Intelligent Reasoning

Promoting, advancing and defending Intelligent Design via data, logic and Intelligent Reasoning and exposing the alleged theory of evolution as the nonsense it is. I also educate evotards about ID and the alleged theory of evolution one tard at a time and sometimes in groups

Wednesday, January 15, 2014

Nested Hiearchy's Defining Property- Summativity

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Summativity- The sum of all entities at one level of organization is equal to the sum of all entities at some other level- Knox "The use of hierarchies as organizational models of systematics" Biological Journal of the Linnean Society (1998), 63:1-49, page 8

For example in Linnean taxonomy*, ie a nested hierarchy, the Animal Kingdom consists of and contains all of the levels and entities below it. It is the sum of its parts.

Linnean Classification:
The standard system of classification in which every organism is assigned a kingdom, phylum, class, order, family, genus, and species. This system groups organisms into ever smaller and smaller groups (like a series of boxes within boxes, called a nested hierarchy).

Looking closer at the nested hierarchy of living organisms we have the animal kingdom. To be placed in the animal kingdom an organism must have all of the criteria of an animal:

All members of the Animalia are multicellular (eukaryotes), and all are heterotrophs (that is, they rely directly or indirectly on other organisms for their nourishment). Most ingest food and digest it in an internal cavity.

Animal cells lack the rigid cell walls that characterize plant cells. The bodies of most animals (all except sponges) are made up of cells organized into tissues, each tissue specialized to some degree to perform specific functions.
The next level (after kingdom) contain the phyla. Phyla have all the characteristics of the kingdom PLUS other criteria.

For example one phylum under the Kingdom Animalia, is Chordata.

Chordates have all the characteristics of the Kingdom PLUS the following:

Chordates are defined as organisms that possess a structure called a notochord, at least during some part of their development. The notochord is a rod that extends most of the length of the body when it is fully developed. Lying dorsal to the gut but ventral to the central nervous system, it stiffens the body and acts as support during locomotion. Other characteristics shared by chordates include the following (from Hickman and Roberts, 1994):

bilateral symmetry
segmented body, including segmented muscles
three germ layers and a well-developed coelom.
single, dorsal, hollow nerve cord, usually with an enlarged anterior end (brain)
tail projecting beyond (posterior to) the anus at some stage of development
pharyngeal pouches present at some stage of development
ventral heart, with dorsal and ventral blood vessels and a closed blood system
complete digestive system
bony or cartilaginous endoskeleton usually present.


The next level is the class. All classes have the criteria of the kingdom, plus all the criteria of its phylum PLUS the criteria of its class.

This is important because it shows there is a direction- one of additive characteristics. That is how containment is kept and summativity is met.

(NOTE: evolution does NOT have a direction. Characteristics can be lost as well as gained. And characteristics can remain stable.)


An Army can also be put into a nested hierarchy- with the Army example we would be classifying the US Army which is broken up into Field Armies, which contain and consist of Corps, which contain and consist of Divisions, which contain and consist of Brigades, which contain and consist of Battalions, which contain and consist of Companies, which contain and consist of Platoons, which contain and consist of Squads & Sections. Squads and sections contain and consist of soldiers. Each level, down to the soldier, has a well defined role and place in the scheme.

The Army consists of and contains, soldiers- it exhibits summativity. Andy Schueler didn't even know what summativity was.

See also the summary of the principles of hierarchy theory:

The Hierarchy theory is a dialect of general systems theory. It has emerged as part of a movement toward a general science of complexity. Rooted in the work of economist, Herbert Simon, chemist, Ilya Prigogine, and psychologist, Jean Piaget, hierarchy theory focuses upon levels of organization and issues of scale. There is significant emphasis upon the observer in the system.

Hierarchies occur in social systems, biological structures, and in the biological taxonomies. Since scholars and laypersons use hierarchy and hierarchical concepts commonly, it would seem reasonable to have a theory of hierarchies. Hierarchy theory uses a relatively small set of principles to keep track of the complex structure and a behavior of systems with multiple levels. A set of definitions and principles follows immediately:

Hierarchy: in mathematical terms, it is a partially ordered set. In less austere terms, a hierarchy is a collection of parts with ordered asymmetric relationships inside a whole. That is to say, upper levels are above lower levels, and the relationship upwards is asymmetric with the relationships downwards.

