(September 14, 2018 at 4:50 am)RoadRunner79 Wrote: Why do you think that the law of identity is not thought through very well?  It would seem that without it; we cannot have a rational conversation. Tree is a language concept as well.

As Neo pointed out, you seem to be assuming the answer to your question in your argument (that if you cannot observe the number it ildoesnt exist). In any case the number as a description is not dependent on the subject. It is describing an external part of reality, not giving information about the person who holds the view.

No. Counting external things is describing an external reality. That is using a *mathematical model*, albeit a very simple one. And such a model may or may not be appropriate for any given physical situation. Whether it is or not is a matter of observation and testing.

Please define 'a number as a description' in a way that does not depend on the subject. You make the claim that the number 4 is objective: that it doesn't depend on context or the person using it. I have pointed out a few ways in which it *does* depend on context or the person using it.

(September 14, 2018 at 7:42 am)polymath257 Wrote:

(September 14, 2018 at 4:50 am)RoadRunner79 Wrote: Why do you think that the law of identity is not thought through very well?  It would seem that without it; we cannot have a rational conversation. Tree is a language concept as well.

As Neo pointed out, you seem to be assuming the answer to your question in your argument (that if you cannot observe the number it ildoesnt exist). In any case the number as a description is not dependent on the subject. It is describing an external part of reality, not giving information about the person who holds the view.

No. Counting external things is describing an external reality. That is using a *mathematical model*, albeit a very simple one. And such a model may or may not be appropriate for any given physical situation. Whether it is or not is a matter of observation and testing.

Please define 'a number as a description' in a way that does not depend on the subject. You make the claim that the number 4 is objective: that it doesn't depend on context or the person using it. I have pointed out a few ways in which it *does* depend on context or the person using it.

Again, you seem to be confusing language with the external reality of things.   If there are 4 trees, then there is four tree's.   Whether you or anyone else knows it, and if you incorrectly count 5 tree's.   Even in your argument here, you appeal to an objective reality outside of the subject.  I would agree, that there is a subjective component to our observations, and our understanding.   But that relates to an external objective reality.   As you keep appealing to yourself.   I don't disagree, that we can be incorrect, or that we may call it different things (due to the conventions of language).  These things do not make something ontologically subjective.

Counting provides epistemic objectivity (the only kind of objectivity required for math or for science).  We can know that the statement "there are four things over there" is true or false.  It does not provide an objective ontology for "four", regardless of how much intersubjectivity may be present. "Four", as a descriptor, is necessarily ontologically subjective. A concept, a word, a term that we have made up as a referent for x.

There are four trees - epistemic.
The trees are four - ontological.

(September 14, 2018 at 4:50 am)RoadRunner79 Wrote: Why do you think that the law of identity is not thought through very well?  It would seem that without it; we cannot have a rational conversation. Tree is a language concept as well.

As Neo pointed out, you seem to be assuming the answer to your question in your argument (that if you cannot observe the number it ildoesnt exist). In any case the number as a description is not dependent on the subject. It is describing an external part of reality, not giving information about the person who holds the view.

Well, first of all, most people who use that identity don't distinguish well between *logical* identity (p if and only if q) and *equality* (p=q). They are very different notions and applicable in very different situations.

So, *logical* identity describes the logical statement that "p is true if and only if p is true". This is something that is the case in most logical systems, including classical logic.

Equality is a much more complex and interesting thing. We can use the 'identity of indistinguishables' definition and say that x=y whenever x and y have exactly the same properties. This forms an equivalence relation (x=x, x=y implies y=x, x=y and y=z implies x=z). But there is a problem doing the quantitifcation over *all* properties. What constitutes a property?

Furthermore, most people, when they think they are using equality, are actually using some other equivalence relation. And it is NOT the case that two things equivalent via an equivalence relation must be equal. It isn't just *one* criterion that determines 'indistinguishability'.

In math, the allowed properties are carefully spelled out, so there is no ambiguity. But there are also undefined notions (typically, set membership). Only after the development of set theory does it become possible to define the concept of 'number'.

And you fell into the equivalence relation/identity trap in your next statement when you said that trees are a language concept also. No, trees are wooden plants. They are not part of language. What is part of language is the *word* 'tree'. This is usually called the 'use/mention' distinction. There is noting inherent in reality or in tees that forces us to use the vocalization 'tree' or the English word 'tree'. The word is NOT an objective part of reality. It is a subjective tradition that we adopt for communication. But, you would use a different word for the same reality if you spoke a different language.

And, you also bring up another very important issue: how do you define the verb 'to exist'? A LOT of care is required here. We need a definition that allows us to talk about non-existent things like Sherlock Holmes while also allowing us to say that the chair in my room really exists. But we can have that for another discussion, or later in this one.

existence-as

Holmes exists as a fictional character in a novel.

