Aspasius and Aristotle on Virtue as a Mean
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- Опубліковано 12 лип 2023
- Aspasius wrote the earliest surviving commentary on Aristotle, starting a tradition that would last for a millennium. He raises a number of interesting issues, including this one: Is the mean that defines virtue a point or a region? How hard is it to be virtuous?@PhiloofAlexandria
Thank you for another informative video.
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Welcome!!
Just playing with the Archer analogy:
If it is possible, albeit difficult, to hit the center without proper technique or training...
Is it possible to act according to the perfect virtue by mere luck?
Interesting. I've done a lot of thinking about Aristotle's Virtue as a Mean. I've never thought of it from Aspasius' point of view though. I really like Aspasius' argument. I think essentially they can be viewed in a similar fashion or unified in some way and they are not all together all that different.
In other words I'd like to illustrate how the meaning of a point to Aristotle and the meaning of a region to Aspasius are basically the same thing.
Imagine first Aristotle's view that the mean of a single virtue is a single point if the mean was on a number line then mathematically we'll imagine this number line as the integers (e.g. ...-5,-4,-3,-2,-1,0,1,2,3,4,5...). Now we will do this to illustrate a difference between the view point of Aristotle's and Aspasius' viewpoint.
The mean for example here can just be assumed to be an arbitrary number/point on the line lets say 0 (arbitrary meaning the choice doesn't matter the logic still follows with any other choice). Well since we are working with integers there is no concept of something like 0.25 or 0.6, so essentially these are in someway disregarded in Aristotle's view of the mean. Therefore to him there is only one point, in our case 0, which hits the mark of virtue and there are infinite such points that don't hit virtue. Also, it means that there is one singular correct answer. Now what I believe what Aristotle meant by the virtue being a point was not that it was impossible to hit, but that it was very hard without recognizing your target. In other words to hit the target of virtue it is a sufficient condition (though not technically absolutely necessary) to know where the target is.
Though it isn't absolutely necessary to hit the target without knowing where it lies on the line. Since the line is infinite it is probability 0 of actually hitting the virtue from an infinite set of choices without somehow atleast narrowing down to a subset of the line (i.e. once you pick a set of integers that are possible you no longer have an infinite set to pick a single number from).
Now let's consider why Aspasius' was confused by Aristotle. I believe he viewed Aristotle's view of the mean more as if the virtue exists on the real number line (a.k.a the virtue was some number say 0, 0.0000001, 0.1, 0.2, 3.14159,etc.). Well again lets go with the possibility of a point being one number on the reals and one number only. The problem with this is it would be a probability of 0 to get any one specific point/number not just on the whole number line but on any given region of the number line, so it would be practically impossible even while narrowing down the region (for evidence of this see 3blue1browns great video on what probability of 0 means ua-cam.com/video/ZA4JkHKZM50/v-deo.htmlsi=EtDhMZAczMNZhFUp). Now this is a different sort of improbability than Aristotle was talking about. When Aristotle spoke of the virtue he spoke as if it was attainable by some greater degree, and as I showed above in the last paragraph if we could somehow narrow down and know where the virtue might lie and where it doesn't it would become more attainable. Well from Aspasius' point of view from the virtue being on the set of real numbers (a.k.a virtue being on the real number line) then the virtue wouldn't even be obtainable thus seemingly contradicting Aristotle's view on the matter, but there is a way to rectify this.
So, how does one rectify Aristotle's virtue as a mean as an integer on a number line from Aspasius' view of virtue as a real on the number line; well, Aspasius' view can be unified into Aristotle's view by introducing regions (much like Aspasius' invisioned and much like the 3blue1brown video covers in probabilities) which will actually make it much like Aristotle's view. If suddenly instead of picking a single number as the virtue on the reals you picked instead a region as the virtue for example let's say that the region is roughly (-0.5, 0.5) (a.k.a -0.5 to 0.5, exclusive) as the virtue (the region is arbitrarily picked again, but this time to coincide with the original). Now with this arbitrarily picked region we can make a (bijective) mapping from Aspasius' view to Aristotle's which means we turn the virtue in Aspasius' view to the virtue in Aristotle's view (and vice versa) and also turn the "regioned" reals in Aspasius' view to the integers in Aristotle's view (and vice versa). In this case all we need to do to get to Aspasius' view to Aristotle's is apply a rounding function from the reals to make it into the integers. To get from the integers to the reals for each integer x we create a region from the number line on the integers to the number line on the integers namely (x - 0.5, x + 0.5). The thing to note here is the decision for the region was arbitrary and could work for practically any given region (though it would need a a different bijective mapping.)
Now to summarize I hope you basically in some way saw that the meaning of a point to Aristotle and the meaning of a region to Aspasius is basically the same thing.
Perfect is the enemy of the good😉
As with everything coherency misses the mark. Is there a theory of action? Is there a perfect act? It seems ridiculous to speak of a perfect act.
Virtue defined as "a mean between extremes" falls short of sense. While it may be "a" coherent description it lacks moral and physical and spiritual explanation - it cannot justify sacrifice.
Virtue without sacrifice is talk. Talk is cheap.
Should you beat your child to prevent them from going into the street or not? In each case what are you sacrificing and what is the child sacrificing? Who is sacrificing more? Every contract requires agreement. How can a child "agree" to anything?
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