Hierarchical levels: levels are populated by entities whose properties characterize the level in question. A given entity may belong to any number of levels, depending on the criteria used to link levels above and below. For example, an individual human being may be a member of the level i) human, ii) primate, iii) organism or iv) host of a parasite, depending on the relationship of the level in question to those above and below.

Level of organization: this type of level fits into its hierarchy by virtue of set of definitions that lock the level in question to those above and below. For example, a biological population level is an aggregate of entities from the organism level of organization, but it is only so by definition. There is no particular scale involved in the population level of organization, in that some organisms are larger than some populations, as in the case of skin parasites.

Level of observation: this type of level fits into its hierarchy by virtue of relative scaling considerations. For example, the host of a skin parasite represents the context for the population of parasites; it is a landscape, even though the host may be seen as belonging to a level of organization, organism, that is lower than the collection of parasites, a population.

The criterion for observation: when a system is observed, there are two separate considerations. One is the spatiotemporal scale at which the observations are made. The other is the criterion for observation, which defines the system in the foreground away from all the rest in the background. The criterion for observation uses the types of parts and their relationships to each other to characterize the system in the foreground. If criteria for observation are linked together in an asymmetric fashion, then the criteria lead to levels of organization. Otherwise, criteria for observation merely generate isolated classes.

The ordering of levels: there are several criteria whereby other levels reside above lower levels. These criteria often run in parallel, but sometimes only one or a few of them apply. Upper levels are above lower levels by virtue of: 1) being the context of, 2) offering constraint to, 3) behaving more slowly at a lower frequency than, 4) being populated by entities with greater integrity and higher bond strength than, and 5), containing and being made of - lower levels.

Nested and non-nested hierarchies: nested hierarchies involve levels which consist of, and contain, lower levels. Non-nested hierarchies are more general in that the requirement of containment of lower levels is relaxed. For example, an army consists of a collection of soldiers and is made up of them. Thus an army is a nested hierarchy. On the other hand, the general at the top of a military command does not consist of his soldiers and so the military command is a non-nested hierarchy with regard to the soldiers in the army. Pecking orders and a food chains are also non-nested hierarchies.

To achieve summativity the criteria "consist of and contain" must be met. NOTE- A parent population does NOT consist of nor contain it's daughter populations. That is why any tree of life is not a nested hierarchy.

69 Comments:

  • At 12:05 PM, Blogger Zachriel said…

    Joe G: That is why any tree of life is not a nested hierarchy.

    The leaves on the tree are a nested hierarchy.

     
  • At 1:26 PM, Blogger Joe G said…

    That doesn't make any sense at all.

    When a nested hierarchy is laid out like a branching pattern, the whole thing is the nested hierarchy.

    Zachriel is trying to say that only the base level is a nested hierarchy.

    SUMMATIVITY- Zachriel is still cannot grasp summativity.

     
  • At 1:40 PM, Blogger Zachriel said…

    Joe G: When a nested hierarchy is laid out like a branching pattern, the whole thing is the nested hierarchy.

    The leaves on each branch form a nested hierarchy.

     
  • At 1:52 PM, Blogger Joe G said…

    Zachriel:
    The leaves on each branch form a nested hierarchy.

    Not according to the sources I cited. But go ahead and try to make your case as opposed to just repeating yourself.

     
  • At 2:12 PM, Blogger Zachriel said…

    "The sum of entities at one level at one level of organization is equal to the sum of entities at some other level"

    Consider a simplified tree, leaf, twig, branch, limb, trunk. Each leaf is associated with a twig, each twig with a branch, each branch with a limb, each limb with the trunk.

    The leaves on a twig form a set. The leaves on each of the twigs on a branch form a set, such that the sum of leaves on the twigs associated with a branch is the same as the leaves associated with the branch.

