Talk:Quantity

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Contents 1 Substantial revision 2 Introduction 3 Quantitative Relationsips 4 Quantity in mathematics 5 Let's try to reach agreement on a definition, as a first step 6 Magnitudes 7 Points which need to be addressed 8 Much/muchly

[edit] Substantial revision

I have made a substantial revision to previous version.

[AA: which we are trying to revise properly in a cooperative spirit].

I think intro needs to be clear, to the point, and orient the reader to the main points. There were a number of uncited statments and the essence of key points appeared to depend heavily on Aristotle, whereas there have been major developments since!

[AA: we shouldn't undervalue the background knowledge on quantity].

I have omitted certain statements that were either very difficult to follow or erroneous as formulated: e.g. the statement that units are not divisible is not correct unqualified - units of continuous quantity are divisible, units of 'multitudes' are not (e.g. an applie is no longer a unit in a count of applies if sliced in half). I am open to discussion and debate on these points but I strongly urge citations to justify the re-introduction of omissions. The article still needs further revision and omissions, but this revision is a start. Holon 14:00, 21 February 2006 (UTC)

[edit] Introduction

HOLON insists on such an intro: In science and philosophy a quantity is a property or relation that exists in a range of magnitudes, such as the range of all lengths. [AA: in reality (as a matter of fact), quantity is a basic property of things that exists as magnitudes and multitudes]. All the following is irrelevant to introduction or just defective and unverified: <Examples of quantitative properties are mass, time, distance, heat, and angular separation.> [ AA: in fact, the cases of quantitative properties are both physical quantities and mathematical quantities, as well as numbers].

In classical terms, two magnitudes of a continuous quantity stand in relation to one another as ratios which, in turn, are real numbers. Such continuous quantities possess a particular structure, which was first explicitly characterized by Hölder (1901) as a set of axioms which define such features as identites and relations between mangitudes.[AA comments: unverified statement]. The term quantity may also refer to a multitude such as a number of apples or sub-atomic particles [AA comment: this property must be included in the definition, not mentioned at the end]

AZAMAT included the following in intro: "Commonly, quantity is viewed as the state of being much, or the basic property of things existing as magnitudes or multitudes." Quantity is not the basic property of things existing as magnitudes or multitudes. A given thing may have many properties that are quantitative, such as mass, volume, charge and so on. Quantity is a type of property that exists in a range of magnitudes. [right is Quantity is a type of property existing as magnitude and multitude]. Azamat also included the following in intro: "Of entities which pertain to quantities, some are such by their inner nature (as number), while others are functioning as states (properties, dimensions, attributes) and modifications like as heavy and light, long and short, broad and narrow, small and great, or much and little." The statement: "of entities which pertain to quantities ..." is confusing -- entities may possess quantitative properties, but it is unclear what is meant by entities which pertain to quantities. Is this supposed to mean abstract entities which are quantities?? [read as: of things which pertain to quantities] In what sense do they 'function as states'? [As STATES of Substances or Objects]. I have replaced the introduction, [worsening it]. Please discuss these changes: they do not enhance the article. Holon 12:23, 23 February 2006 (UTC)

Various sections other than the introduction are also unclear, but I have not had time to make comments. I will do so soon. [AA: don't do anything, before discussion]. The article must be balanced. Quantity is important in science, not only philosophy. Regards. Holon 10:44, 24 February 2006 (UTC)

I tried working with some ideas I had and I got this for an intro:

"Quantity refers to number or amount as a property of abstract or concrete objects. In modern thinking it is commonly compared with the notion of quality. In the case of abstract objects, quantity and relationships between quantities have mathematical foundations. With concrete objects, quantities are measurements or observations of physical objects or systems, such as position measuring relative distances or temperature measuring the average energy of particles’ speed in a system.

In mathematics, quantity is essentially another term for number. Numbers are said to be discrete or continuous (see reals/real numbers/continuum). Numbers can also be further characterized by certain notable subsets of real numbers, the rational numbers being an example. In certain contexts quantities are grouped together in ways like vectors, matrices, tensors, sequences, and more generally as sets."

