If the "whole" is the sum of its parts,
then if some of the parts are removed,
at what point is the "whole" no longer
the "whole"??

In other words, if I have an orange
and I remove part of the peel, we
would still say that I'm holding an
orange, right?
But at what point is it no longer an
orange; when is it orange juice or
some mold infested rot?
What makes an orange an orange?

I suppose this is a question of "essence."

Other examples can be given, but
I think you get what I'm asking about.

Thanks,
Matthew

__________________
Matthew Scheffer
Christ The Redeemer (non-denominational)
http://www.christredeemer.com
Spokane, WA

If you remove a little of the peel from an orange, it is no longer the same orange, but a different one. The part you removed (the portion of the peel) is either an orange or not an orange, depending on the definition of an orange.

__________________
Brian Withnell
Deacon, OPC
Leesburg, Virginia

You cannot train for war in the midst of a battle. Prepare before the battle starts; if the battle is long and hard, you will wish you had.

So Dad walks in and says "Peter, where is the orange I laid on the counter this morning." Peter, having taken a bite out of it says "there it is on the table."

It is the same orange. Peter could have added qualifiers such as it is smaller now, or it is decomposing due to my saliva, etc. It is still the subject, whatever is being predicated of it.

__________________
Bob, elder, RBC Louisville. 1689 LBCF

"... Of such also, or of those who make a credible profession of being such, all those particular churches consist, which constitute our Lord's visible kingdom. ... Consequently, all the subjects of His government must have spiritual dispositions, , and yield spiritual obedience- obedience proceeding from an enlightened understanding, an awakened conscience, and a renewed heart."- Abraham Booth 1788

The question then is whether, when we refer to a bitten orange as the same thing as the non-bitten orange, we are speaking colloquially or philosophically.

__________________
Ben Maas. . . . .Facebook
In college, attending First Presbyterian Church (PCUSA), Ada, OH, and
Belle Center Reformed Presbyterian Church (RPCNA), Belle Center, OH
When at home, attending Covenant Presbyterian Church (OPC), Mansfield, OH

“Prayer is as natural an expression of faith as breathing is of life.”
-Jonathan Edwards-

The bitten orange is a continuation of the non-bitten orange. To call it the same thing would be inaccurate, but at the same time there is a connection.

We'll call the orange O and the bitten orange O(a). O and O(a) are different, yet they both belong in the category of O-ness. They both answer to the form of O.

__________________
Philip
Potomac Hills Presbyterian Church (PCA) Leesburg, VA
Attending Reformed Presbyterian Church, Lookout Mountain, GA
Student Covenant College

The Importance of Being Orthodox

O.

__________________
We shall not adjust our Bible to the age; but before we have done with it, by God's grace, we shall adjust the age to the Bible. - Charles Haddon Spurgeon

Lawrence Underwood, Jr.
Pastor - Providence Family Fellowship / Mobile, Alabama
1644/46 LBC
My Blog - Imprimis

Curious. If you have lost 8,000 brain cells since the time of posting this and now, are you still you, or no longer still you?

Jonathan Edwards would say that he is the same person only by God's arbitrary decree.

Bob,
That's the question that I'm asking.
If I lose an arm or a leg or some brain cells,
then I'd still be "Matthew," but what I'm asking
is what makes something what it is?

God Himself is both one and many.
God is one, yet Jesus is not the Father
the Spirit is not the Son, etc.

Some Bible teachers have claimed that
the biblical understanding of the Trinity
gives the only correct answer for understanding
the "one and the many" issue that Greek
philosophers had, but I'm curious if someone
can please flesh this out for me.

We are made up of many cells, joints, muscles, etc.
yet we are "one" person.

So what I'm asking is at what point does a thing
cease to be what it is?
Can we definitively know the answer to this?

Or at what point does something become what it is?
(a girl becomes a woman; caterpillar becomes a
butterfly, etc.)

When does a Bible translation cease to be the
Word of God (non-literal or paraphrased)?

If you're familiar with the philosophical question,
then I think you know what I'm asking.

Maybe it's simply that we (as humans) are not
the primary interpreters of "things" and only to
the degree that our interpretation of a "thing"
lines up with what God says that a "thing" is,
then we are correct in saying that such-and-such
is an apple or orange or a ship.

Thanks

I remember being helped with this topic by a few pages in R.J. Rushdoony's The One and the Many, though I don't have it on me.

