Modern Chimera

One of any chimera’s favorite quotations, (you can probably guess why) is “The whole is greater than the sum of its parts.” This phrase is usually attributed to Aristotle. A quick post today to delve into the saying more deeply…

The phrase is fundamental to Gestalt psychology and often said to have originated with famous Gestalt psychologist Kurt Koffka[1]—albeit as, “the whole is other than the sum of its parts.” It turns out that the quote attributed to Koffka is actually closer to the original Aristotelean:

In the case of all things which have several parts and in which the totality is not, as it were, a mere heap, but the whole is something besides the parts, there is a cause.^[2]

An alternative translation I found only emphasizes the point:

“In all things which have a plurality of parts, and which are not a total aggregate but a whole of some sort distinct from the parts, there is some cause.”[3]

In the second translation we have parts that are “distinct” from the whole rather than “besides” it. By the way, it is unlikely someone erroneously mistranslated Aristotle as saying greater. For example: The word greater would not be hard to spot if it had been there. In ancient Greek it’s meǵhlos. It the word we get our “mega” from. It’s megalýteri in modern Greek. Both authoritative translations get away from the ‘sum’ so common in the quoted phrase, which is good, because ‘sum’ evokes maths and Euclid.

Indeed, “…the sum of” is is found in Euclid’s famous Elements, published around 300BC as one of his four “Common Notions” (CNs):

1. Things which equal the same thing also equal one another.
2. If equals are added to equals, then the wholes are equal.
3. If equals are subtracted from equals, then the remainders are equal.
4. Things which coincide with one another equal one another.
5. The whole is greater than the part[4].

CN #5, “the whole is greater than the part,” could be interpreted as a definition of ‘greater than’: “To say one magnitude B is a part of another A could be taken as saying that A is the sum of B and C for some third magnitude C, the remainder.”[5] It can be presumed that Aristotle’s concern with these words was not the same as Euclid’s.

Apparently the CNs weren’t included in the original publication. Furthermore, it is stated that “Christopher Clavius (1538–1612) added the axiom that the whole is the equal to the sum of its parts.” This axiom does not conflict with the idea that the parts are other than the whole. However, in Book VI of Aristotle’s Topics, the author says in chapter 13:  

“… that the whole is not the same as the sum of its parts are useful in meeting the type just described; for a man who defines in this way seems to assert that the parts are the same as the whole. The arguments are particularly appropriate in cases where the process of putting the parts together is obvious, as in a house and other things of that sort: for there, clearly, you may have the parts and yet not have the whole, so that parts and whole cannot be the same.”[6]

To sum up (ouch!), we have to conclude that Aristotle did not say the whole is greater than the sum of its parts. Greater and sum of are particularly problematic when one considers the actual translation we have just uncovered: “The whole is something besides the parts.”

Laters!
–MC.

References

[1] https://www.psywww.com/intropsych/ch04-senses/gestalt-psychology.html

[2] https://se-scholar.com/se-blog/2017/6/23/who-said-the-whole-is-greater-than-the-sum-of-the-parts

[3] Aristotle. Aristotle in 23 Volumes, Vols.17, 18, translated by Hugh Tredennick. Cambridge, MA, Harvard University Press; London, William Heinemann Ltd. 1933, 1989. Retrieved September 22, 2021 from http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0052%3Abook%3D8%3Asection%3D1045a

[4] https://mathcs.clarku.edu/~djoyce/elements/bookI/cn.html

[5] Ibid.

[6] Aristotle 100a, Topics, Translated by W. D. Ross Retrieved on September 22, 2021 from https://se-scholar.com/se-blog/2017/6/23/who-said-the-whole-is-greater-than-the-sum-of-the-parts