### Something akin to Monism

Jonathan Schaffer has recently posted a paper called "The Internal Relatedness of All Things" in which he argues for Priority Monism. He presents a couple arguments in his paper, each one in two stages. His arguments, as Schaffer admits rely on rather heavy Mereological principles. I believe there are arguments, analogous to the ones Schaffer presents, for a thesis akin to Priority Monism. Before I introduce the thesis akin to Priority Monism and the arguments for that thesis, I suggest that everyone read Schaffer's paper first (or at least the first 10 pages of it).

Schaffer's argument is presented in two stages. In the first stage, he argues for the conclusion that all things are internally related in ways that make them interdependent. In the second stage, he argues that this internal relatedness implies Priority Monism (the thesis that there is one Basic concrete thing and it is the Universe). Schaffer focuses on the second stage first and that is the stage that will concern me in this post.

I will not be arguing for Priority Monism, though. I am going to be arguing for something akin to Priority Monism. To spell out this view, I will first introduce a priority relation which is slightly different than Schaffer's. Schaffer says that some things are prior to others. For example, I am prior to the proposition that I exist. I will introduce a plurals version of this relation. A two place relation that takes pluralities and individuals rather than just individuals as relata. Just as I am prior (in Schaffer's sense) to the proposition that I exist, so too the philosophers in New York are prior (in the new sense) to the singular existential propositions about those philosophers. We might think that this relation is distributive. That is, the philosophers in New York are prior to the singular existential propositions about them in virtue of the fact that each philosopher in New York is prior to the singular existential proposition about him or her. But, I will argue that this is false. I am going to argue for Non-Distributive Priority Ensemblism. This is the thesis that there are some things that are jointly and non-distributively basic and they encompass all of reality (if anyone asks I'll spell this out in more detail in the comments).

Schaffer gives two arguments for Priority Monism in the second stage of his project. I will give an analogue to the first of these arguments for Non-Distributive Priority Ensemblism. Moreover, my argument will rely on less controversial principles than Schaffer's. I will also point out how an analogue to the second of Schaffer's arguments would also be less controversial than Schaffer's own argument.

Here are Schaffer's mereological presuppositions: First, there is some concrete thing such that every concrete thing is a part of it. Second, any concrete thing that has a concrete proper part has another concrete proper part disjoint form the first (Concrete Weak Supplementation). I believe that the first of these presuppositions is

In my argument I will use two fairly uncontentious presuppositions about plurals. First, some concrete things are such that anythings whatsoever are either amongst the first things or are such that each of their parts overlaps with some things amongst the first things. That presupposition is a bit of a mouthful (and might need to be qualified a bit more), but it is true. Consider all the concrete atoms in the universe. Everything is either one of those atoms or is such that all of its parts overlaps with those atoms. My second presupposition is that if some concrete things are properly amongst some other concrete things (each of which is discrete from one another), then there are some third concrete things that are distinct from the first things and also property amongst the second. This is just a plurals analogue of Weak Supplementation. Unlike the mereological principle Weak Supplementation, this plural principle is not suspect at all.

Now, let 'xxMyy' mean the xx are modally independent of the yy. Let 'Bxx' mean that the xx are jointly basic (let it remain neutral as to weather they are non-distributively basic). Let, xxDyy mean that the xx are pairwise disjoint form the yy. Now, my analogues of Schaffer's Assumptions are as follows:

AS1: No pairwise disjoint things are modally independent: (xx)(yy) (if xxDyy, then ~xxMyy)

AS2: There are some basic things: (Exx) Bxx

AS3: Any things that are jointly basic will be modally independent of any things they are pairwise disjoint from: (x)(y) ((Bxx & xxDyy) then xxMyy)

AS1 is argued for in the first stage of the project. Unfortunately, I am not going to recreate the first stage in this post. So, although it seems suspect, I am not going to say anything more in this post about it. AS2 seems true. As Schaffer points out, AS3 just embodies an intuition that certain things (namely disjoint and basic things) are modally recombinable. I believe AS3 has as much plausibility as Schaffer's third assumption.