Basically, we can see many temporal ones-and-manies, e.g. a state containing citizens, a church containing believers, a universal concept of "cow" containing many particular cows, etc. The fact that these two can exist in a perfect balance suggests that there is a balanced eternal one-and-many, the Trinity. As Rushdoony shows in the aforementioned book, views of reality based on an overarching unity lead to overemphasis of the "one" (e.g. fascist totalitarianism), while views of reality based on an overarching particularity lead to overemphasis of the "many" (e.g. anarchy). Only by the eternal one-and-many dictating exactly where the balance is in His Word can we understand the extent of the one and extent of the many.

The illustration I like to use in understanding how we are to properly limit the extent of oneness and "manyness" (?) is of a baby in a playpen. You don't want to leave him too free in his options by giving him knives and guns to play with, but you don't want to strap him into a chair and keep him from moving. There is a perfect balance between the one and the many, and only the Creator of the world, the eternal one-and-many, can properly tell us what this balance is. For instance, when we follow His law perfectly, we are living most freely -- otherwise, we would either have access to the guns and knives or be tying ourselves in a chair. Only when we follow His law perfectly do we have that perfect balance.

At any rate, I don't suggest using the argument that the Trinity "solves the problem of the one and the many" as a means of presuppositional argumentation. I doubt it will go too well.

Otherwise, I think the questions you are asking (when a girl becomes a woman, etc.) have more to do with the concept of what comprises something's nature, and how changes in that thing affect its nature, if at all. I have basically nothing to say regarding that, but this is about all I can say regarding the one and the many.

Bob,
That's the question that I'm asking.
If I lose an arm or a leg or some brain cells,
then I'd still be "Matthew," but what I'm asking
is what makes something what it is?

God Himself is both one and many.
God is one, yet Jesus is not the Father
the Spirit is not the Son, etc.

Some Bible teachers have claimed that
the biblical understanding of the Trinity
gives the only correct answer for understanding
the "one and the many" issue that Greek
philosophers had, but I'm curious if someone
can please flesh this out for me.

God is unique. He is the only non-created being in the Universe. All else that is, is created reality. It has its being and identity from God. It is what it is because God wills it to be so, just so. Its continuation, in its God given identity, maintains just so long as He pleases.

We are made up of many cells, joints, muscles, etc.
yet we are "one" person.

Our “person-ness” i.e. our identity is the imago Dei. We are His image. As body/soul entities we are the image of God. Amputations and death notwithstanding our identity is immutable, and that eternally.

So what I'm asking is at what point does a thing
cease to be what it is?

Men and Angels never cease to be what they are because they never cease to be. That is, they maintain their Divinely ordained identity forever, whether fallen or unfallen, redeemed or not.

Can we definitively know the answer to this?

Yes

Or at what point does something become what it is?
(a girl becomes a woman; caterpillar becomes a
butterfly, etc.)

The girl’s identity as the imago Dei known before the foundation of the world and knit together in her mother’s womb never changes. She is distinguished at various points in her existence by age, appearance, etc. but her essential identity remains unchanged.

When does a Bible translation cease to be the
Word of God (non-literal or paraphrased)?

The Word of God is eternal. God inspired men to pen it. It has been copied, translated, preserved, etc. Even the original autographs were but marks on animal skins and their primary usefulness was to preserve the Word(s) of God to the first and all subsequent generations.

If you're familiar with the philosophical question,
then I think you know what I'm asking.

Maybe it's simply that we (as humans) are not
the primary interpreters of "things" and only to
the degree that our interpretation of a "thing"
lines up with what God says that a "thing" is,
then we are correct in saying that such-and-such
is an apple or orange or a ship.

Hello Gentlemen,

For someone to know what an orange is they would need to know two things: (1) what unifies an orange with other things, and (2) what distinguishes it from other things. For example, you have the unifying concept of an orange being a fruit, but you also have plurality in that an orange and an apple are distinct fruits. In other words, the world seems to be such that unity and plurality are related yet distinct. Expressions of unity manifest in relations of commonality, and expressions of plurality manifest in relations of distinctions. The problem of the one and the many is simply to ask, "Which aspect is ultimate - unity or plurality?"

If plurality is ultimate, then the foundation of all reality is utter dissimilarity. However, if ultimate reality is composed of utterly dissimilar things, then they cannot be known. There is no unifying thing to bring them together. If there was some unifying principle, then ultimate reality is not utterly dissimilar. On the other hand, if unity is ultimate, then the foundation of all reality is monistic. But you fall into a similar problem. If everything is monistic, then nothing can be known. There is no distinguishing principle to make differentiations. If there was a distinguishing principle, then unity is not ultimate.

