I argue that parts can have properties that the wholes which they form with other parts lack. — Troodon Roar

Then the "parts" aren't part of the whole, but something else entirely.

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. — 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”.

Interesting. Its name notwithstanding, a semicircle is evidently not a part of a circle. But this is by no means clear. What's needed, then, is a definition of "part" that will make the thing clear. You guys?

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”.

In any case, the point I insist upon is that the relationship which a semicircle bears to a circle, whether we call it “being a part” or not, is the same relationship that an atom bears to a chair, or a cell bears to a living multicellular organism.

Imho, fair enough and well done! I think you're on to something, but I haven't yet got a decent grip on it.

Implied seems to be that "greater than" means the whole contains all the properties of the parts and more besides in virtue of both being more and a whole. Hmmm. Question: this could all hinge on definitions - but behind, or under, is there a substance lurking for us to dig out and examine?

Arguably a part, to be a part, is a part of the whole of which it is a part. By that understanding, a semi-circle by itself, with the properties that make it a semi-circle, just is not, in respect of those properties, a part; rather it is a whole.

On the other hand, a semi-circle as a part of a circle does not have those distinctive parts. Perhaps then, a circle as a whole can be decomposed into other wholes, with different properties, but that in respect of those different properties, are no longer parts.

But, is this a language game? Is it just a matter of a precision in thinking and usage most of us don't usually access? Or is there something more?

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. — Troodon Roar

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.

You've posted the exact same argument before. You didn't get much of a discussion, because the idea is trivial and there is not much to discuss.

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.

Yes, the parts have different properties than the whole but the properties of the whole are formed by the properties of the parts.

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.

So this is clearly a case of a part having properties that the whole does not have. — Troodon Roar

I find this an interesting idea applied to communities or society.

I find this an interesting idea applied to communities or society — Brett

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

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. — Brett

:ok:

Alright OP, but why make it a universal?

You've posted the exact same argument before. You didn't get much of a discussion, because the idea is trivial and there is not much to discuss. — SophistiCat

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.

Two cells are not identical to one cell. So you can run the same argument in that case as well: one cell has a property that two cells lack: its numeric count, for one, or the property of occupying a continuous volume of space (also its total weight, volume, surface area, etc.)

Two cells are not identical to one cell. — SophistiCat

Yeah, two anythings are not identical. I'm a nominalist.

You're not denying cell division are you?

Humanity is neither male nor female, though it's parts have those properties. Something is lost in wholeness.

The act of identifying a whole is the act of discarding some of the properties of the parts. Unless it's a fractal.

Your reasoning seems backwards. The semicircle is as much a whole as is the circle, but consists of more parts. The circle consists of two parts; a line, and an equidistant point. The semicircle contains these same parts, and adds two end points which the circle lacks. Similarly, the circle is an essential part of any radius or diameter since without it they're just lines. I think your assertion that the semicircle is a part of the circle is false, and that the whole approach is weird.

Set { {A} ,{B} } has cardinality 2. {A} and {B} are parts of it. Each have cardinality 1, so they don't have cardinality 2. Wholes can have properties the parts lack, parts can have properties the wholes lack.

I argue that parts can have properties that the wholes which they form with other parts lack. — Troodon Roar

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.

There are some more obvious examples than the circle. One due to Bertrand Russel: a brick wall might be very heavy, although none of the bricks on their own are heavy.

There are some more obvious examples than the circle. One due to Bertrand Russel: a brick wall might be very heavy, although none of the bricks on their own are heavy. — PossibleAaran

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.

Protons and electrons have a charge when separate. Together the charges cancel.