As I see there is a somewhat heated debate on what to have in the intro (the current one seems to me unintelligible), I'll leave my ideas for everyone else to work with, so feel free use it any way. Tachikoma's All Memory 04:20, 15 March 2007 (UTC)

[edit] Quantitative Relationsips

I omitted the section due to problems with the following:

There are three sorts of relationships between different types of quantities, namely ratio, rate, and scale. The ratio follows the classic definition of Euclid and expressed as a quotient. The ratio is always between two quantities of the same kind, i.e., between commensurable magnitudes or commensurable multitudes.

Firstly, in what sense is scale a relationship? [AA: there are two senses of 'scale', as a relative magnitude or as a proportion, the ratio between the size of something and its representation, we say the scale of mapping. Secondly, stating that relationships are always between quantities of the same kind is problematic. F=MA implies M=F/A which is a ratio of two different types of quantities.

[AA comment: it is a ratio (kindly don't mix with relationships generally), which is between commensurable quantities; while A is a rate (of increase of velocity].

Although I happen to agree a case can be made for the contention, it is not a simple issue and needs to be better explained and justified to say the least.

[AA: the issue is not really so complicated].

Thirdly, on what basis is it claimed there are three sorts of relationship? To use the same example, what about does F=MA? (rate is one relationship involved, but not the only one)

[AA: please don't mix the ratio, the relative magnitudes of commensurable quantities, with the rate, a magnitude related to a time unit].

Lastly, although this could be fixed, the use of colons and semicolons in the subsequent lists was also of a poor standard. Holon 05:15, 25 February 2006 (UTC) [AA: also let's edit the content in the Microsoft word editor, not on-line, for typos may appear].

[edit] Quantity in mathematics

I would appreciate comment on this section -- I think it needs serious attention if it is to remain in the article. For example, the following statement is in need a lot of work: The essential part of mathematical quantities is made up with a collection variables each assuming a set of values and coming as scalar, vectors, or tensors, and functioning as infinitesimal, arguments, independent or dependent variables, or random and stochastic quantities. Why not just say quantities in mathematics can be scalars, vectors or tensors?

[AZAMAT: in mathematics, there are numerical quantities, variable quantities, and constant quantities. Scalars, vectors, and tensors are just sorts of variable quantities]

The use of the term functioning is very confusing given it appears the text refers in part to functions. Why not just say, for example, that in mathematics, a quantity may be expressed as a function of one or more other quantities? Holon 09:04, 25 February 2006 (UTC)

(Talks to self: Remember WP:CIVIL, remember WP:CIVIL.)

I can assert, without fear of contradiction by mathematicians, that this section is neither mathematics nor can easily be interpreted to refer to mathematics. To forstall attempts to impune my intelligence, I should let you know that my IQ was measured at over 160. But this shouldn't be necessary. The distinction between "magnitude" and "multitude" is real (pun intended), but not well expressed. As for scalars, vectors, and tensors -- although I don't think a vector or tensor can be a "quantity", the present state of the article and one of the comments above has conflated the dimensionality of the output (scalar, vector, tensor), with the dimensionality of the input (scalar, scalar field aka function). Arthur Rubin | (talk) 18:01, 25 February 2006 (UTC)

On second thought -- are you (AA) referring to vectors and tensors as representing the value of the corresponding multilinear form? That might make them "quantities". However, a line or line segment is still not a quantity, in reference to the geometry example. Arthur Rubin | (talk) 18:10, 25 February 2006 (UTC)

[edit] Let's try to reach agreement on a definition, as a first step

Azamat, let’s focus on some of the points and how we might best express them, Okay?

In science and philosophy a quantity is a property or relation that exists in a range of magnitudes, such as the range of all lengths.

AA: in reality, quantity is a basic property of things that exists as magnitudes and multitudes

In what reality, according to whom or what criteria? Reality is a theory-laden term. Would you please provide examples of things that exist as magnitudes and multitudes. I think doing so may help to clarify a pivotal point so we can move on.

AA: right is Quantity is a type of property existing as magnitude and multitude

I agree -- quantity is a kind of property which exists as magnitude or multitude -- so hopefully we can clarify the problem and agree on a way to express the definition.

