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2016-05-13
Parthood vs Membership
Could anyone explain the difference between being part and being member (if any)? References to existing literature are welcome. 

2016-05-16
Parthood vs Membership
Hi, I think that the difference is this in terms of logic: consider a model M. M is a description of the state of affairs. We can say, that one-place predicate P is part of this model. Now this one-place predicate is defined by its extensions in M, which means, that P is defined as a subset of the domain of M. When we say that x belongs to this subset, we say that x is a member of this subset.

2016-05-16
Parthood vs Membership
the part-whole relationship is transitive, whereas the member-set relationship is not.La parte della parte di un tutto è anche parte di questo  tutto, ma il membro di un membro di un insieme può non essere membro dell'insieme.

2016-05-16
Parthood vs Membership
The difference is an elementary one in set theory. An example may help to understand it.

Cameron is an Englishman = Cameron is a member of the English people;

The Englishmen are British = The English people are part of the British people.

For an elementary introduction to set theory, see e.g. P.R. Halmos, Naive Set Theory, van Nostrand, Amsterdam 1960.

2016-05-16
Parthood vs Membership
This passage from Oliver and Smiley (2013) might help. It's in the context of arguing why, on a singular analysis of plural terms, a set (which has members) would be preferable to a mereological sum or fusion (which have parts):

...sets have the necessary unique articulation into members, unlike wholes, which can be decomposed into parts in many ways. This is why mereological sums or fusions are ineligible [as the denotation of plural terms]. Suppose there are two tables. Then each table is the sum of its parts and the sum of the tables is the sum of their parts. (This is how things are supposed to be; it does not say how things would be if the parts were rearranged or dispersed.) So 'the tables' and 'the parts of the tables' represent different decompositions of the same sum, but giving them that sum as their common denotation leads to trouble. The tables may lean against one another but their parts do not; the tables are two in numbers, but their parts are vastly more. So the tables are not identical to their parts (plural identity) even if the sum of the tables is identical to the sum of their parts (singular identity). (Oliver and Smiley (2013) pp.34-35.)

So, as I see it, a set has only one way of decomposing into members; whereas a fusion has multiple ways of decomposing into parts.

Hope that helps!

2016-05-16
Parthood vs Membership
Hi, 
They're very different. A sum of parts creates a fusion, which is nothing above and beyond the sum of its parts. For instance, the parts of my goldfish together just are my goldfish. 

This is not true of set membership (which I what I take you to mean by being a member). For instance, the set of my goldfish is distinct from my goldfish (the same is true of the set of parts of my goldfish, but my goldfish alone is a clearer example). 

If you are interested, Lewis' Parts of Classes is perhaps the Standard reference for mereology (the study of parts) and he develops it as a replacement, of sorts, for set theory.

Potter discusses the difference between parthood and membership at the start of his set theory and its philosophy. 

2016-05-16
Parthood vs Membership
"Part" is logically a relation of mereology &/or mereotopology, while "member" (or "element of") is the basic relation of set theory.The definitive text on mereology is Peter Simons' Parts: A Study in Ontology (Clarendon Press: Oxford, 1987).

While there are such things as "non-well founded" sets, it is typically the case that a member will be "atomic", that is, foundational, while a mereological part need not in any way be bounded in such a fashion.

2016-05-16
Parthood vs Membership
"Set" is an abstract entity, "whole" is a concrete one. If all the passengers of the Tytanic sank, their whole sank as well, but the set did not.parthood is transitive: If my finger is a part of my hand and my hand is a part of my body my finger is a part of my body. Membership is non-transitive: if my father is a member of the set (or class) of engineers and the set of engineers is a member of the set of sets, my father is not a set.


2016-05-16
Parthood vs Membership
Here is how category theory makes the distinction.  For further details of what I'm about to say I recommend Lawvere and Rosebrugh's great textbook Sets for Mathematics, in particular, chapter 2.  
Let us have a set X.  We distinguish between elements of X and parts of X, the latter being a special case of the former.  An element of X is any function with codomain X, and a part of X is any injective function with codomain X (more exactly, monomorphism with codomain X).  Lawvere and Rosebrugh nicely explain why these definitions make sense and reflect the actual practice of mathematics.  

Now, without getting into too much detail, the distinction you are after is made as follows.  

1. To be a member of is a relationship between an element of X and a part of X, i.e., does the element belong to the part?  Let our element of X be the function f and the part the function i.  Then f belongs to or is a member of i iff there is a map g from the domain of f to the domain of i s.t. ig = f.  

2. To be a part of is a relationship between parts of X.  Here we tend to say that a part is included in another or not.  A part is included in another provided a function g like above exists.  One can prove that this g must too be injective.  This is not so for membership.  

Then one can go on to prove all the usual factts about membership and inclusions, e.g., if x is a member of part i of X and i is included in part j of X, then x is a member of j.  

Notably, the 'arrows only' formulation of these definitions means you can consider elements, parts, and membership and inclusion relations between them for things that are not sets.

Also, our usual notion of element is seen as a map to X with domain some singleton.  Note such elements are in fact parts of X.