    The leaves associated with a branch on a limb form a set, such that the sum of leaves on the branches associated with the limb is the same as the leaves associated with the limb.

    The leaves associated with a limb on the trunk form a set, such that the sum of leaves on the limbs associated with the trunk is the same as the leaves associated with the trunk.

     
  • At 2:26 PM, Blogger Joe G said…

    Umm the nested hierarchy has to include the branches and trunk- summativity.

    In any tree of life there would be organisms on the branches and trunk.

    The organisms at the leaves do not add up to the organisms on the branches. The organisms on the branches do not consist of nor contain the organisms at the leaves.

     
  • At 9:27 AM, Blogger Zachriel said…

    We had commented, but it never appeared.

    Joe G: Umm the nested hierarchy has to include the branches and trunk- summativity.

    The leaves that are associated with each branch are equal to the leaves that are associated with the limb.

    Joe G: In any tree of life there would be organisms on the branches and trunk.

    We didn't mention anything about "organisms".

     
  • At 9:53 AM, Blogger Joe G said…

    Your comment never made it to moderation.

    ?The leaves that are associated with each branch are equal to the leaves that are associated with the limb.

    So what? You quoted Knox and he was talking about multiple levelks. Leaves only reside on one level.

    We didn't mention anything about "organisms".

    Umm YOU posted on the tree of life and the tree of life is composed of organisms.

     
  • At 9:55 AM, Blogger Joe G said…

    Umm the nested hierarchy has to include the branches and trunk- summativity.

    Zachriel:
    The leaves that are associated with each branch are equal to the leaves that are associated with the limb.

    Non-sequitur. Try again...

     
  • At 10:02 AM, Blogger Zachriel said…

    Joe G: Non-sequitur.

    It's hardly a non sequitur. The definition requires it.

     
  • At 10:16 AM, Blogger Joe G said…

    It's a non-sequitur because it does not follow what I said. It isn't a response to what I said.

    try again...

     
  • At 10:20 AM, Blogger Zachriel said…

    It's precisely what we answered.

    A limb is associated with a set of branches. Each branch is associated with a unique set of leaves. The set union (sum) of the set of leaves of the branches is equal to the set of leaves associated with the limb.

     
  • At 10:23 AM, Blogger Joe G said…

    Umm the nested hierarchy has to include the branches and trunk- summativity.

    A limb is associated with a set of branches.

    So what? That still isn't a response to what I said.

    Each branch is associated with a unique set of leaves. The set union (sum) of the set of leaves of the branches is equal to the set of leaves associated with the limb.

    Again- so what? That still isn't a response to what I said.

    It's as if you have no idea what a tree of life entails and you are proud of it.

     
  • At 10:26 AM, Blogger Zachriel said…

    This is your statement:

    Joe G: Umm the nested hierarchy has to include the branches and trunk- summativity.

    We stated that the leaves form a nested hierarchy. The branches and trunk are not part of the nested hierarchy, if that is your confusion.

     
  • At 10:28 AM, Blogger Joe G said…

    Zachriel:
    We stated that the leaves form a nested hierarchy.

    And I demonstrated that you are wrong. Leaves are only ONE level and nested hierarchies require multiple levels.

    The branches and trunk are not part of the nested hierarchy,

    Why not? In a tree of life the twigs, branches, limbs and trunk all represent organisms and they have to be included.

    Again the confusion is all yours.

     
  • At 10:29 AM, Blogger Joe G said…

    Zachriel showed up earlier today trying to refute something I said wrt any tree of life not producing a nested hierarchy. Zachriel sed that the leaves form the nested hierarchy and to try to support his case he provided the quote in that thread's OP by Eric Knox.

    Unfortunately for Zachriel Knox was talking about multiple levels and the leaves on a tree only occupy one. Perhaps he realized that after he posted it and that is why he ran away.

    Also, as I pointed out to Zachriel, with any tree of life organisms occupy the twigs, branches and trunk of the tree. That is the whole point of the tree- to show diverging lines of descent with modification...

     
  • At 10:33 AM, Blogger Zachriel said…

    Joe G: Leaves are only ONE level and nested hierarchies require multiple levels.