Such continuous quantities possess a particular structure, which was first explicitly characterized by Hölder (1901) as a set of axioms which define such features as identites and relations between mangitudes.

AA comments: unverified statement, )

Azamat, please read the text carefully: the statement is clearly cited.

I mean a public accessibility of the reference.

Let's focus on points of difference first, see if we can agree. Later on, if necessary we may need to agree to disagree on certain points and to each put alternative points of view across.Holon 03:14, 26 February 2006 (UTC)

Update. AA, I have attempted to merge our introductions as a starting point. On a specific point, a relation such as an angle (e.g. between two pieces of metal) is a fundamental kind of quantity, so I have retained this in the introduction (citation if you wish). I think we need to clarify quantity in mathematics before even trying to include reference to it in the intro, although some reference is of course implied as things stand. Holon 09:44, 26 February 2006 (UTC)

It is a good try but still doesn't impress as a part of feature article, and i feel some discomfort with its logical coherency. Consider for your attention or revision the following allighment of both intro with a minimum disturbance of the inner logic of both parts.

Quantity is a kind of property which exists as magnitude or multitude. It is among the basic classes of things along with quality, substance, change, and relation. Quantity was first introduced as quantum, an entity having quantity. Being a fundamental term, quantity is used to refer to any type of quantitative properties or attributes of things. Some quantities are such by their inner nature (as number), while others are functioning as states (properties, dimensions, attributes) of things like as heavy and light, long and short, broad and narrow, small and great, or much and little. Two basic divisions of quantity, magnitude and multitude (or number), imply the principal distinction between continuity (continuum) and discontinuity. Under the names of multitude come what is discontinuous and discrete and divisible into indivisibles, all cases of collective nouns: army, fleet, flock, government, company, party, people, chorus, crowd, mess, and number. Under the names of magnitude come what is continuous and unified and divisible into divisibles, all cases of non-collective nouns: the universe, matter, mass, energy, liquid, material, animal, plant, tree. Along with analyzing its nature and classification, the issues of quantity involve such closely related topics as the relation of magnitudes and multitudes, dimensionality, equality, proportion, the measurements of quantities, the units of measurements, number and numbering systems, the types of numbers and their relations to each other as numerical ratios. Thus quantity is a property that exists in a range of magnitudes or multitudes. For example, mass, time, distance, heat, and angular separation are among the familiar examples of quantitative properties. Two magnitudes of a continuous quantity have to one another the ratio which a number has to a number. Such continuous quantities possess a particular structure, which was explicitly characterized by Hölder (1901) as a set of axioms which define such features as identities and relations between magnitudes.

Seeing your sincere intent to produce the quality article, i made some modifications and removed all the comments irrelevant to the matter (if something missed feel free to delete it). Azamat Abdoullaev 11:44, 28 February 2006 (UTC)

Holon, hearing no comment from you, i put a new version of intro; feel free to revise it. Azamat Abdoullaev 08:33, 1 March 2006 (UTC)

Thanks, I will take a look soon. Holon 09:05, 1 March 2006 (UTC)

[edit] Magnitudes

Azamat, I would like to clarify an important point regarding the following:

Under the names of magnitude come what is continuous and unified and divisible into divisibles, all cases of non-collective nouns: the universe, matter, mass, energy, liquid, material, animal, plant, tree.

I do not follow precisely what this is trying to say: it may be the way you use English, I'm not sure. What exactly do you mean by "Under the names of magnitude come ..."? An issue here is that liquid is not a quantity. Properties of liquids, such as density and temperature, are quantities. The same issue applies to animal, plant, and so forth. I can change this again but we may just keep going around in circles if we don't firstly clarify the intention of the statement. Holon 04:06, 2 March 2006 (UTC)

Holon, this is the old wisdom: with respect to quantity, all entity names can be divided as the names of multitude (the continuous things) and the names of magnitude (the discrete things). The expression may need better and clear edition like as: With respect to quantity, all entity names can be divided as the names of multitude (the discrete things ) and the names of magnitude (continuous things). The former involves..., while the latter involves....