One might argue that the unifying concept 'orange' must already be understood in order to explicate those distinguishing properties that can be properly said to make up an orange. Yet, how can we understand the unifying concept 'orange' if we do not already understand those distinguishing properties that make up an orange? Yet, how does one know which distinguishing properties should be brought together to properly capture the unifying concept of 'orange' if we don't already know what an 'orange' is? And around and around we go. That is the problem of the one and the many.

Brian

__________________
Brian Bosse
Faith Community Church
Tucson, Arizona

I'm trying to think in what system of logic you are operating. Only a mathematical definition of identity would lead to the conclusion that if a quality (size, shape, location, color, etc.) changes then the object is no longer the same object. I think almost all philosophers since Aristotle have worked with some concept of substance and accidence, in which the change of an accident (perceivable quality) does not affect the underlying substance. Ask them to explain what substance is, and watch the veins pulse.

I think a better answer to the question would be in the realm of analytic philosophy, in which we realize that all definitions are fuzzy. Since words can only be defined by other words, nothing can ever be defined with 100% referential accuracy. For example, can one really distinguish exactly between a string, a cord, and a rope; or between big, huge, and enormous?

__________________
Charlie Johnson
Downtown Presbyterian Church (PCA)
Greenville Presbyterian Theological Seminary, student

Semantic fog? What do you get if you ask someone to pass you the milk? The jug - presumably, which contains the milk!

__________________
Independent Reformed Baptist Church (NE England, nr. Durham)

I'm going to see if I can oversimplify this; I think to truly understand what something is, we have to understand it exhaustively. Even with are super powered microscopes, how confident are we that we cannot reduce an atom into a smaller unit of measure? But for the sake of argument lets say we can, whenever the object of reference changes state(no matter how small the change is) it ceases to be what it originally was defined as before.

This reminds me of irreducible complexity. If you take any part of the bacterial flagellum out it ceases to perform the function it is required to do as has been observed. So you have the many(the parts) and the one(the entity as to what it does). You cannot have the one without the other.

Of course in all of this, you need to assume your premises are correct in relation to what your referencing which is no guarantee that it is correct or not fragmented. My .02.

__________________
PuritanGeek
Member of LakeOPC
Wickliffe, Oh
Blog: What Justin's Thinking

Yes.

My ultimate answer to the question of the one and the many is "yes". The resolution for the question is ultimately found in the trinity--three distinct persons forming one godhead.

You have that right -- a mathematician in a family that leans toward engineering. Likely what is in play here is that A cannot be non-A. Any change in A (often expressed in terms of quantity) makes it non-A, and A cannot be non-A.

Thinking along more classical philosophical terms, I'm not sure you can create a whole category out of one object, even if that one object can be broken into its component parts. I think that is why the philosophical systems outside of Christianity have a hard time dealing with the presence of both universals and particulars at the same time.

In other words, you can make a statement to define oranges -- say all oranges have a rough, bumpy orange-colored peel. And from that you can add another premise, say object A has the requisite peel, and therefore conclude it is an orange. Or you could say, this object is smooth and has no peel, therefore it is not an orange. But you could not say that a piece of a peel is an orange in and of itself. The main point that comes to mind here, is the informal fallacy that says you cannot take a part to prove the whole.

__________________
JWithnell
Member Bethel OPC
Virginia
http://learningyesican.blogspot.com/

Hello Jwithnell,

I know this may be a little off topic, but this seems to be incorrect. My core body temperature changes all of the time. My nails are constantly growing. My blood is constantly moving, and new blood cells are constanly being made - not to mention numerous other things that make changes to me. It seems extreme to say that as these things change I am no longer me. Perhaps, a better way to think of this is in terms of essential attributes. If X is an essential attribute for something P to be an A, then given something P that is an A, if X in P changes in an essential way so that X is no longer an X, then P is no longer an A, i.e., P now belongs to the class of ¬A.

Sincerely,

Brian

I'll defer to the mathematicians here -- I'm more apt to deal in more classical logic.

Hello Gents,

In classical logic, the Law of Non-Contradiction says that you cannot have both A and not-A at the same time and in the same relationship. Symbolically, this can be represented as follows...