    Leaves are grouped into levels of organization per the definition you provided.

    Joe G: Why not?

    Because that's the claim you're arguing against.

    Z: The leaves on the tree are a nested hierarchy.

     
  • At 10:36 AM, Blogger Joe G said…

    Zachriel:
    Leaves are grouped into levels of organization per the definition you provided.

    So you don't have any clue at all and you are just spewing shit.

    With a tree of life lhe leaves occupy one level. Twigs occupy another level. Branches yet another and the trunk yet another.

    IOW you don't know what you are talking about, as usual.

     
  • At 10:37 AM, Blogger Joe G said…

    The branches and trunk are not part of the nested hierarchy,

    Why not? In a tree of life the twigs, branches, limbs and trunk all represent organisms and they have to be included.

    Because that's the claim you're arguing against.

    It's that claim that proves that you are clueless.

     
  • At 10:38 AM, Blogger Joe G said…

    Zachriel showed up earlier today trying to refute something I said wrt any tree of life not producing a nested hierarchy. Zachriel sed that the leaves form the nested hierarchy and to try to support his case he provided the quote in that thread's OP by Eric Knox.

    Unfortunately for Zachriel Knox was talking about multiple levels and the leaves on a tree only occupy one. Perhaps he realized that after he posted it and that is why he ran away.

    Also, as I pointed out to Zachriel, with any tree of life organisms occupy the twigs, branches and trunk of the tree. That is the whole point of the tree- to show diverging lines of descent with modification...


     
  • At 10:41 AM, Blogger Zachriel said…

    Joe G: With a tree of life lhe leaves occupy one level.

    It's organizational level.

    Joe G: In a tree of life the twigs, branches, limbs and trunk all represent organisms and they have to be included.

    Perhaps, but that's not the claim you took issue with.

     
  • At 10:46 AM, Blogger Joe G said…

    With a tree of life lhe leaves occupy one level.

    It's organizational level.

    It's the bottom level of organization. There have to be other levels above it.

    : In a tree of life the twigs, branches, limbs and trunk all represent organisms and they have to be included.

    Perhaps, but that's not the claim you took issue with.

    Perhaps? It refutes your claim about leaves being the nested hierarchy.

    Are you really that dim?

     
  • At 10:48 AM, Blogger Zachriel said…

    Joe G: It's the bottom level of organization. There has to be other levels above it.

    They are organized by branch and limb. The set of leaves on a limb is comprised to sets of leaves on the branches associated with that limb. The limb-set is 'higher' than the branch-sets.

     
  • At 10:50 AM, Blogger Joe G said…

    It's the bottom level of organization. There has to be other levels above it.

    They are organized by branch and limb.

    You just refuted your original claim. Well done.

     
  • At 10:58 AM, Blogger Zachriel said…

    Joe G: You just refuted your original claim. Well done.

    Not at all. The various sets only include leaves, but the organization is by branch and limb.

     
  • At 11:01 AM, Blogger Joe G said…

    : You just refuted your original claim. Well done.

    Not at all.

    You definitely refuted your original claim. Perhaps you don't think it was well done but you definitely did it.

    The various sets only include leaves,

    Not in a nested hierarchy. Phyla make up sets and Phyla do not occupy the leaves- only the species do- that is in a nested hierrachy.

    With a tree of life organisms occupy every part of the tree. Your failure is refusing to grasp that fact.

     
  • At 11:05 AM, Blogger Zachriel said…

    Here's a very simple tree.

    http://www.zachriel.com/blog/eukarya1.png

    There are three leaves. For convenience, they are label with pictures of a a tree, a mushroom, and a sponge. Notice the mushroom and sponge group together. So we have this:

    {tree, {mushroom, sponge}}

    a simple nested hierarchy. We did not include the branches themselves, only the leaves.

     
  • At 11:09 AM, Blogger Zachriel said…

    Joe G: Not in a nested hierarchy.

    "an army consists of a collection of soldiers and is made up of them"

    Joe G: Phyla make up sets and Phyla do not occupy the leaves- only the species do- that is in a nested hierrachy.