Chairs exist as a group of things we can sit on.

(September 14, 2018 at 7:52 am)RoadRunner79 Wrote:

(September 14, 2018 at 7:42 am)polymath257 Wrote: No. Counting external things is describing an external reality. That is using a *mathematical model*, albeit a very simple one. And such a model may or may not be appropriate for any given physical situation. Whether it is or not is a matter of observation and testing.

Please define 'a number as a description' in a way that does not depend on the subject. You make the claim that the number 4 is objective: that it doesn't depend on context or the person using it. I have pointed out a few ways in which it *does* depend on context or the person using it.

Again, you seem to be confusing language with the external reality of things.   If there are 4 trees, then there is four tree's.   Whether you or anyone else knows it, and if you incorrectly count 5 tree's.   Even in your argument here, you appeal to an objective reality outside of the subject.  I would agree, that there is a subjective component to our observations, and our understanding.   But that relates to an external objective reality.   As you keep appealing to yourself.   I don't disagree, that we can be incorrect, or that we may call it different things (due to the conventions of language).  These things do not make something ontologically subjective.

Suppose I have four plants and you consider one to be a tree and I consider that one to be a bush. You would say there are four trees and I would say there are three. And we could both be correct. The method of counting is the mathematical model: how to apply the abstract language to a particular real world situation. The reality didn't change: it was only our interpretation that differs.

(September 14, 2018 at 8:08 am)polymath257 Wrote:

(September 14, 2018 at 7:52 am)RoadRunner79 Wrote: Again, you seem to be confusing language with the external reality of things.   If there are 4 trees, then there is four tree's.   Whether you or anyone else knows it, and if you incorrectly count 5 tree's.   Even in your argument here, you appeal to an objective reality outside of the subject.  I would agree, that there is a subjective component to our observations, and our understanding.   But that relates to an external objective reality.   As you keep appealing to yourself.   I don't disagree, that we can be incorrect, or that we may call it different things (due to the conventions of language).  These things do not make something ontologically subjective.

Suppose I have four plants and you consider one to be a tree and I consider that one to be a bush. You would say there are four trees and I would say there are three. And we could both be correct. The method of counting is the mathematical model: how to apply the abstract language to a particular real world situation. The reality didn't change: it was only our interpretation that differs.

Here you are arguing that they are ontologically objective.  The number of things did not change and was not effected by the subject or their opinions. We are describing something external and not internal to the subject.

The number of things did change, and that change was based upon subjects and their opinions. This is true even if we are describing something external to ourselves..and even if we could classify one opinion or the other as epistemically objective - the "right" opinion. More on this in a moment.

We make epistemically objective statements about ontologically subjective things with regularity. The best way to get over that speedbump, begins with acknowledging this. State your assumptions, define your variables, produce your work. So long as we do this even a mereological nihilist can accept that the epistemic statements are objective even if the underlying reality (whatever that is) is not. That even if parts and wholes do not exist...the statements we make about them are an accurate description of our observations.

Now, about the bit above.."things" were defined as a variable in polys statement. Trees, specifically. If in one formulation there are four trees and in another three...retreating to a more general concept of things is to -affirm- the mereological nihilists pov, not counter it. Implicit in your rebuttal is a denial of a difference between things (trees)..and not things (not trees). The only difference between the two disparate statements has nothing to do with "trees" or "things"..but, more properly, with the observers making the disparate statements.

(September 14, 2018 at 8:19 am)RoadRunner79 Wrote:

(September 14, 2018 at 8:08 am)polymath257 Wrote: Suppose I have four plants and you consider one to be a tree and I consider that one to be a bush. You would say there are four trees and I would say there are three. And we could both be correct. The method of counting is the mathematical model: how to apply the abstract language to a particular real world situation. The reality didn't change: it was only our interpretation that differs.

Here you are arguing that they are ontologically objective.  The number of things did not change and was not effected by the subject or their opinions. We are describing something external and not internal to the subject.

No, I *am* saying the number is subjective: it does depend on the observer and their biases.

But, more importantly, the actual identity of the number 4 is not agreed upon. Is it the set {{{{}}}}? Or is it the set {0,1,2,3}, where 3={0,1,2}, 2={0,1}, 1={0}, and 0={}?

Or do we use the notion in the integers (equivalence classes of order pairs of natural numbers)? Or in the rational numbers (equivalence classes of order pairs of integers)? Or in the real numbers (Dedekind cuts? equivalence classes of Cauchy sequences?)? Or maybe in the complex numbers (ordered pairs of real number? Or the algebraic quotient field obtained from real polynomials after modding out by x^2 +1?)

