ambiguity" to cop a phrase from Quine — to one or more individuals.

3.  Now if concept F is instantiated, then it is instantiated by an individual that exists.  This is obvious, as Sousedik remarks.  What is less obvious, but still quite clear, is that the instantiating individuals cannot exist in the sense of being instantiated.  Obviously, no individual is instantiable; only concepts are instantiable.  If you insist that existence is the second-level relational property of being instantiated, then you obviously cannot say that the existence of Socrates is the second-level relational property of being instantiated.

4.  What this shows is that the 'Fressellian' attempt to reduce existence to instantiation fails miserably.  It ends up presupposing as irreducible what it tries to reduce, namely, genuine (pound the lectern, stamp the foot!) existence.  Another way of saying that the account presupposes what it tries to reduce is by saying that it is circular.  We want to know what existence is.  We are told that existence is a  property of concepts, the property of being instantiated.  Reflection on this property, however, reveals it to be relational and thus parasitic upon the dyadic relation of instantiation.  For this relation to hold, however, its terms must exist, and not in the sense of being instantiated.  So we are brought back to what we were trying to reduce to instantiation, namely, the existence that belongs to individuals.

Despite the clarity of the above, Peter L. balks, and London Ed baulks.  It is high time for both of them to cry 'uncle' and admit that I am right about this. Or must I sic the Czech contingent on them? [grin]

Original and Derived Intentionality, Circles, and Regresses

1. Original/Derived Intentionality. All will agree that there is some sort of distinction to be made here. A map is not about a chunk of terrain just in virtue of the map's physical and geometrical properties. Consider the contour lines on a topographical map. The closer together, the steeper the terrain. But that closer together should mean steeper is a meaning assigned by the community of map-makers and map-users. This meaning is not intrinsic to the map qua physical object. Closer together might have meant anything, e.g., that the likelihood of falling into an abandoned mine shaft is greater.

So some things derive their referential and semantic properties from other things. What about these other things? I draw you a map so that you can find my camp. I use the Greek phi to mark my camp and the Greek psi to mark the camp of a heavily-armed crazy man that you are well advised to avoid. I intend that phi designate my camp. That intending (narrow sense) is a case of intentionality (broad sense). This is not in dispute. What is in dispute is whether my intending is a case of original or of derived intentionality.

If the latter, then a regress ensues which appears to be both infinite and vicious. But before discussing this further, I need to bring in another point.

Continue reading “Original and Derived Intentionality, Circles, and Regresses”