Plato and Decision Trees (The Sophist)
I was reading Plato’s dialogue “The Sophist”
recently, and realized that Socrates was using something very much akin to
Decision Trees in his analysis of the concept of a sophist. I suppose that you could also call what Plato
used in The Sophist a flow chart, which is a sort of decision tree. At any rate, it is an interesting example of
how apparently new ideas (data science Decision Trees or Random Forests) often have
ancient (or at least old) roots. By the
way, I am claiming no particular expertise in Plato’s works or philosophy in
general – I just find his ideas to be interesting and his writing style to be surprisingly
approachable. If you haven't read him, you should give it a try. You'll probably be surprised.
No doubt the idea of categorizing concepts
via binary decision points is a longstanding one, but I would imagine this is
the first detailed explanation of the devise ever put down in writing. It is no surprise that Plato (through someone
he calls “the Eleatic Stranger”, rather than Socrates, his usual speaker) was
the first to propound it at length, given his emphasis on the roots of
knowledge and understanding.
There is a lot more to The Sophist than
this decision tree idea; he gets into ideas such as being versus non-being, idealism
vs materialism, rest vs motion, and the various paradoxes (real or apparent)
than can be found in these notions. But I was most interested in the comparison
of his methods with current data science techniques, so I will stick to that in
this blog.
Plato is interested in “catching” the
Sophist, a species of intellectual that he distrusts and whom he feels gives
true philosophy a bad name. To this end,
he uses this decision trees form of analysis to attempt to net the Sophist, and
discover his true nature.
First, however, he has his speaker lead us
on a journey to catch a simpler example of humanity, namely the angler (i.e.
fisherman). The path to catch the angler
goes something like this (slightly abbreviated from the original):
1 - Does the person have an Art?
Yes, he has an Art (so he could be an
angler) --------- > No (not an angler)
2 - An Acquisitive or Creative Art?
Yes, Acquisitive (so he could be an
angler) --------- > No (not an angler)
3 - Acquisition by Conquest or Exchange?
Yes, Conquest (so he could be an angler) ---------
> No (not an angler)
4 - Conquest by Hunting or Fighting?
Yes, Hunting (so he could be an angler) ---------
> No (not an angler)
5 - Hunts Living or Non-living?
Yes, Living (so he could be an angler) ---------
> No (not an angler)
6 - Water Animal or Land Animal?
Yes, Water (so he could be an angler) ---------
> No (not an angler)
7 - Fish or Fowl?
Yes, Fish (so he could be an angler) ---------
> No (not an angler)
8 - Catches by Blow or Enclosure?
Yes, by Blow (so he could be an angler) ---------
> No (not an angler)
9 - Uses Hook or Spear?
Yes, Hook, (so he is an angler) ---------
> No (not an angler)
So, via this series of divisions, Plato has categorized
the essence of his angler in about nine moves.
He then uses this approach on the much trickier Sophist, having the
series of divisions diverge at point 7.
1 - Does the person have an Art?
Yes, he has an Art (so he could be a Sophist)
--------- > No (not a Sophist)
2 - An Acquisitive or Creative Art?
Yes, Acquisitive (so he could be a Sophist)
--------- > No (not a Sophist)
3 - Acquisition by Conquest or Exchange?
Yes, Conquest (so he could be a Sophist) ---------
> No (not a Sophist)
4 - Conquest by Hunting or Fighting?
Yes, Hunting (so he could be a Sophist) ---------
> No (not a Sophist)
5 - Hunts Living or Non-living?
Yes, Living (so he could be a Sophist) ---------
> No (not a Sophist)
6 - Water Animal or Land Animal?
Yes, Land (so he could be a Sophist) ---------
> No (not a Sophist)
7 – Catches Prey by Persuasion or Violence?
Yes, Persuasion (so he could be a Sophist)
--------- > No (not a Sophist)
8 – Public or Private Persuasion ?
Yes, Public so he (could be a Sophist) ---------
> No (not a Sophist)
9 – Professes to Teach Virtue or Merely
Flatters?