    A phyla is a set, a set of leaves.

     
  • At 11:33 AM, Blogger Zachriel said…

    Joe G: Not in a nested hierarchy.

    "an army consists of a collection of soldiers and is made up of them"

    Joe G: Phyla make up sets

    Phyla are sets, just like the leaves on a limb are a set.

    Here's a very simple example.

    http://zachriel.com/blog/eukarya1.png

    The leaves are labeled for convenience; tree, mushroom, sponge. If we group by branch, we have {tree, {mushroom, sponge}}, a simple nested hierarchy. Noticed we don't include the branches themselves in the nested hierarchy, but if you like, we can label them as eukaryota and opisthokonta. When we talk about the opisthokonts, we are referring to the leaves on the branch that includes mushroom and sponge. When we are talking about the branch with the tree, we may also call it plantae, which only has one leaf. When we talk about eukaryotes, we are referring to the leaves on the limb that includes tree, mushroom and sponge.

    Opisthokonta = "mushroom, sponge"
    Plantae = "tree"
    Eukaryota = "tree, mushroom, sponge"

    Opisthokona ⊂ Eukaryota
    Plantae ⊂ Eukaryota
    Plantae ∪ Opisthokona = Eukaryota

     
  • At 11:36 AM, Blogger Joe G said…

    Zachriel's original claim:

    The leaves on the tree are a nested hierarchy.

    Zachriel refuted that claim with:

    They are organized by branch and limb.

    That means the nested hierarchy includes the branches and limbs and therefor is NOT just the leaves.

     
  • At 11:37 AM, Blogger Joe G said…

    {tree, {mushroom, sponge}}

    a simple nested hierarchy.


    In what way is that a nested hierarchy? Please be specific.

     
  • At 11:38 AM, Blogger Joe G said…

    A phyla is a set, a set of leaves.

    The leaves are species. A tree of life doesn't allow for phyla.

    As I said you have no clue at all.

     
  • At 11:40 AM, Blogger Joe G said…

    The leaves are labeled for convenience; tree, mushroom, sponge. If we group by branch, we have {tree, {mushroom, sponge}}, a simple nested hierarchy.

    In what way is it a nested hierrachy? You have not defined anything. You are obviously just a troll.

     
  • At 11:46 AM, Blogger Joe G said…

    If the leaves on the tree are organized by branch and limb, as Zachriel said, that means those branches and limbs are part of the nested hierarchy and that refutes Zachriel's original claim The leaves on the tree are a nested hierarchy.

    Also Zachriel is missing the point that with a tree of life organisms occupy more than the leaves.

     
  • At 11:51 AM, Blogger Zachriel said…

    Joe G: You are obviously just a troll.

    Can't help yourself, can you?

     
  • At 11:56 AM, Blogger Joe G said…

    Obvioulsy YOU can't help yourself.

    1- You have yet to deal with the argument that you are attempting to refute

    2- You refuted your own "argument"

    3- That evidence points to you being a troll

    So don't blame me for making the observation based on the evidence.

     
  • At 12:02 PM, Blogger Zachriel said…

    Joe G: Not in a nested hierarchy.

    "an army consists of a collection of soldiers and is made up of them"

    Joe G: Phyla make up sets

    Phyla are sets, just like the leaves on a limb are a set.

    Here's a very simple example.

    http://zachriel.com/blog/eukarya1.png

    The leaves are labeled for convenience; tree, mushroom, sponge. If we group by branch, we have {tree, {mushroom, sponge}}, a simple nested hierarchy. Noticed we don't include the branches themselves in the nested hierarchy, but if you like, we can define them as eukaryota and opisthokonta. When we talk about the opisthokonts, we are referring to the leaves on the branch that includes mushroom and sponge. When we are talking about the branch with the tree, we may also call it plantae, which only has one leaf. When we talk about eukaryotes, we are referring to the leaves on the limb that includes tree, mushroom and sponge.