Now here is the argument: Arbitrarily choose somethings that are pairwise disjoint from one another and jointly encompass all of concrete reality. Call those things 'uu'. Now assume that some things properly amongst those things are basic. Using 'xxAyy' to represent that the xx are properly amongst the yy, we can formulate this reductio assumption as follows:

1. (Exx) (Bxx & xxPAuu)

Now we existentially instantiate and call those basic things the aa:

2. Baa & aaPAuu

Now from (2) and Weak Supplementation of Plurals we get:

3. (Ex) aaDxx

existentially instantiate:

4. aaDbb

From (2) and (4) and AS3, we get:

5. aaMbb

But (4) and AS1 imply that:

6. ~aaMbb

Since we have arrived at a contradiction, we may conclude that our assumption is false:

7. ~(Ex) (Bxx & xxPAuu)

But, since AS2 says that some things are basic, we may conclude that:

8. Buu

Moreover, these things are non-distributively basic since, in accordance with (7), no things amongst them are basic. Hence, Non-Distributive Priority Ensemblism is true. One cool thing about this argument is that we learn that the plural property of being basic is a non-distributive plural property. Moreover, we learned this without the heavy mereological assumption that there is some concrete thing such that every concrete thing is a part of it.

Schaffer has a second argument that relies on even stronger mereological principles. Namely, it relies on complementation: the thesis that for any thing, there is another thing disjoint from the first and the two together compose the universe. So, for example, there is something that is all of the universe except my left pinkie toe. That is a weird thing. But, there is a plural analogue of this second argument and, moreover, complementation with respect to pluralities is not a controversial thesis. So, again, we'll be able to argue for Non-Distributive Priority Ensemblism without the heavy tools that Schaffer uses. (I still need to work this one out though)

Now, I think that the argument is cool as it stands. But, someone like Schaffer might want to argue for priority monism. Well, we can do so if we introduce the following principle:

(Basic Plurals to Basic thing) If some things are pairwise disjoint and non-distributively basic then they jointly compose something that is basic.

I don't know if this principle is true, but it sounds like something someone would believe. Moreover, it sounds like something defensible. But, with this principle we can get from my conclusion to Schaffer's conclusion. That is, we can get from Non-Distributive Priority Ensemblism to Priority Monism.

Schaffer's argument is presented in two stages. In the first stage, he argues for the conclusion that all things are internally related in ways that make them interdependent. In the second stage, he argues that this internal relatedness implies Priority Monism (the thesis that there is one Basic concrete thing and it is the Universe). Schaffer focuses on the second stage first and that is the stage that will concern me in this post.

I will not be arguing for Priority Monism, though. I am going to be arguing for something akin to Priority Monism. To spell out this view, I will first introduce a priority relation which is slightly different than Schaffer's. Schaffer says that some things are prior to others. For example, I am prior to the proposition that I exist. I will introduce a plurals version of this relation. A two place relation that takes pluralities and individuals rather than just individuals as relata. Just as I am prior (in Schaffer's sense) to the proposition that I exist, so too the philosophers in New York are prior (in the new sense) to the singular existential propositions about those philosophers. We might think that this relation is distributive. That is, the philosophers in New York are prior to the singular existential propositions about them in virtue of the fact that each philosopher in New York is prior to the singular existential proposition about him or her. But, I will argue that this is false. I am going to argue for Non-Distributive Priority Ensemblism. This is the thesis that there are some things that are jointly and non-distributively basic and they encompass all of reality (if anyone asks I'll spell this out in more detail in the comments).

Schaffer gives two arguments for Priority Monism in the second stage of his project. I will give an analogue to the first of these arguments for Non-Distributive Priority Ensemblism. Moreover, my argument will rely on less controversial principles than Schaffer's. I will also point out how an analogue to the second of Schaffer's arguments would also be less controversial than Schaffer's own argument.

