Our At Home Schooling math program got lost on the road to arguing and veered into philosophy. Next we added our normal rigorous methodology...

There are so many different fields within philosophy. The only two that I'm familiar with are logic (known as logic) and the structure of a good argument (known as arguing). There are so many fields. Where to begin?

I settled on this question. Did mathematicians discover the circle, or did they invent it?

This is a nice baby step. A child as young as 10 should immediately appreciate the need to define 'invent' and 'discover' before answering the question. My job as the team member is to follow up each assertion with a question doubting it's validity. Of course, there is no answer, and I don't care for one. I want to see thinking.

This is also a good exercise for 'going deeper', although ironically my 10 year old went much deeper than my 13 year old. Here's the potential of this problem:

- Did Columbus discover America even though there were people living here already?
- Or did he discover it for the queen of Spain who didn't know it existed?
- Does anyone invent anything?
- Does every invention exist within an infinite permutation of words, colors and atoms, or do they just pluck it out of the realm of possibilities that already exist? (That was my contribution.)
- Does a painter create a painting or does he just make one that already exists conceptually?
- Does he invent the concept or just put together things that already exist?
- Then is an invention really new or just a combination of things that exist?
- If I tape a flashlight to a broom, did I invent something?
- What is a circle? Did they discover it by looking at the sun?
- Or is it all points equidistant from a center point, in which case it doesn't exist in nature?

I presume the second step is a framework for tackling the problem. Something like a solution strategy. We're not making progress, just asking more questions. Maybe our questions are the formulation of a strategy. We're not that far along yet as philosophers.

We need baby steps here is well, like assuming the definition of invention and discovery and then applying it to the circle. This is a solution strategy from math. Or we look for examples of invention and discovery and categorize them looking for patterns. Again, math. Or take the simplest of all examples - use a stone to break a rock, and see what comes of it, working our way up from there (stone tied to a stick). Math. The only thing you can't do strategy-wise is try out every answer from a pick list because even though I have one I won't share it. That leaves adding the missing equation, working backwards, and problem decomposition, but these solution strategies naturally emerged from analyzing the problem.

In case you're interested, I just paraphrased the Big Five solution strategies from math plus The Solution Super Strategy (aka the stone). I wonder if the mechanics of philosophy presents an additional strategy or just redefines the usual suspects from math.

We're getting no where. Switching sides, changing our minds, tossing out steps of reasoning that lead no-where, and asking a lot of questions. My counter questions are frustrating because every answer has multiple follow up questions. I think this is the point of philosophy.

My philosophy partner decided that ideas can be invented, and an invention is the application of the idea or concept to a bunch of prediscovered objects. Each person can discover something or be told about it from the discoverer. The same thing can be discovered by many people. That's why Columbus was able to discover the new world, even though there were people already living there that obviously already knew about it. If you attach a flashlight to a broom, you invented the concept (The Night Sweeper 2000), but you didn't invent or discover its parts.

Good enough for now. Your answers may vary.

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