2016-05-17
Parthood vs Membership
Let me explain you the problem I faced. I’m trying to clarify the notion of ‘manifold’ in Husserl’s theory of perception. Consider an actual sequence of three perceptions of one and the same object. This latter is the unity of a manifold (formed by the three perceptions). Can I describe the manifold as a whole? Or it is better to conceive it as a set? Formally Husserl defines a ‘manifold’ as a set ordered by a law, but he also defines a ‘set’ as a whole in which the contents are unified by a ‘collective connection’. Indeed some interpreters describe the manifold at issue as a whole in which each perception is an independent part (for each of them can exist out of the actual manifold). I’m tempted to describe it as a set. It seems to me that both descriptions are correct – a wrong description would be one according to which perceptions are non-independent parts of the sequence – for the following reason: just as a member of a set S can exist out of S, an indipendent part can exist out of its whole. Both seem to be “in” something in the same way. But I’m not sure whether the notion of ‘independent part’ can be “translated” in that of ‘member’. 
Please note these points: 
  • For Husserl ‘part’ means what is distinguishable in something.   
  • Often the expression ‘x belongs to A’ (membership) is paraphrased with ‘x is in A’.    
  • My question is not regarding the difference between inclusion (A is a subset of B) and membership (x belongs to A), but that between parthood (mereology) and membership (set theory).


2016-05-17
Parthood vs Membership
Reply to Carlo Lori
Thank you Carlo. Potter's discussion is exactly what I was looking for!  

2016-05-17
Parthood vs Membership
If that is what you are interested in, you might have a look at the article: E. Casari, On the relationship between parts and wholes in Husserl's phenomenology. In L. Boi, P. Kerszberg,&F. Patras (Eds.), Rediscovering phenomenology, Springer, Berlin 2007, pp. 67-102.
On the same relationship in mereology, you might have a look at the book: C. Calosi & P. Graziani (Eds.), Mereology and the sciences: Parts and wholes in the contemporary scientific context, Springer,Berlin 2014.


2016-05-18
Parthood vs Membership
A Finnish philosopher Eino Kaila made a distinction to p-objects, f-objects and physical objects. I think that would also be usefull for you, especially the concept of p-object. If I look at a chair from different viewpoints of course it will look different each time. But there is some invariance in this experience, which Kaila charactarize as the p-object "this chair". He also made an interesting argument that this p-object can't be reduced to a sequence of perceptions, because what is also needed is the activity of mind i.e. activity of mind+perceptional sequence. 

2016-05-20
Parthood vs Membership
It sounds as if maybe the consensus is that Husserl really meant parts and wholes and not members and sets. It reminds me of Chomsky talking of sets in the context of Merge, which again seemed to be the wrong term, or at least lacking in any explanatory usefulness.
Maybe an important aspect of this is facing up to deciding what the real individuals (potential 'members') are and whether a real individual can actually have parts. I guess individuals might be 'actual occasions' or 'petits perceptions' in the phenomenal context but I am not sure how you decide in a phenomenological description. True dynamic individuals might be easier to define in physics but how that links to the phenomenology...

2016-05-24
Parthood vs Membership
In the sentence: "John is leader of the team," "John" is a description of a state of affairs, M. The one-place predicate "is leader of the team" P is part of "John." Yet as John is leader  no member can be part of that subset, as only John can be leader.

2016-05-24
Parthood vs Membership
It is the difference between being an element of a set  and being a subset of a set.  Every set is a collection of individual elements.  Subsets of a set  either contain elements of the set or is the empty subset.  

2016-05-31
Parthood vs Membership
Why wouldn't you say that "the leader of the team" is a definite description of John, while the "is" is identity, not predication?

2016-06-01
Parthood vs Membership
Reply to David Ozonoff
If the "is" is one of identity then identity in terms of what? Is he leader in terms of membership. I think not. Is he leader in terms of participation? I think not. So what term accounts for the identity/?

2016-06-01
Parthood vs Membership
I am new here and a psychologist, which has of course foundations in philosophy as everything does, but I'm a nubie, out of my element, in the event I've ever found one.  So, that aside...
I am an activist, and have been heavily spiritually attacked by fascist ignoramuses, a very small smear of feces on the tightly whities of humanity.  I've been droned, diseased, psychically attacked, daunted by witchcraft you name it, for being a dedicated child of God.  So ALL of that aside...  

My association to your forum topic, having ministered to a lot of fascist runner pigs in an attempt to survive and reach/stop them (at present appears impossible-- psychopathic narcissists-- goners) is that we were created as individual organisms by the Almighty GOD.  We are wholes if we chose to look out our eyeballs and be constructive MEMBERS who contribute to a community.  In the Jungian sense I believe there is a collective soul, the overlap in the Venn Diagrams of connected individuals in dyadic, triadic... Relationships to each other and the larger communities of individual benevelent whole organisms of GOD.  Wholes can overlap without pathologically merging as fascists blobs of psychopathic scum do.  Not sure if this is relevant, editor will decide.  God bless.  


2016-06-01
Parthood vs Membership
A collection  is a gathering or grouping of entities based on a common property.  The -members- of the collection are members purely by virtue of possessing this common property.  On the other hand things are parts of structures.  Some parts connect or interact with other parts.  Parts are structural or functional participants of the whole,  not merely a part of a mental gathering.  Parts have to touch or interact with other parts.  Members do not have to act at all....

2016-06-03
Parthood vs Membership
"John" is a Proper Name for the person picked out by the Definite Description, "the leader of the team."

2016-06-06
Parthood vs Membership
Reply to Tami Williams
I want to add that in the overlap of those Venn diagrams (overlapping wholes with the organismic integrity that GOD gave us, that we retained) learning occurs.

2016-06-07
Parthood vs Membership
Reply to David Ozonoff
In Jaakkola's reply to Marchesi, logic shows a state of affairs as described by a model, M of which P, its predicate, is part and a subset of M, its domain, has x as a member. Suppose M describes, the state of affairs "John is the leader." ["John" as proper noun, is a place, filling a variable, "x" in Mx]
John [or "the Leader"] is neither a member nor a part of the team. Consider the following sentence;
"John, the leader expects every member to play her or his part." John is not addressing himself nor does he have any part he need tell himself to play.