Or do we simply mean SSSS0 in an inductive set with first element 0 and successor function S (in which case, there are many, many, many different specific notions)?

(September 13, 2018 at 1:15 pm)RoadRunner79 Wrote:

(September 13, 2018 at 12:45 pm)Jörmungandr Wrote: Don't try to guess what my endpoint is, just answer the questions.  If you prefer, we can speak of parts and wholes.  Do parts and wholes exist independent of the machinations of the mind?

I’m not trying to guess where you are going. As I said, I don’t understand what you are saying.

A simple answer to your question here, I do believe that the whole exists and the parts of things exist, outside of human conception. I believe that hydrogen and oxygen exist, as well as the combination of them known as water, apart from a persons knowledge of it.

Okay, a simple thought experiment. Let's say that you and I each have a lump of gold, me at my location, and you at yours. Now we know that these two lumps of gold are not part of the same lump of gold, the atoms from each are separated by considerable distance. Any two atoms in the respective lumps of gold are not part of the same lump of gold. Now take a single lump of gold. There will be two atoms in it that are adjacent to each other. Both atoms are a part of the same lump of gold. Between the atoms is empty space. Now suppose we start gradually expanding the space between the atoms in the lump of gold, first by 5%, then 10%, eventually by 100%, 200%, 3000% -- eventually the individual atoms will be as far apart as the lumps of gold in our respective pockets. Keep expanding and eventually the two atoms are farther apart than the entire width of the universe. The immediate question that comes to mind is, at what point do the two atoms stop being a part of the same lump of gold, but more importantly, why? What is it about the distance between them that makes one pair of atoms, separated by an arbitrary amount of empty space, different from two other atoms, equally separated by an arbitrary amount of empty space? This is similar in many ways to what is known as the Problem Of The Many, and as a glance at that page from the Stanford Encyclopedia of Philosophy will tell you, there are multiple incompatible answers to the paradox. Some suggest that this is just an example of the sorites paradox or the paradox of the heap, that it is a problem in the vagueness of the boundary, that something changes, even though there is no clear line or point at which it changes. Others disagree with this, and see the problem of the many differently. One solution which occurs to me immediately is that when the atoms are close together, they interact with each other by way of forces such as gravity and the other four forces. But this doesn't solve the problem, as no matter how far apart the atoms are, they still interact, albeit weakly, it is only a change in the strength of the interaction. To argue that it has to do with interaction would then be to assert that there is an arbitrary strength of interaction which defines whether two atoms belong to the same object or not.

Now, I don't really expect to convince you that parts and wholes do not exist. I suspect your intuitions about the matter, as well as perhaps your prior philosophical commitments make that unlikely. But if you'll recall, the original complaint was that the position that number, which requires parts and whole distinctions, being subjective was not so far fetched that, as Neo put it, no rational person would believe that number, like parts and wholes, is subjective. At minimum, I think this example, as well as the problem of the many, is not as far out as your intuitions, Steve's hyperbole, and Neo's contemptuous remarks made it out to be. If not, then what is your answer to the lump of gold problem, and your answer to the problem of the many? (And ultimately all objects are like the cloud in the problem of the many, a cloud of particles, interacting in various strengths through various forces. What makes the cloud of atoms that is my desk a whole with parts, and a cloud composed of water droplets problematic? There is the problem of the boundary in the case of the desk, as the surface of the desk trails off and it becomes difficult to say which atoms are a part of the desk, and which are not, and that indeed may be an example of the sorities paradox, yet the question remains, what makes this particular "desk-like ensemble of particles" a whole in the first place?)

Ultimately, as I said to Neo in the thread on delusion and religion, number, and the concepts it is dependent on, are a mystery. I can suggest that number, being an example of reasoning using parts and wholes, only exists in so far as we make arbitrary identity judgements, about what is a part of what, and what is a whole. But our intuitions tend to marshall against us, at the very least, and it's not entirely clear that number is subjective in its entirety, that it doesn't have an independent, objective substance of some sort. Yet when we go the other direction, and assert that number, and part/whole distinctions are objective, we run into problems in that direction as well, problems which seem equally intractable. So we're left with a mystery, I think, and to declare that number, or parts & wholes, is definitely objective, is, to my mind, to embrace an opinion that is not in any sense fully justified. At minimum, if you can't prove that number is objective, that leaves the door open, no matter how slightly, that number is subjective, as it must be one or the other, it can't be both. So, QED, as it were, I think I've shown that number and parts & wholes being a product of mind is not a view that is as far fetched as Neo and Steve made it sound. If you disagree, please explain why.

(To rephrase in terms of your example, what makes two hydrogen atoms and an oxygen atom, close together, strongly interacting, a molecule of water, and the same group of atoms, separated by several light years of empty space, not a molecule of water?)