Wholes Can Lack Properties That Their Parts Have
I argue that parts can have properties that the wholes which they form with other parts lack.
For example, a semicircle is half of a circle, but the semicircle has two corners/edges/vertices and has a straight side as well as a curved side, whereas the circle has no corners/edges/vertices and has just one curved “side” enclosing it.
So the semicircle has at least two properties — having corners/edges/vertices and having a straight side — which the circle it forms along with another semicircle lacks.
So this is clearly a case of a part having properties that the whole does not have.
So the whole is not necessarily greater, in every way, than the part.
For example, a semicircle is half of a circle, but the semicircle has two corners/edges/vertices and has a straight side as well as a curved side, whereas the circle has no corners/edges/vertices and has just one curved “side” enclosing it.
So the semicircle has at least two properties — having corners/edges/vertices and having a straight side — which the circle it forms along with another semicircle lacks.
So this is clearly a case of a part having properties that the whole does not have.
So the whole is not necessarily greater, in every way, than the part.
Comments (41)
Then the "parts" aren't part of the whole, but something else entirely.
Quoting Troodon Roar
A semi-circle is not part of a circle. It is a different shape entirely.
It seems pretty clear to me that a semicircle is, indeed, part of a circle. However, I do definitely agree with you that it is a different shape entirely. It is both a part of a circle, as well as a different shape entirely from it. In fact, that is my point. My point is that parts can be completely different entities from wholes, which have their own distinctive features that the wholes which they are parts of lack.
If you still aren’t convinced that a semicircle is part of a circle, just go out and find two semicircular objects, put them together, and you will find that they make a circle.
It is a completely different shape from a circle, but it is also a part — half, to be exact — of a circle. Hence its name, “semicircle”, which literally means “half-circle”.
A semicircle isn’t necessarily always part of a circle. It can exist on its own without being a part of a circle.
In the same way, an atom isn’t necessarily always part of a chair. It can exist on its own without being a part of a chair.
What I mean by “part” is something that, if it is combined with some other thing, forms some whole alongside that other thing it is combined with.
Perhaps I should say that a semicircle is potentially part of a circle, and an atom is potentially part of a chair.
And any time you have a circle, you can always split it in half to get a semicircle. Just as how, any time you have a chair, you can always split it into its gazillions (I don’t know the exact number, but I know it must be enormous) of atoms.
That’s what I mean by “part”.
So the only way to make a circle is by putting two semi-circles together?
If I can make a circle without using two semi-circles as parts, then doesnt that mean that semicircles arent necessarily parts of a circle?
In the same way, you could arguably create a shark without putting together organs, but only by putting together atoms.
But organs are still parts of a shark.
Likewise, you can create a circle by putting together, say, four one-fourths of a circle, whatever that shape is called, or one hundred one-one hundredths of a circle, whatever that shape is called, or any number of any other shape that can be part of a circle, ad infinitum.
You can construct a circle in infinite other ways than by putting two semicircles together, yes, but any way is still going to implicitly include semicircles. You can just choose not to focus on them. In the same way, you can construct a shark by putting a gazillion atoms together, without recognizing the existence of the intermediate structures (cells, tissues, organs, organ systems, etc.) of the shark, but that doesn’t mean that the shark doesn’t have organs.
Basically, what I’m trying to say here is that, if we’re going to say that a semicircle is not part of a circle because we can construct a circle in other ways than by putting two semicircles together, then, to be logically consistent, we ought to also say that a liver is not part of a shark because we can construct a shark in other ways than by putting a liver and the other organs together. But since we all clearly recognize that the liver is still part of the shark despite that, we should also recognize, to be logically consistent, that the semicircle is still part of the circle despite that.
Organs are distinct and separate parts of a body. On the other hand, semi-circles are not necessarily distinct and separate parts of a circle. This is because a circle exists primarily as a concept. In reality we have objects which approximate to spheres or rounded portions. There are no shapes existing as distinct and separate objects in nature, they can only be derived as conceptual properties of objects in nature.
absolutely. When you add more variables to an equation you can drastically change the original shape that the equation formed. This is something every one should be required to learn in high school. Thanks for posting this.
