protophilosophers are the founders of philosophy, few of them learnt from any other protophilosophers and none of them learnt from philsoophers, they are the presocratics, Thales, Anaximenes, Anaximander, Anaxagoras, etc
polethics is a colexification I propose, one of politics and ethics taken as a single subject.

a heap isn't defined only by the geometric amount of grains, but by the artihmetic amount to, in simpler words, it isn't defined only by how many grains there are but by how they are placed in relation to each other. if you have a fine layer 1 grain thick of 10000000 grains you don't have a heap, you have a film of grains, if you have 3 grains arranged in a pyramid you have yoruself a heap.

Yes you can

I believe your understanding of soveriagnty isn't what was Rousseau's or that of other believers in the social contract, but concentrating on that is derailing the topic, which is Anaximenes and Thales and their worth as philosophers, I guess your point is that their worth is merely historical.

Muchas gracias, un gran saludo para ti también.

I am Peruvian, thanks for the links.

at the other philosophy forum I was told that I could finish my studies in that kind of university, but I was simultaneously insulted in being told that I am a basement dweller, but you are making me wonder if that university accepts students who aren't from Spain,

i guess we've reached an impasse.

oh great, since it was a university that taught from afar I was afraid they weren't reliable, I mean, had the video credited Salamanca university as its source and the source of its professors i would have immediately sadi, this is gold, but I am biased against universities that do not have "clases presenciales". Thanks again for your answer.

when I think about it more the smallest heap is 3, but only if arranged with 1 grain sitting atop two other grains (one part of it resting on one grain and another part resting on another grain).

a single grain is 1, a completely bald man is by definition someone with 0 hairs, not 1. so... he is hairless, hairy on the other hand is 66.66666666%+1

oh, by the way, i found this video, https://www.youtube.com/watch?v=D6S9ppPTJUw I read elsewhere you are a Spaniard, does that university has any good reputation or i must be careful of that video?

if that looks like a heap to you, it is 1, for you.

I will struggle against insomnia for a while but I am doing so in order to see what develops from my question on how to make protophilosophers appealing to young kids... But my point is that freedom of thought, ethics and politics, well, polethics, they are something philosophy has conquered, not science, science is great, but so is philosophy.

science wouldn't be where it is if Rousseau hadn't inspired the French revolution, if Giordano Bruno, Voltaire or the skeptics hadn't existed we would still be venerating some wicked concept of the divine without regards to science. i could go on but my insomnia is wearing off.

Varies from individual to individual. Its subjective, unlike other matters.

I guess the critical point is one of proportion and perspective and that is why the brain is such a relevant issue to this seemingly emergentist solution... To a man-sized being a heap has more than a "few" grains arranged one upon another, to a giant that's invisible and you need more grains or larger grains, to a bug you need finer grains... and so forth.

That sounds Nietzschean, while not a fan of Nietzsche I see your point, yeah, I think i can work with that, I will still appreciate other contribution if anyone wants to give it, but i can work with the Nitzchean premise for both Thales and Anaximenes. Thanks.

oh, and thanks for your answer.

I am not really a teacher, i never graduated from philosophy but I really love it and believe everyone should be a philosopher-sovereign, with sovereignty understood as participation in one's civic duties to control one's country as part of the aggregate of citizens of said country. I would use your approach in a classroom but I am a writer and trying to teach through a trade picutre book or similar outlet, basically, through picture books or through comics. I can teach that for Thales the arge was water and for Anaximenes it was air... but... Why where those two so important if both got it all so wrong? What wre the benefits of their mistakes? I am trying to find a good reason for children to respect those two philosophers. I respect the presocratics more than i respect Socrates, but a quick glance and it seems that neither Thales nor Anaximenes contributed something of value to philosophy, as i am seeing it, they both delayed the advancement of philosophy, but I feel i am wrong. If anyone is willing to prove me wrong with good arguments I would appreciate it.

Sorry for butting in without reading the many answers it has already revised but, what you are saying isn't just a variant of emergentism? I mean the critical point determines when a heap/pile becomes such.