Here are Schaffer's mereological presuppositions: First, there is some concrete thing such that every concrete thing is a part of it. Second, any concrete thing that has a concrete proper part has another concrete proper part disjoint form the first (Concrete Weak Supplementation). I believe that the first of these presuppositions is

*highly*suspect and I am also slightly suspicious of the second.In my argument I will use two fairly uncontentious presuppositions about plurals. First, some concrete things are such that anythings whatsoever are either amongst the first things or are such that each of their parts overlaps with some things amongst the first things. That presupposition is a bit of a mouthful (and might need to be qualified a bit more), but it is true. Consider all the concrete atoms in the universe. Everything is either one of those atoms or is such that all of its parts overlaps with those atoms. My second presupposition is that if some concrete things are properly amongst some other concrete things (each of which is discrete from one another), then there are some third concrete things that are distinct from the first things and also property amongst the second. This is just a plurals analogue of Weak Supplementation. Unlike the mereological principle Weak Supplementation, this plural principle is not suspect at all.

Now, let 'xxMyy' mean the xx are modally independent of the yy. Let 'Bxx' mean that the xx are jointly basic (let it remain neutral as to weather they are non-distributively basic). Let, xxDyy mean that the xx are pairwise disjoint form the yy. Now, my analogues of Schaffer's Assumptions are as follows:

AS1: No pairwise disjoint things are modally independent: (xx)(yy) (if xxDyy, then ~xxMyy)

AS2: There are some basic things: (Exx) Bxx

AS3: Any things that are jointly basic will be modally independent of any things they are pairwise disjoint from: (x)(y) ((Bxx & xxDyy) then xxMyy)

AS1 is argued for in the first stage of the project. Unfortunately, I am not going to recreate the first stage in this post. So, although it seems suspect, I am not going to say anything more in this post about it. AS2 seems true. As Schaffer points out, AS3 just embodies an intuition that certain things (namely disjoint and basic things) are modally recombinable. I believe AS3 has as much plausibility as Schaffer's third assumption.

Now here is the argument: Arbitrarily choose somethings that are pairwise disjoint from one another and jointly encompass all of concrete reality. Call those things 'uu'. Now assume that some things properly amongst those things are basic. Using 'xxAyy' to represent that the xx are properly amongst the yy, we can formulate this reductio assumption as follows:

1. (Exx) (Bxx & xxPAuu)

Now we existentially instantiate and call those basic things the aa:

2. Baa & aaPAuu

Now from (2) and Weak Supplementation of Plurals we get:

3. (Ex) aaDxx

existentially instantiate:

4. aaDbb

From (2) and (4) and AS3, we get:

5. aaMbb

But (4) and AS1 imply that:

6. ~aaMbb

Since we have arrived at a contradiction, we may conclude that our assumption is false:

7. ~(Ex) (Bxx & xxPAuu)

But, since AS2 says that some things are basic, we may conclude that:

8. Buu

Moreover, these things are non-distributively basic since, in accordance with (7), no things amongst them are basic. Hence, Non-Distributive Priority Ensemblism is true. One cool thing about this argument is that we learn that the plural property of being basic is a non-distributive plural property. Moreover, we learned this without the heavy mereological assumption that there is some concrete thing such that every concrete thing is a part of it.

Schaffer has a second argument that relies on even stronger mereological principles. Namely, it relies on complementation: the thesis that for any thing, there is another thing disjoint from the first and the two together compose the universe. So, for example, there is something that is all of the universe except my left pinkie toe. That is a weird thing. But, there is a plural analogue of this second argument and, moreover, complementation with respect to pluralities is not a controversial thesis. So, again, we'll be able to argue for Non-Distributive Priority Ensemblism without the heavy tools that Schaffer uses. (I still need to work this one out though)

Now, I think that the argument is cool as it stands. But, someone like Schaffer might want to argue for priority monism. Well, we can do so if we introduce the following principle:

(Basic Plurals to Basic thing) If some things are pairwise disjoint and non-distributively basic then they jointly compose something that is basic.

I don't know if this principle is true, but it sounds like something someone would believe. Moreover, it sounds like something defensible. But, with this principle we can get from my conclusion to Schaffer's conclusion. That is, we can get from Non-Distributive Priority Ensemblism to Priority Monism.