    Opisthokonta = "mushroom, sponge"
    Plantae = "tree"
    Eukaryota = "tree, mushroom, sponge"

    Opisthokona ⊂ Eukaryota
    Plantae ⊂ Eukaryota
    Plantae ∪ Opisthokona = Eukaryota

     
  • At 12:07 PM, Blogger Joe G said…

    Zachriel,

    Your picture does not represent a tree of life.

    Not only that it isn't a nested hierarchy as you have not defined anything.

     
  • At 12:08 PM, Blogger Joe G said…

    But all of that is moot because:

    If the leaves on the tree are organized by branch and limb, as Zachriel said, that means those branches and limbs are part of the nested hierarchy and that refutes Zachriel's original claim The leaves on the tree are a nested hierarchy.

    Also Zachriel is missing the point that with a tree of life organisms occupy more than the leaves.

     
  • At 12:09 PM, Blogger Joe G said…

    Also you have failed to even address the argument that you arectrying to refute. Your out-of-context quote just proves what I said about you.

     
  • At 12:10 PM, Blogger Zachriel said…

    Joe G: Your picture does not represent a tree of life.

    It's a tree with three leaves.

    Joe G: Not only that it isn't a nested hierarchy as you have not defined anything.

    Sure we did. We labeled the leaves with arbitrary names, then we grouped by branch and limb, giving the groups names, as follows:

    Opisthokonta = "mushroom, sponge"
    Plantae = "tree"
    Eukaryota = "tree, mushroom, sponge"

    Joe G: Zachriel said, that means those branches and limbs are part of the nested hierarchy and that refutes Zachriel's original claim The leaves on the tree are a nested hierarchy.

    No, if you look at the sets we defined, they only include the leaves.

     
  • At 12:17 PM, Blogger Joe G said…

    Your picture does not represent a tree of life.

    It's a tree with three leaves.

    It is NOT a tree of life. Therefor you are a loser for even bringing it up.

    : Not only that it isn't a nested hierarchy as you have not defined anything.

    Sure we did. We labeled the leaves with arbitrary names

    Arbitrary names are NOT definitions.

    No, if you look at the sets we defined, they only include the leaves.

    You didn't define anything- names are not definitions and yoiurs is not a nested hierarchy. And yours is not a tree of life.

    You lose

     
  • At 1:22 PM, Blogger Zachriel said…

    Joe G: It is NOT a tree of life.

    That wasn't our claim.

    Z: The leaves on a tree are a nested hierarchy.

    Joe G: names are not definitions and yoiurs is not a nested hierarchy

    Giving something a name is a definition.

    We labeled the leaves with arbitrary names, then we grouped by branch and limb, giving the groups names, as follows:

    Opisthokonta = "mushroom, sponge"
    Plantae = "tree"
    Eukaryota = "tree, mushroom, sponge"

    Please note that
    Opisthokona ⊂ Eukaryota
    Plantae ⊂ Eukaryota
    Opisthokona ∩ Plantae = ∅
    Plantae ∪ Opisthokona = Eukaryota

    The last is called summativity.

     
  • At 2:21 PM, Blogger Zachriel said…

    Joe G: Arbitrary names are NOT definitions.

    definition, a statement of the meaning of a word or word group or a sign or symbol.

    Here's a simple mathematical definition of the symbol P: Let P be a set such that P = {red, green, blue}.

     
  • At 4:36 PM, Blogger Joe G said…

    Thanks for proving that you did NOT provide any definitions.

     
  • At 4:38 PM, Blogger Joe G said…

    It is NOT a tree of life.

    That wasn't our claim.

    Your entire "argument" was that a tree of life produces a nested hierarchy.

    Giving something a name is a definition.

    Only to a moron.

    Plantae ∪ Opisthokona = Eukaryota

    The last is called summativity.


    But that has nothing to do with your original claim.

     
  • At 4:41 PM, Blogger Joe G said…

    Zachriel,

    When are you going to address what I said in the OP? Your first entrance to this thread you took my quote out-of-context.

    So what the fuck is your purpose here?

     
  • At 3:54 PM, Blogger Zachriel said…

    Joe G: Your entire "argument" was that a tree of life produces a nested hierarchy.

