The Fallacy of Composition and the Cosmological Arguments

[Chrawnus]

I've noticed that there is a certain fallacy that skeptics tend to bring to the table pretty frequently when discussing various cosmological arguments (especially the Kalam Cosmological Argument and the Contingency Argument), namely the Fallacy of Composition. A specific version of this fallacy (there are atleast two, but we are only interested in one version of it) is committed when it is argued (without justification), that because all parts of the whole X has some specific property (property A) it must follow that the whole X also has that property. One example of where this fallacy is committed would be if one argues that just because all individual parts of an elephant are light, it must follow that the whole elephant taken together is light. Or that just because the individual parts of an elephant are small (depending on how small chunks you divide the elephant into) it must follow that the whole elephant is small.

A type argument in favour of the premise of either the finite past of the universe, or the contingency of the universe (depending on which cosmological argument we are talking about) is that it seems that the individual parts that make up the universe seem to have a finite past/be contingent and that therefore it is proper to conclude that it's likely that the universe itself also has a finite past, or is contingent. To this the skeptic will usually respond that this is an example of the fallacy of composition and that the argument therefore fails.

The problem is, however, is that it seems like the Fallacy of Composition isn't necessarily committed just because one reasons that the whole must have a specific property X just because all individual parts of the whole has property X. For example, it would be correct to conclude that if all parts of a wall are made of stone/bricks, then the wall as a whole will be made of stone/bricks, or that if all parts of a thing is made out of matter, then the whole thing itself is made out of matter.

What I've been wondering is this (The following is the main topic of the thread): Is it possible to generalise different types of properties based on whether the property is of the type that will carry over from the parts to the whole, or is this something that must be done on a case-by-case basis? And secondly, if it is possible to generalise different types of properties on the basis of whether they will carry over from the parts to the whole, will the properties of having a finite past (or being contingent) be in the class of properties that applies to the whole as long as they apply to the parts of the whole, or will they be in the class of properties that doesn't necessarily apply to the whole, even if they would apply to all parts of the whole?

I've already got some thoughts about this matter, but I think I'll let you guys see what you think about this before I write anything more.

[GioD]

Good points, and good question. Since the Universe is definitionally the collective of all matter, energy, forces, space, and time, if a single thing in the Universe were shown to be contingent, the Universe as a whole would be contingent based on the definition of contingency.

Finitude is harder, but the fact that everything in the Universe is finite would indicate the universe itself is finite, as nothing in existence = no universe.

[Chrawnus]

Good points, and good question. Since the Universe is definitionally the collective of all matter, energy, forces, space, and time, if a single thing in the Universe were shown to be contingent, the Universe as a whole would be contingent based on the definition of contingency.

Finitude is harder, but the fact that everything in the Universe is finite would indicate the universe itself is finite, as nothing in existence = no universe.

Well, what you've written above is all good and well, but it's not really what I'm interested in discussing, or atleast it's only a secondary issue . What I'm mainly trying to find out is if it's possible to differentiate between properties that are necessarily shared between (all) parts of an object and the object as a whole (Let's call this category A) and properties that are not necessarily shared between (all) parts of an object and the object as a whole (category B).

If/after this has been resolved, one could then discuss if it's possible to determine if contingency and finitude are properties in category A or B.

If we go back to the two properties of the examples where the Fallacy of Composition undoubtedly applied, namely the size and weight of an object, it seems that what these two properties have in common is that they are both relative and measurable. Another thing of note is that it might be more proper in the context of this discussion not to speak of parts as being big, small, heavy or light as I did when I gave the examples with the elephant, but instead as having a specific size s or specific weight w.

Something that could be interesting to discuss is whether it makes any difference whether a given property X is such that object O has this property independent of any other property of O, or if the property is dependent upon another property Z of the O, so that when property Z changes, so does property X. Or to really complicate matters, one could try ask if this need even be a limited to a single object, or if a property X of object O could depend on a property Z of object P and whether this has any difference in figuring out whether the property falls in category A, or B (Which were defined in the first paragraph of this post.)

Let me know if this post is unclear in someway.

[robertb]

The fallacy, in the context I believe you are intending, usually results from an equivocation surrounding the use of the word universe, as I pointed out in the other thread.

In usual context, the universe is everything that exists. Removing an element from the set of everything that exists still leaves you with a set of everything that exists.

[robertb]

Good points, and good question. Since the Universe is definitionally the collective of all matter, energy, forces, space, and time, if a single thing in the Universe were shown to be contingent, the Universe as a whole would be contingent based on the definition of contingency.

If something within the collection of everything that exists ceases to exist, there remains a collection of everything that exists.

Therefore it is not true that the contingency of the set of everything that exists depends upon the contingency of any thing that exists.

Finitude is harder, but the fact that everything in the Universe is finite would indicate the universe itself is finite, as nothing in existence = no universe.

Same issue as above, however in this case the universe is simply an empty set.

[Chrawnus]

The fallacy, in the context I believe you are intending, usually results from an equivocation surrounding the use of the word universe, as I pointed out in the other thread.

