Refuting Oneself Elegantly: Plato’s Third Man Argument

In the Parmenides, Plato did what he knew would be done by someone else anyway: he refuted a central plank of his own philosophy, the Theory of Forms. When Aristotle came along to do what Plato had already foreseen and further the refutation, the argument was already old hat. Nevertheless, Aristotle had chosen a far better example to illustrate the point, an example which also lent itself to a snappy title by which the argument is now known: the Third Man argument.

The Third Man argument is a nifty delight that is often confusingly expounded. I reckon I can do better, so here now I explicate either triumphantly or to no avail.

The Simple Part

There’s a single Form for each recognisable object or quality in the real world, all of which are the imprecise and inferior copies of their respective ideal Forms. Thus, we can recognise all real-life rectangles as rectangles, for instance, because we have the Form or essence of rectangles in our heads. So when presented with soccer pitches, books and rulers, we can assign them to the group headed by the ideal rectangle that we have a mental picture of and dub them all rectangles.

The Confusing Part
Soccer pitches, books and rulers are very distinct yet are nevertheless rectangles. If these rectangles are so distinct from each other, the one ideal rectangle must be just as distinct from the variety of rectangles in the real world as the real-world rectangles are all distinct from each other. Thus, how can the one ideal rectangle be of use in categorising all real-world rectangles as rectangles? Alternatively put, if the one ideal rectangle is itself a rectangle that heads the group that includes soccer pitches, books and rulers, how is the ideal rectangle itself recognised as a rectangle let alone as the ideal rectangle?

The ideal rectangle must itself be recognised as an ideal rectangle just as a real-world rectangle is recognised as a real-world rectangle. A real-world rectangle is recognised as a real-world rectangle via the ideal rectangle. Thus, if we want to identify the ideal rectangle as the ideal rectangle, we can do so only via the ideal of the ideal rectangle.

The Easy Part Once You’ve Understood the Confusing Part
Of course, we’ve now got ourselves a reductio ad infinitum or an infinite regress: if the ideal of the ideal rectangle is needed to identify the ideal rectangle, then the ideal of the ideal of the ideal rectangle will be needed to identify the ideal of the ideal rectangle and so on to infinity. And if we’ve got an infinite regress, than the Theory of Forms doesn’t explain much at all.

The Third Man Argument in But Three of its Forms

Substitue man for rectangle in the explanation above and you have Aristotle’s Third Man argument (the first man is the real-world man, the second the ideal man, the third the ideal of the ideal man). Substitute large for rectangle in the explanation above and you have Plato’s own refutation of his Theory of Forms. (Large, though, is a confusing example because it’s so difficult to imagine an ideal of something that is a relative quality. Cold is the absence of heat, so small can be considered the absence of large, nevertheless it’s still difficult to conceive of the ideal of large). Leave rectangle as rectangle in the example above and you have my own somewhat simplified version of the Third Man argument.

7 thoughts on “Refuting Oneself Elegantly: Plato’s Third Man Argument

  1. I have been looking for an explanation for the 3rd man argument for ages, and I think I might finally understand it! Cheers.

  2. Good post.

    I just wanted to point out that this also explodes Plato’s moral theories. Although (to my deep irritation) most popular and classroom treatments of Plato’s moral theories ignores his metaphysical views, it is clear that in the Dialogues Plato considers his ethical and metaethical views to be dependent upon and derived from his metaphysical views. Without ‘the form of the Good’, Plato’s morality is nothing more than a shell game in which all cups are empty.

  3. Yep, I think you’re strictly right, Anatola, but if we save Plato from himself, we can interpret his ethics without reference to the Forms.

    For instance, if we interpret Plato as saying that we all have a moral sense, an inner knowledge of what is good and what is not, and philosophers have a better ability to articulate and grasp that moral core in every one of us, then there is no mention of the Forms and Plato’s ethics seems defensible (whether or not it’s right or not is another question).

    Now I believe that’s the essence of what Plato argued and the Forms are not necessarily that important in his ethics. In fact, I would argue that Plato created his metaphysical views to add support to his ethical views, not the other way around.

  4. Isn’t the ideal rectangle “that which can not be any more rectangular” ? I mean – you can’t have a more ideal rectangle than an ideal rectangle. I thought the whole point of a Form was that you couldn’t have anything more perfect. Do Form’s need their own Forms? The Third Man Argument always confused me… :)

  5. An alternative way of stating Plato’s criticism of his own theory is by trying to answer questions about the relationship between forms and presumed instances of them. What is for a triangle to be an intance of an ideal triange the form of triangle In Plato’s terms – what is for triagnle to particapate in the form of triangles ? Is there a form for that participation relationship? If so then then that relatonship must be intance of itself and there must be another or third f0rm for the particapation relation and so on ad infinitum.

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