    What we said was The leaves on the tree are a nested hierarchy.

    Joe G: But that has nothing to do with your original claim.

    Sure it does. Here it is again:

    Opisthokonta = "mushroom, sponge"
    Plantae = "tree"
    Eukaryota = "tree, mushroom, sponge"

    Please note that
    Opisthokona ⊂ Eukaryota
    Plantae ⊂ Eukaryota
    Opisthokona ∩ Plantae = ∅
    Plantae ∪ Opisthokona = Eukaryota

     
  • At 7:56 PM, Blogger Joe G said…

    What we said was The leaves on the tree are a nested hierarchy.

    And you refuted that argument.

    But that has nothing to do with your original claim.

    Sure it does. Here it is again:

    No, it doesn't.

    Opisthokonta = "mushroom, sponge"
    Plantae = "tree"
    Eukaryota = "tree, mushroom, sponge"


    Yes, Linnean Classification forms a nested hierarchy. And Linnean Classification dpesn't have anything to do with a tree of life and it definitely doesn't support your refuted claim that "The leaves on the tree are a nested hierarchy. "

    IOW you are totally full of shit.

     
  • At 8:13 PM, Blogger Joe G said…

    Zachriel 1:
    The leaves on the tree are a nested hierarchy.

    Zachriel 2:
    We labeled the leaves with arbitrary names, then we grouped by branch and limb, giving the groups names, as follows:

    If the leaves are grouped by branch and limb then it is a GIVEN that the leaves on the tree do NOT form a nested hierarchy because the branch and limbs are not leaves and are part of the nested hierarchy.

    And in any tree of life the twigs, branches, limbs and trunk are organisms and as such have to be included. IOW only a dishonest moron would try to leave them out. (pun intended)

     
  • At 8:12 AM, Blogger Zachriel said…

    Joe G: Linnean Classification forms a nested hierarchy.

    Yes, it does. So do the leaves of a tree when organized by branch and stem.

    Joe G: If the leaves are grouped by branch and limb then it is a GIVEN that the leaves on the tree do NOT form a nested hierarchy because the branch and limbs are not leaves and are part of the nested hierarchy.

    No. Being organized by branch and stem doesn't mean the branch and stem are part of the sets, any more than being classified by scale and hair means scale and hair are part of the sets.

     
  • At 8:25 AM, Blogger Joe G said…

    Zachriel:
    So do the leaves of a tree when organized by branch and stem.

    Reference please. No one believes you so your say-so is meaningless.

    If the leaves are grouped by branch and limb then it is a GIVEN that the leaves on the tree do NOT form a nested hierarchy because the branch and limbs are not leaves and are part of the nested hierarchy.

    No.

    You are wrong Zachriel.

    Being organized by branch and stem doesn't mean the branch and stem are part of the sets,

    Yes it does.

    any more than being classified by scale and hair means scale and hair are part of the sets.

    Scale and hair are charactertistics. Leaves are NOT charcterized by their position on the tree- that is NOT a defining charactertistic.

     
  • At 8:27 AM, Blogger Joe G said…

    By Zachriel's "logic", with Linnean Classification, nothing above species is part of a set. And we know that is incorrect because Phyla make up a set.

    You lose Zachriel. Stop being an ignorant little whining baby

     
  • At 8:36 AM, Blogger Zachriel said…

    Joe G: Leaves are NOT charcterized by their position on the tree- that is NOT a defining charactertistic.

    We just defined it so: The leaves of a tree form a nested hierarchy when grouped by branch and stem.

    Joe G: By Zachriel's "logic", with Linnean Classification, nothing above species is part of a set.

    You are very confused about sets.

    Mammals = {rabbits, bears}
    Vertebrates = {Mammals, Fish}

    Having defined mammals as a set, we can now use the label to refer to the set. So, are Mammals ⊂ Vertebrates? Of course. Mammals are a set of species. Vertebrates are a set of species, including the species in the set Mammals.

