OK, when I started to write this it seemed like good idea, but now it seems so trivial as to border silly, so I’m wondering if it is worth to post it. But if you are reading it, once you remove the impossible, however implausible may it be means that I decided to post it.
Let’s say an easy problem is presented to us in our daily work…
Our boss says that we need to cover a piece of land which is planted with strawberry seeds, with nylon sheets, so that they don’t freeze through the winter.
He tells us that the land is flat surface, in form of square with sides of 2 meters. He says that we have square nylon sheets with sides of 1 meter, and asks us to determine how many sheets we need to cover the surface. Alas we haven’t learn any math, and so we can’t mechanically answer. We need to think…
Here is how our thinking process might go… We imagine a flat square surface with sides of two meters, and now while keeping the surface in mind, we figure out (still in our minds) that the square can be divided in middle into two stripes adjacent to each-other. Those stripes aren’t imagined as separate things, they are parts of the original square. The comprehension of the equality between the original 2meters by 2meters square, and the two slides as parts of it is not done by appealing to some other justification (or learned rule), the equality is there in the whole (the imagined square) where we can choose to focus on the whole as one, or to focus on it as divisible to two stripes, each with the width of the square (2 meters), and length of half of the square (1m). While still holding in mind the starting square, and those two stripes, we can also figure out that each of the each 2meter by 1meter stripes, can be divided in turn in the middle (now by width), and that we will get for each stripe a two squares of 1meter by 1meter. Not leaving the starting whole for a moment, we are able to comprehend that it is divisible then to 4 squares of 1meter by 1meter.
The equality to which we came is a priori because what we figure out is just that we can look at two ways at one and the same thing. Namely that if a surface is universal U1 (square with dimensions 2meters by 2meters), it can be also looked upon as universal U2 – two stripes 2meters by 1meter, or can be looked upon as U3 – four squares of size 1meter by 1meter adjacent to each other.
Because the boss told us that the concrete land in question is that specific universal U1, we can conclude now that it will be also U3, and we can use 4 of our nylon sheets to cover it.
So, while the example might seem trivial, here is what I wanted to point to:
- We can figure out necessary relation between universals without employing a formalism of any kind, by being able to comprehend that if a imagined particular falls under one universal (or – is the first universal), it will also necessarily fall under the second (or – will be the second universal).
- Figuring out the a priori relations between universals is not done through ignoring the particularity, but particularity is base in which the two universals are seen to coincide (necessarily).
- The universals considered here are simple geometrical forms, but this can be true for much more complex universals.
- Because the relation between the universals is based on comprehension that necessarily if particular is U1, it will be also U2; it is normal that the relation will be true for any particular which fall under the universal. If the particular is the universal (as in this case the land is U1) whatever we figured out a priori will be true for the particular also (e.g. that itis U3). Or said otherwise – whatever (any particular) is U1 is also U3. So, if we figure out a priori relation between universals, that relation will hold (necessarily) for any particular in the world which are that universal.