ProtagorasNotes

Plato's Protagoras

Someone asks Socrates how it's going with Alcibiades, and Socrates says he's preoccupied with other things and launches into a recounting of how he came to talk with Protagoras.
In telling that story, he starts with how the young Hippocrates came to him all excited about Protagoras.

Socrates tells Hippocrates (313aff.) that you have to be careful with the sophists: if you go to one, you absorb what they are teaching without examining it (cf. Callard's untimely questions?): that seems in many ways wrong to me (surely you can think about and reject what someone teaches you?)

in Athens, when it comes to public policies and laws, etc., everyone can speak in the assembly: it's not run by a few experts, but by everyone. So everyone is considered to have expertise.

compare this to Socrates' elenchus: it is often performed on 'experts,' but sometimes not (Theaetetus is an example that comes to mind)

does Socrates' us of the elenchus assume that just anyone might figure out what virtue is?
or is Theaetetus an anomaly? is what he says in the Apology, that he approaches those who think they know things, more accurate?

note, however, that Pericles is used as an example: Socrates was not necessarily an admirer of Pericles, so this example seems ad hominem (directed at Protagoras in particular)
or perhaps it is directed at what most Athenians believe, and Protagoras is just defending that

so when someone teaches virtue, they are not offering some expertise that is particular to them, but rather offering something available to all, like when I teach English to someone

Socrates says yes
Protagoras claims that courage is a virtue and is not knowledge or wisdom 348bff

is virtue an end in itself or pursued for its consequences (pleasure being the key suggestion here)
is it possible to knowingly do wrong

acrasia/akrasia is the name for knowing what is right but not doing it, or doing wrong knowingly
discussed 346a briefly and 351bff.

we weigh pleasures (good) against pain (bad) and choose options that maximize pleasure and minimize pain
to weigh one thing against another, they have to share one single quality (weight) that is quantifiable in the same way for every occurrence of it: they must be commensurable

Important note 1: time may matter: Socrates simplifies by suggesting future pains have the same value as present ones, etc. Surely we apply some sort of discount. But whatever that discount is, it still requires commensurability.
Important note 2: whether or not Plato is right that pleasures and pains are all commensurable, and whether or not Plato is right that pleasure in and of itself is good and pain is in and of itself bad, and whether or not Plato is right that there is no other good or bad than pleasure and pain, and thus whether or not Plato is right that calculations about pleasure and pain are the way we ought to set our priorities in life, it is nonetheless true that we need some single criterion by which to decide whether to do this or that, no matter what this and that are.
To understand why, consider that whenever we decide between two things, one of two things must be true: we either weigh up the "pros and cons" and find that this outweighs that, or we have no good reason for choosing this over that. In order to compare this to that, this has to be like that in a relevant way: otherwise, we are simply comparing apples to oranges, and they are not comparable.
Sometimes we simply have to decide between this and that, even when there is no preponderance of "pros and cons" for this rather than that. Thus, we make a "decision" that is not based on good reasoning about the pros and cons.

We face a "forced decision": it is more important to decide than it is to decide based on a sufficient reason. That was the case for Buridan's famous ass, who was caught between two bales of hay and supposedly starved to death for lack of a sufficient reason to choose this one over that one: for the ass, it was clearly more important to eat than to have a sufficient reason to choose which bale to eat.
The counterargument to that objection is that when we face a "forced choice," there must still be some antecedent decision that involves "pros and cons." The ass has to decide based on the pros and cons that eating beats all other possible activities.

connected to acrasia because of claim that acrasia can happen when pleasure outweighs wisdom
acrasia is philosophically controversial even today

we can bring in cases of addiction, but I think that is clearly not what Socrates is talking about, so maybe we need to hold off on doing so until we solve it for 'ordinary' cases, such as where someone says something like "I knew that it was a bad idea to x (e.g. watch that movie), because of all sorts of good reasons, but I did it anyway because I was overcome by the temptation to indulge myself and just have a little pleasure."

my own suggestion is not found in Plato: we need to take into account uncertainty and vagueness: I do not know if I will die tonight, so there is some value to getting as much of what I value NOW as I can, and discounting future instances of what I value. But the discount rate I should apply is unclear. In such cases we should hedge our bets: we should diversify to spread the risk. So grab some of what I value NOW and postpone some of it to get more of what I value tomorrow, but don't do either to excess. The only way to have a perfect calculus is thru hindsight.

in Crito, for instance, there is no appeal to or weighing of pleasure: that was a serious case, life or death, and pleasure had no purchase anywhere in the dialogue: that means that either we cannot interpret across dialogues, or we must find a way to discount the apparent Socratic hedonism on display here

Socrates gets ready to depart at one point when Protagoras doesn't seem to want to engage one-on-one 336b

Plato's Socrates requires sincerity: 331c: he is testing people, not just detached hypotheses

they discuss the poetry of Simonides (344ff.)
347cff. Socrates says it is not good to talk about poets/authors who are not present to defend their views: cf. Socrates' claim that Homer is not there to defend his text.