     
  • At 8:36 AM, Blogger Zachriel said…

    Joe G: Stop being an ignorant little whining baby

    You just can't help yourself.

     
  • At 8:47 AM, Blogger Joe G said…

    No, I can't help pointing out the facts.

     
  • At 8:50 AM, Blogger Joe G said…

    Zachriel:
    We just defined it so: The leaves of a tree form a nested hierarchy when grouped by branch and stem.

    All that does is prove that you are totally ignorant of nested hierarchies.

    By Zachriel's "logic", with Linnean Classification, nothing above species is part of a set.

    You are very confused about sets.

    Coming from a cowardly shit like you that means nothing.

    Having defined mammals as a set, we can now use the label to refer to the set. So, are Mammals ⊂ Vertebrates? Of course. Mammals are a set of species. Vertebrates are a set of species, including the species in the set Mammals.

    Again with the Linnean Classification which has nothing to do with a tree of life.

    Zachriel, it is obvious that you are just a bloviating ass who couldn't support its claims if its life depended on it.

     
  • At 8:52 AM, Blogger Joe G said…

    And Zachriel- it is very telling that you refuse to provide a refernce to support your claim.

     
  • At 8:57 AM, Blogger Zachriel said…

    Joe G: Again with the Linnean Classification which has nothing to do with a tree of life.

    Your claim was that if we classify leaves by branch and stem, that the branch and stem become part of the nested hierarchy. That's like saying that if we classify organisms by hair and scale, that hair and scale become part of the nested hierarchy.

    Joe G: it is very telling that you refuse to provide a refernce to support your claim.

    We used the definition you provided.

    Joe G: Coming from a cowardly shit like you that means nothing... it is obvious that you are just a bloviating ass

    You just can't help yourself.

     
  • At 9:01 AM, Blogger Joe G said…

    Zachriel,

    Find valid support for your claim or stop making it.

    Your claim was that if we classify leaves by branch and stem, that the branch and stem become part of the nested hierarchy.

    My claim is that your spewage is total unsupported nonsense.

    I also claim that the way you are "classifying"/ "defining" leaves proves that you are an ignorant ass. THAT is an observation.

     
  • At 9:03 AM, Blogger Joe G said…

    In order for tree to be a nested hierrachy the entire tree has to be in that nested hierarchy. Period, end of story.

    Leaves on a tree do not form a nested hierarchy and that is per Dr Allen.

     
  • At 9:08 AM, Blogger Joe G said…

    We used the definition you provided.

    And yet I didn't provide any definitions.

    YOU just can't help yourself

     
  • At 9:10 AM, Blogger Zachriel said…

    Joe G: Find valid support for your claim or stop making it.

    We used the definition you provided.

    Joe G: My claim is that your spewage is total unsupported nonsense... I also claim that the way you are "classifying"/ "defining" leaves proves that you are an ignorant ass. THAT is an observation.

    You apparently can't help yourself.

     
  • At 9:12 AM, Blogger Joe G said…

    Zachriel:
    We used the definition you provided.

    I didn't provide any definition. You are lying because you just can't help yourself.

     
  • At 9:19 AM, Blogger Zachriel said…

    Joe G: I didn't provide any definition.

    Sure you did. You cited Knox, and then stated "To achieve summativity the criteria 'consist of and contain' must be met."

    But if you prefer, you can provide your definition explicitly in your next comment.

     
  • At 9:27 AM, Blogger Joe G said…

    Zachriel,

    That definition does NOT support your claim. So either you are just a freak and asshole or you are too ignorant to discuss anything.

     
  • At 9:28 AM, Blogger Joe G said…

    OK to recap- Zachriel shows up, takes a quote out-of-context and then refuses to provide a reference to support his claim.

    Typical cowardly Virginian

     
  • At 12:03 PM, Blogger Zachriel said…

    Joe G: That definition does NOT support your claim.

    Well, at least you now admit that you did provide a definition.

     
  • At 12:35 PM, Blogger Joe G said…

    Context is important. And in the context of what was being discussed, I did NOT provide any definitions.

    So thank you for continuing to prove that you are an asshole.

     

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