Azamat Abdoullaev 12:56, 2 March 2006 (UTC)

[edit] Points which need to be addressed

• Repeating point from above: A relation such as an angle (e.g. between two pieces of metal) is a fundamental kind of quantity. Reference to relations as quantites has been removed but this point has still not been addressed.

Just add it in proper place within the current context.

Azamat Abdoullaev 12:56, 2 March 2006 (UTC)

• The word "few" has no definate numerical value. It is used for comparison (eg "Bob had fewer apples that Tom"). Suggest removing "few refers to three or four objects".

Cymro 3:25:42pm, 25th August 2006

• Comments were made by Arthur Rubin above regarding the section quantity on mathematics and a question posed. I am planning to omit the whole section if no one can address the issues.

As for Arthur's comment regarding a line status: it must be clar the every line is a limited length, which belong to a fundamental quantity (as measure) along with mass, time period and temperature.

Concerning scalars, vectore and tensors, they are first of all variable quantities (variables assuming a set of values) that can be resolved into components; although other properties can be added up as well.

Azamat Abdoullaev 12:56, 2 March 2006 (UTC)

• Related to previous point, Some quantities are such by their inner nature (as number) clearly implies that numbers are quantities. If this view has been put forward by someone, can it be cited?

Yes, it was clearly stated by Plotinus, and come as his achievement. This distinction very important; for there are things which are quantities in the primary sense, and there are things which are quantities in the secondary senses. Azamat Abdoullaev 12:56, 2 March 2006 (UTC)

Please cite. As it stands, the article reads as though this POV and distinction is prominent. See list of criteria below. Also 'primary sense' and 'secondary sense' need to be propertly explained. Holon 03:33, 3 March 2006 (UTC)

Otherwise, I plan to remove the statement on the basis that it is not suitable for an encyclopedia. Citations have been produced regarding continuous quantities and multitudes as quantities. In addition, all continuous quantities can be said to be such "by their inner nature": they possess quantitative structure by nature of their being. Consequently, saying numbers are quantities by their inner nature is doubly confusing.

Holon 09:50, 2 March 2006 (UTC)

I try follow one common rule fit for a good encylopedia, to put only well-verified knowledge.

Azamat Abdoullaev 12:56, 2 March 2006 (UTC)

Azamat, the problem is that it doesn't meet the verifiability criteria as things stand. Also, the weight given to a POV should be proportional to its prominence. I don't have much time at the moment but the weight given to the viewpoint that number is quantity is out of proportion currently given the way quantity was understood by Newton, Wallis, Euclid, and Holder, and as it is commonly understood in science. From POV:

• If a viewpoint is in the majority, then it should be easy to substantiate it with reference to commonly accepted reference texts;
• If a viewpoint is held by a significant minority, then it should be easy to name prominent adherents;
• If a viewpoint is held by an extremely small (or vastly limited) minority, it doesn't belong in Wikipedia (except perhaps in some ancillary article) regardless of whether it's true or not; and regardless of whether you can prove it or not

If there is a prominent adherent, then it is reasonable to include a position, but it must not be conveyed as a prominent one unless it meets the criteria. Regards, Holon 03:14, 3 March 2006 (UTC)

In the study of quantity and its basic kinds as multitude (the discrete things as numbers) and magnitude (the continuous things as masses) , there are some established references to be guided:

Whitehead and Russell. Principa Mathematica, Parts III-IV; Whitehead. Introduction to Mathematics; Russell. Introduction into Mathematical Philosophy; Dedekind. Essays on the Theory of Numbers; Frege. The Foundations of Arithmetics; Nagel. On the Logic of Measurement; Peirce. Collected Papers; Tarski. Introduction to Logic

But i don't think we need to embarass the reader with all this. I am away of Wiki till the 7th of March. Azamat Abdoullaev 12:49, 3 March 2006 (UTC)

Multitude and magnitude are not what require citation. The reference to number as being quantity 'by its inner nature', quantity in 'primary sense' and 'secondary sense do. The list of references does not support any specific point in question. Holon 13:24, 3 March 2006 (UTC)

[edit] Much/muchly

"One form of much, muchly is used to say that something is likely to happen." This doesn't make sense to me. If there is no objection it should be deleted. Zeyn1 (talk) 14:25, 19 May 2008 (UTC)