LNC: ¬(A ∧ ¬A)

Notice, the LNC does not speak to what it is that makes an A an A or a ¬A a ¬A for that matter. The LNC simply notes that you cannot have both an A and a ¬A. As such, one would need more information to apply the LNC; namely, what it is that makes an A an A in the first place. Only then can you distigush between an A and a ¬A. Of course, this leads you right down the path of the problem of the one and the many. Yet, in every day discourse, we rarely dig deep enough to run into trouble. We intuitively have a surface level understanding as to what is an orange and what is not an orange. Only philosophers make us go deeper, and that is when the trouble starts.

Brian

Perhaps there is no "one" essence that all oranges have in common, but rather a "type" that all oranges resemble. They may not match perfectly but they are close enough that they are recognizable as an orange.

__________________
Jonathan
Audio Engineer
Reformed Anabaptist
Ohio

Moroni's magical glasses of proper interpretation:

Jonathan, you solution works on one level, but even with your solution you will shortly encounter the same problem. At heart, you have just moved the problem back one step, by not considering the essence as inhering in the thing, but considering the form in which it participates, to speak crudely. In the end, you are still left with defining your form or "type" of the "Platonic orange" floating off somewhere in the invisible world of forms, which your particular oranges are "resembling" (or in which they are participating). You can't know if something resembles "it," if you don't know what "it" is.

__________________
Paul Korte
OPC
Flint, MI

They who perceive in themselves discoveries of the divine goodness, so full and absolutely perfect, and who make them the subject of earnest meditation, will never embrace new doctrines, by which the very grace they feel so powerfully in themselves is thrown into the shade. --John Calvin

Click to get: Board Rules -- Signature Requirements -- Suggestions?

What we have with this idea of categories is the essential debate between Platonists and Aristotelians. Platonism holds that all oranges are shadows of a perfect "idea-orange" whereas Aristotle taught that we see similarities between various objects and decide that they are similar enough to categorize as "oranges" (and even this category can be subcategorized by varieties of orange).

My answer to the dilemma is, as I said, "yes."

My logic class was a longggg time ago. In fact, I think Aristotle was still on the faculty of the next college over .....

Van Til would have said that it is because God knows what an orange is, that we can know what an orange is.

Maybe someone can unpack that (orange) for me.

__________________
Richard
communicant member, FCoS
Perth, Scotland UK

His Name forever shall endure;
last like the sun it shall:
Men shall be blessed in Him,
and blessed all nations shall Him call (Ps. 72:17)

I would say that it is self-evident that we can know what an orange is for one good reason: we do, in fact, know what an orange is. We may not be able to explain it propositionally, to a Clarkian's satisfaction, but we are not required to be able do so in order to know what an orange is.

An "orange" is a fruit distinct from apples, peaches, berries, and all other kinds of fruit.

Yeah, the Clarkian demand that all terms must be defined in some way is an impossible standard, for we can only define terms with other words, which can only be defined with other words, etc., ad infinitum. There has to be some point at which we have a basic, tacit understanding of terms; otherwise we couldn't speak intelligibly on any subject at all.

If a thing suddenly becomes a different thing just by a change in its make-up, then you have a good anti-materialist argument: our bodies are changing all the time, including our brain, and yet we remain the same, so we are not our bodies.

__________________
Steven Nemes
Phoenix, AZ

Good philosophy must exist, if for no other reason, because bad philosophy must be answered - C.S. Lewis

At the time of my regeneration, I became a new creature in Christ, and that without the change of any of the cells of my body. Am I the same man I was 30 years ago? Heaven forfend!

You are talking to Brian, husband of Jean, teacher of mathematics. Of course I deal with things mathematically. Philosophy without mathematics is a waste of time. If you don't have the axioms, undefined terms and definitions for a system, you have no logic. I do accept what undefined terms are, but then one has to enumerate the undefined terms ... if "substance" is one of those undefined terms, then a description (not definition) is needed to tell when two things are not the same substance. If you cannot tell when an isometry exists between two things, then it makes no sense in saying the objects are the same substance unless they are the same object without transformation.

Fuzzy philosophy is just an excuse for not stating what the presumptions are. I think of it as either a lack of thorough thought. While it could be that someone hides the axioms of a system because they know those axioms are evil, I tend to think it more the former, though I could easily be convinced some hide the axioms because they know the evil they promulgate (think evolutionist here).

Have pity on my poor wife Jean ... she hit the nail on the head in her reply.

I would argue that you are more yourself now than you were then. You are the same person and yet you are not the same person.

Absolutely, we cannot define everything ... that is why in geometry the first thing to be discussed is undefined terms ... line, point, plane ... but even though they are undefined, we discuss what we mean by them without definition, so when we talk about them we have a sense of what is meant. Rigor means having a minimal set of undefined terms, and all other terms are defined in terms of them.