In usual context, the universe is everything that exists. Removing an element from the set of everything that exists still leaves you with a set of everything that exists.

Well, this isn't really what I'm interested in discussing, even if it is interesting. I apologize if I seem unnecessary strict, but I want to keep this this thread as on-topic as possible.

But just to clarify. No, this isn't really the argument I'm thinking of. What I'm thinking of is the argument that every element (or all elements that we know of) in the set called the Universe is either contingent and/or finite in the past and that therefore the Universe as a whole is contingent and/or finite in the past.

The question I'm really trying to figure out is if properties like being contingent, or having a finite past, is like the properties of size and weight, where the whole won't have the same weight or size as it's individual parts, even if all the parts weigh the same, or if these properties are more like the properties of redness (colour) or chemical structure, such as if all parts of the whole are red then the set/object as a whole will be red, or if all parts of the object/set are made of wood, then the object/set as a whole will be made of wood.

Atleast intuitively it would seem to me like the properties of being contingent and having a finite past is more like the properties of being red and being made out of wood in the sense that the property is shared between all parts and the whole, in opposition to being more like the properties of size and weight, where the property (or atleast it's values) aren't the same, even if the properties (or their values) of the individual parts are all the same. But I'm not really content with just having an intuition, I'm interested in figuring out what exactly it is about properties that makes it so that some properties are shared between individual parts and the whole, and what makes it so that some properties are not shared between individual parts and the whole, even if all individual parts have that property.



I'd encourage anyone intending to post in this thread to keep what I wrote in my OP in mind:

What I've been wondering is this (The following is the main topic of the thread): Is it possible to generalise different types of properties based on whether the property is of the type that will carry over from the parts to the whole, or is this something that must be done on a case-by-case basis? And secondly, if it is possible to generalise different types of properties on the basis of whether they will carry over from the parts to the whole, will the properties of having a finite past (or being contingent) be in the class of properties that applies to the whole as long as they apply to the parts of the whole, or will they be in the class of properties that doesn't necessarily apply to the whole, even if they would apply to all parts of the whole?

If your post doesn't touch upon anything in the above paragraph then it's out of the area of this discussion.

[Chrawnus]

If something within the collection of everything that exists ceases to exist, there remains a collection of everything that exists.

Therefore it is not true that the contingency of the set of everything that exists depends upon the contingency of any thing that exists.



Same issue as above, however in this case the universe is simply an empty set.

I'd prefer it if we kept this thread on-topic, please.

[robertb]

I'd prefer it if we kept this thread on-topic, please.

Chrawnus I am a bit confused.

You say the following:

What I'm thinking of is the argument that every element (or all elements that we know of) in the set called the Universe is either contingent and/or finite in the past and that therefore the Universe as a whole is contingent and/or finite in the past.

That is exactly the question I answered. So, I'll try again and relate it to your own words as best I can.

The set of "every element" = universe

element = singular and within the set of every element which is the definition of the universe.

The question is:
Does the contingency of each and every element within the set of every element determine the contingency of the set of every element?

Is this correct so far?

If so, then as I replied earlier, it is not true that the contingency of an individual element within a set determines the contingency of the set of every element because if you remove each and every element you remain with a set of every element with no members.

[robertb]

The question I'm really trying to figure out is if properties like being contingent, or having a finite past, is like the properties of size and weight, where the whole won't have the same weight or size as it's individual parts, even if all the parts weigh the same, or if these properties are more like the properties of redness (colour) or chemical structure, such as if all parts of the whole are red then the set/object as a whole will be red, or if all parts of the object/set are made of wood, then the object/set as a whole will be made of wood.

Why do you call the terms contingent and 'having a finite past' properties in the first place? They seem more like words that imply a state.

How are you defining the word property? This may help to clear up what it is you are looking for.

Regardless, I think the real issue here is the application. Remeber, it is a category error to analogize the universe to a singular object, the universe to a wooden bench. A better analogy would be to analogize the universe to the set of all wooden benches.

[robertb]

The problem is, however, is that it seems like the Fallacy of Composition isn't necessarily committed just because one reasons that the whole must have a specific property X just because all individual parts of the whole has property X. For example, it would be correct to conclude that if all parts of a wall are made of stone/bricks, then the wall as a whole will be made of stone/bricks, or that if all parts of a thing is made out of matter, then the whole thing itself is made out of matter.

Just to see if I can help you see this better. Take this bit, from the OP.

It is true that the Fallacy of Composition isn't necessarily committed just because one reasons that the whole must have a specific property X just because all individual parts of the whole has property X. It is not true that the specific property X of all individual parts of the whole necessarily means that the whole itself has the specific property X.

The analogy given above work for some things, but do not work for others.

If all parts of a wall are made out of bricks, this says nothing about the composition of all walls.

Does this help?

[Chrawnus]

Chrawnus I am a bit confused.

You say the following:



That is exactly the question I answered. So, I'll try again and relate it to your own words as best I can.

That was not a question, that's simply the relevant argument in question. The question(s) I'm interested in are the ones in the OP, which I quoted in post #6.

The set of "every element" = universe

element = singular and within the set of every element which is the definition of the universe.