That sounds very interesting. Could you please elaborate on this further? Thank you.
If A is not identical to B then there is a property that A has and B doesn't, and conversely, there is a property that B has and A doesn't. So if a part is not identical with a whole, then it trivially follows that the part has something that the whole lacks.
In your example the straight side of a semicircle is the diameter of the whole circle and the corners are simply points where the diameter meets the circumference.
What would be interesting is if the whole has properties that can't be explained in terms of the properties of the parts or if the part somehow included the whole. I suggest you look at fractals where the parts and the whole are quite literally identical.
I find this an interesting idea applied to communities or society.
Why if I may ask?
It’s the idea that the community is the collective, (the whole), of the people (the parts).
If the parts have properties/qualities different from the whole then it’s in conflict with the whole, and vice versa. Then the community is not representative of the people, as it’s purported to be.
y = mx + b
equation for a line (sometimes a curved line)
this isn't the best example but this is something i pulled off of the top of my head.
if you change anyone of the variables above 10 = mx + b and 20 = mx+b
or y = m(21) + b or y = m(22) + b
The line will drastically change. If your line is a line from a quadratic equation this is true even more so
Believe it or not you can draw a 3 dimensional object by using nothing more than equations for lines.
You can actually do this for higher and lower dimensions too.
Anyway changing one variable or coefficient in a line will often drastically change the line.
On a different not i would argue alot of problems in the world can be illustrated and solved using 1 dimensional, 2 dimensional and higher dimensional graphs. The problem you run into is some problems have to be solved quickly and without to much analyzing at that particular moment.
www.math.com
:ok:
Yeah, I don't see how this is arguable, really. You could just point to the fact that cells divide to become two cells with all of the features that one had, but humans do not similarly divide.
Yeah, two anythings are not identical. I'm a nominalist.
You're not denying cell division are you?
The act of identifying a whole is the act of discarding some of the properties of the parts. Unless it's a fractal.
I think so also. A ball is not a bowl. I cannot scoop water with it. Ions are volitile in ways that they are not when in combination, in molecules. The molecules, often, lack this volatility and ability to combine. Many many atoms have properties that are no longer present when in combination with other atoms. A head can roll well, but connected to a body not so well. I would think that there are fairly slight inclines where a head will roll continuously and endlessly but a body will sooner or later stop its motion with a clump of limbs or coming lenghtwise.
Isn't that going in the other direction, wholes having qualities parts do not?
This is exactly why logicians came up with the fallacy of division and the fallacy of composition. Just fyi.
If you are using the term weight strictly, in space we can be weightless.
There is something called nuclear mass defect, where the whole is not equal to parts, the total mass of the parts is greater than mass of the whole after fission.
But that is because the binding energy is converted to mass, if l am not wrong.
You could just frame it as "lightness" instead, or having the property of "weighing 3-4 kg" or whatever the case may be.
(Just noticed that PossibleAaran pointed out the same thing above.)
Quantity is not a property of things, but things are a property of quantity. If there is no thing to quantify then there is no quantity. "Nothing" is no thing, so no quantity.
It doesn't matter if it's lightness or heaviness or weight or mass or whatever because each is a property which both brick and wall possess to a greater or lesser degree.
In the original post we used our magic scissors to part a semicircle from a whole circle, and later we used our magic sledgehammer to part a brick from a whole wall.
What is the whole, and what is the weight of this whole, from which we parted our weightless photon?
Huh? It's definitely a property of a brick that it weighs 3kg on Earth, say (because of its mass).
Huh? It's definitely a property of Earth that it weighs 3kg on a brick, say (because of its mass). And it's definitely a property of the Moon that it weighs 0.5kg on a brick, say (because of it's mass). The property of the brick is mass, the property of the Earth is mass, and the property of the Moon is mass. Weight is a property of our apparatus.
What we quantify is neither brick nor wall nor Earth nor Moon. What we quantify is apparatus.
"X weighs W" is a way of saying something about X's mass. You're trying to claim that it's not a property of X.