You can also look at it in terms of necessity and sufficiency. So long as no necessary components or qualities are removed or as long as one sufficient cause remains you still have the named event or object, in this case an orange.

__________________
Robert K. "Kelly" Brumbelow
In Inquirer's class at Grace Presbyterian (PCA) Cedartown, GA
Cedartown, Georgia

Dear Lord and Father of mankind, Forgive our foolish ways;
Reclothe us in our rightful mind, In purer lives Thy service find,
In deeper reverence, praise. - John Greenleaf Whittier 1807-1892

Then what is the isometry that connects the two? Being fuzzy is just not a good thing. Being fuzzy let Jonestown happen. Being fuzzy is allowing "No doctrine but Christ" yet not realizing in saying that, it espouses a doctrine.

Part of the problem is that we don't define person, and what that means ... we don't even discuss it much for fear of being heretics. (Do you want to make an assertion that is found later to be the equal of Arius or Pelegius?) Make no mistake, I find myself in the same position, but I certainly also know that I have changed. Only God is unchangeable, immortal, invisible, the only God, wise, eternal, etc. We change. We are like the grass that is here one day and gone the next. A man changes his mind like a woman changes the sheets on a bed.

The philosopher talks about essence (or substance) without defining it. We acknowledge there is some use of the idea ("being of one substance with the Father is confessed weekly by many of orthodox (small "o") faith). Yet we have a very loose idea of what essence is. We only know that the substance of the God is different from the substance of the creation apart from the God/Man Jesus who took upon himself the substance of the creature in order to save us. For in Jesus, the substance of both God and Man are joined without conversion, composition or confusion. What we do not comprehend God accomplished.

-----Added 8/2/2009 at 10:22:39 EST-----

A triangle is a polygon (i.e., a closed planar shape consisting of segments such that all segments intersect at both endpoints with exactly two other segments and have no other points in common) with three side.

An equilateral triangle and a right triangle are both triangles, but they are not ever congruent (they are not isometries of each other). That two polygons have three sides is sufficient to prove they are indeed triangles, but it is insufficient to prove they are the same triangle.

If removing a part does not constitute a change, then cut the orange exactly in half, if either half is still the orange, then you have two oranges that are the same orange. Not what I would think even from a sensibility standpoint.

If an orange has part of the peel removed, is it the same orange? Only if we have an understanding of "same" for orange that defines it to be the same.

Yet, Brian, even in the change that I too acknowledge, there is a unity of person and a continuity that, we might say, is your "Brian-ness".

I do change, yes, but I also remain. I am not the same person who I was when I first believed, yet, in some way, I am still that person--there's a "Philip-ness" to me that (I would argue) will only grow as I become more like Christ.

I fail to see how your reply meshes in with my statement that you are replying to. This is because in no way do I see it responding to either necessary or sufficient qualities or causation. The closest I can come is to say that 1/2 of an orange is necessary for an orange but it is not sufficient. In fact 2 x 1/2 of oranges are necessary for an orange but still not sufficient as they could belong to different oranges, however if you had an orange and removed 1/2 of an orange it is no longer an orange as it does not meet the necessary conditions of being an orange.

If, for some strange reason, the quality of being green suddenly became sufficient for being an orange, then I would argue my van is now an orange as it has the colour green. This would still be true no matter how many times you halved it so long as each 1/2 maintained the quality "green". Fortunately however this is not the case and I can drive my van rather than eat it.

Yep. We change (usually) very slowly over time, and so we think of ourselves (and those that see us regularly) as being the same person. But I also have to think that someone that only knew us 30 years ago might not know us at all now if we but changed our names.

Some part of us ... I'm not willing to even suggest what ... is the same, or the promise of salvation is truly hollow. How could God save "me" if "me" doesn't exist 30 years from now. But I am left with something for which I do not know the isometry, and therefore it is without any basis. Sad situation.

Brian are you a Monist? Your reliance on the idea of euclidean isometry and disregard of the admittedly weaker, but more useful, path isometry in your statements is what has caused me to question you on this. Even dealing with n dimensional space you will never find any two objects or even the same object at two different points in time that are truly isometric and one of the axis of n space will be different, as a result euclidean isometry is really only useful in the hypothetical or ideal sense and not in general argumentation.

Well if you change from state "A" to state "B" then how could you remain the same person. I would say that although you are changing state, you are in some sense the same person that is changing over time were actions (both physical & spiritual are being applied to your person to conform you either to the image of Satan or Christ.