The question is:
Does the contingency of each and every element within the set of every element determine the contingency of the set of every element?

Is this correct so far?

That's the relevant argument put in the form of a question, but it's not the main topic of this thread, even if the two are closely related.

If so, then as I replied earlier, it is not true that the contingency of an individual element within a set determines the contingency of the set of every element because if you remove each and every element you remain with a set of every element with no members.

Empty sets exists only in mathematics, and not in the real world.

In the real world, an empty set is the same as a non-existent set. What you're doing above is just semantics. In the end, if you remove all elements from the universe you end up with nothing, you do not end up with an empty set called the universe.

Put another way, the universe is all it's individual parts put together, so that if you remove all parts of the universe, you remove the universe as a whole as well. This applies to virtually all objects/sets in the real world. If you remove all individual parts of an object/set, then you remove the object/set as a whole.

[robertb]

That was not a question, that's simply the relevant argument in question. The question(s) I'm interested in are the ones in the OP, which I quoted in post #6.



That's the relevant argument put in the form of a question, but it's not the main topic of this thread, even if the two are closely related.



Empty sets exists only in mathematics, and not in the real world.

In the real world, an empty set is the same as a non-existent set. What you're doing above is just semantics. In the end, if you remove all elements from the universe you end up with nothing, you do not end up with an empty set called the universe.

Put another way, the universe is all it's individual parts put together, so that if you remove all parts of the universe, you remove the universe as a whole as well. This applies to virtually all objects/sets in the real world. If you remove all individual parts of an object/set, then you remove the object/set as a whole.

You remain mired in the fallacy.

In the real world there are no sets. We create them conceptually. This does not change the issue.

Tell me what you think is wrong with the following:

1. The universe is the set containing everything that exists.

2. Nothing exists

3. Therefore the universe is the set containing everything that exists, which is nothing.

[Chrawnus]

You remain mired in the fallacy.

In the real world there are no sets. We create them conceptually. This does not change the issue.

Tell me what you think is wrong with the following:

1. The universe is the set containing everything that exists.

2. Nothing exists

3. Therefore the universe is the set containing everything that exists, which is nothing.

There's nothing wrong with it, if you're treating sets conceptually, it's just that the fact that you can define absolutely nothing as a set and call it the universe has no implications whatsoever for those of us who live in the real world where empty sets do not matter, other than in mathematics. In the real world, if you remove all parts of the universe, you don't end up with a set called the universe containing nothing, you end up with nothing, nada, zip.

And besides, it's outside the scope of this thread. It shouldn't be this hard to figure out what I want to discuss, it's written in plain language in the OP what the topic of this thread is.

What I'm interested in figuring out is why it is that some properties/attributes/qualities are shared between all parts/elements and the whole set (such as colour), while others (like the size/weigth of the individual parts) are not. I'm also interested in figuring out whether it's possible to know whether contingency and finitude belong to the former or latter category.

[robertb]

What I'm interested in figuring out is why it is that some properties/attributes/qualities are shared between all parts/elements and the whole set (such as colour), while others (like the size/weigth of the individual parts) are not. I'm also interested in figuring out whether it's possible to know whether contingency and finitude belong to the former or latter category.

Well that is much clearer.

The second question first, contingency describes the possible states of being, as in being and non-being. Finitude describes that some specific being will eventually transition to the state of non-being. I am not sure why you would want to categorize these descriptions of states with the other attributes you listed. Are you saying that contingency and finitude are attributes that exist internally within objects? If so, that is an odd way of putting it.

To the first question, some attributes are communicative, like colour and some attributes are additive like weight.

[Chrawnus]

Why do you call the terms contingent and 'having a finite past' properties in the first place? They seem more like words that imply a state.

How are you defining the word property? This may help to clear up what it is you are looking for.

When I'm speaking of a property, quality, attribute, character or trait of something, I'm talking about anything that, if we know about it, will tell us something about that object/concept/idea or it's state. That would mean that even something like it's place, in relation to other objects would be a property, and not merely something like it's colour, and even something like the dependency of an idea on other previous ideas would be a property of said idea.

So, yes, even words that merely imply a state would be treated as a property.

I mean, we intuitively think of the temperature (how warm or cold it is) of an object as a property of said object, even if it in reality it's more about the state of the object (or the state of the molecules of the object) rather than something innate in said object.

Regardless, I think the real issue here is the application. Remeber, it is a category error to analogize the universe to a singular object, the universe to a wooden bench. A better analogy would be to analogize the universe to the set of all wooden benches.

Except that's not what I'm doing in the slightest. I'm not analogizing anything at all, I'm asking if it's possible categorize properties based on whether they carry over from individual parts of an object to the whole of the object or not. We already know that some properties carry over, like colour, so that if all parts of the universe were red then the universe as a whole would be red, but we also know that some properties, such as size value, do not carry over, so that even if we can divide the universe up into parts that are all a particular size Z, it doesn't mean that, if we add up all the Z-sized parts, we get a universe that is size Z. But what exactly is it that makes redness carry over from the parts to the whole, but not size?