Yes, Professes to Teach Virtue, (so he is
a Sophist) --------- > No (not a Sophist)
Plato then uses this method of divisions a
few more times to uncover other aspects of his opponent, the Sophist.
Of course, Plato’s version of a decision tree
makes use of what we might call pre-existing theory about the Sophist to pin
him down, rather than letting the data lead to the categorization. But we can imagine having a large dataset of
responses to such questions representing independent variables, along with
tagged data representing dependent variables (e.g. Sophist vs non-Sophist)
leading us down a decision tree, to useful ways to categorize and define the
Sophist (or other species of humanity), leading to results rather similar to what we see here in Plato.
At any rate, Plato seems to be using a
similar “rule of divisions” that some modern data science techniques use, to
categorize data and understand the world.
However, Plato doesn’t necessarily see the technique as foolproof. As Benjamin Jowett says, in comments on the
Dialogue:
“The question has been asked, whether the
method of 'abscissio infinti,' by which the Sophist is taken, is a real and
valuable logical process. Modern science feels that this, like other processes
of formal logic, presents a very inadequate conception of the actual complex
procedure of the mind by which scientific truth is detected and verified. Plato
himself seems to be aware that mere division is an unsafe and uncertain weapon,
first, in the Statesman, when he says that we should divide in the middle, for
in that way we are more likely to attain species; secondly, in the parallel
precept of the Philebus, that we should not pass from the most general notions
to infinity, but include all the intervening middle principles, until, as he
also says in the Statesman, we arrive at the infima species; thirdly, in the
Phaedrus, when he says that the dialectician will carve the limbs of truth
without mangling them; and once more in the Statesman, if we cannot bisect
species, we must carve them as well as we can. No better image of nature or
truth, as an organic whole, can be conceived than this. So far is Plato from
supposing that mere division and subdivision of general notions will guide men
into all truth.”
Sophist. Plato: The Complete Works (31
Books) . Titan Read Classics. Kindle Edition.
-----------------------------------------------------------------------------------------------------------------
Now that you have read some data science
and philosophy, you should relax and think about taking a real road trip
instead of a mental road trip down a decision tree.
A Drive Across Newfoundland?
Germany: https://www.amazon.de/dp/B07NMR9WM8
Australia:
https://www.amazon.com.au/dp/B07NMR9WM8
Newfoundland, Canada’s most easterly
province, is a region that is both fascinating in its unique culture and
amazing in its vistas of stark beauty. The weather is often wild, with coastal
regions known for steep cliffs and crashing waves (though tranquil beaches
exist too). The inland areas are primarily Precambrian shield, dominated by
forests, rivers, rock formations, and abundant wildlife. The province also
features some of the Earth’s most remarkable geology, notably The Tablelands,
where the mantle rocks of the Earth’s interior have been exposed at the
surface, permitting one to explore an almost alien landscape, an opportunity
available on only a few scattered regions of the planet.
The city of St. John’s is one of Canada’s
most unique urban areas, with a population that maintains many old traditions
and cultural aspects of the British Isles. That’s true of the rest of the
province, as well, where the people are friendly and inclined to chat amiably
with visitors. Plus, they talk with amusing accents and party hard, so what’s
not to like?
This account focusses on a two-week road trip in October 2007, from St. John’s in the southeast, to L’Anse aux Meadows in the far northwest, the only known Viking settlement in North America. It also features a day hike visit to The Tablelands, a remarkable and majestic geological feature. Even those who don’t normally consider themselves very interested in geology will find themselves awe-struck by these other-worldly landscapes.
This account focusses on a two-week road trip in October 2007, from St. John’s in the southeast, to L’Anse aux Meadows in the far northwest, the only known Viking settlement in North America. It also features a day hike visit to The Tablelands, a remarkable and majestic geological feature. Even those who don’t normally consider themselves very interested in geology will find themselves awe-struck by these other-worldly landscapes.
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