Talk:Quantification

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Contents 1 Old material 2 New intro 3 Attention banner needed? 4 Uniform vs pointwise continuity 5 Two meanings of quantification 6 Changes made to article undone 7 is this relevant?

[edit] Old material

This contains material from Universal quantification and Existential quantification. When I finish transferring items (tomorrow?), then I'll remove stuff from those articles that applies to quantification in general and appears here. Then those articles can focus on aspects unique to their particular sort of quantification. For now, those articles remain complete, without relying on this one. -- Toby Bartels 10:30, 31 Jul 2003 (UTC)

These changes have now been made. -- Toby Bartels 21:29, 3 Aug 2003 (UTC)

This is a important article; it was well written but I think some clarification on the rule of formation would be helpful. However, I believe in the scientific method. TEAR IT APART. After all, I'm just a vacuum cleaner.CSTAR 03:56, 12 May 2004 (UTC)

I have continued to make some changes to discuss natural language quantification, informal mathematical quantification and the formal semantics of quantification (at least what is objective quantifcation, as opposed to substitute quantification). Again I think a lot can be removed. Please have a look at this and modify. CSTAR 05:42, 15 May 2004 (UTC)

I will add some stuff on multal and paucal quantification ( quantification such as for almost every x blah...) and then I'll call it quits on this article.

Could we merge the other articles on existential and universal quantification into this one?CSTAR 23:12, 15 May 2004 (UTC)

In Mathematics section there is following phrase:

A similar analysis applies to the disjunction, 1 is prime, or 2 is prime, or 3 is prime, etc.

1 is NOT prime number, but it does not break the disjunction. I'm not sure if it should be fixed as English is not my mothertongue, but this phrase may cause some confustion. Mathemonkey (talk) 21:28, 1 May 2008 (UTC)

[edit] New intro

The new intro is innaccurate. Quantification is not limited to size. Unless there is any objection soon I will revert it.CSTAR 14:03, 19 Nov 2004 (UTC)

Your change is sound, in that what you have written is better than what you replaced, but I've got some reservations about the way the relation between quantifiers and quantities is being treated. I'm not a linguist, and am not entirely comfortable with the following material, but it seems to me that in natural language, mass noun (eg. two pints of beer) and count noun constructions (eg. four cats) are in many respects the paradigmatic instances of quantifiers, with some, no and all being more in the line of special instances. It seems backwards to me to relegate the quantity-related aspects of quanitifers to the back seat. ---- Charles Stewart 14:18, 19 Nov 2004 (UTC)

Sigh, yes, I have to agree with your assertion:

I've got some reservations about the way the relation between quantifiers and quantities is being treated.

In fact the article's treatment of quantification is almost entirely restricted to quantification in formal languages (Mea culpa). Unfortunately, I don't know much about this, I admit. When I first stumbled on this page it only dealt with formal quantification and moreover even with that restricted focus, I thought the material was not very informative and in fact a little condescending to the reader.

Of course feel free to revert back to any previous state or some suitable middle.

Sooner or later I will tackle this problem. I can't think of a 30 second edit that will resolve the issue, and I have little time for WP right now, so I am OK with leaving it as is. ---- Charles Stewart 23:29, 20 Nov 2004 (UTC)

[edit] Attention banner needed?

Should we put in an attention banner? Yes, I now have pangs of guilt about this article. Please, someone, absolve me of the burden of this guilt. CSTAR 15:29, 19 Nov 2004 (UTC)

No guilt feelings are deserved. What is an attention banner? ---- Charles Stewart 23:29, 20 Nov 2004 (UTC)

The following is an attention banner:

CSTAR 23:33, 20 Nov 2004 (UTC)

[edit] Uniform vs pointwise continuity

Let f be a real-valued function on R.

• A: Pointwise continuity of f on R:

which is the same as

• A': Pointwise continuity of f on R:

This differs from

• B: Uniform continuity of f on R:

by exchange of two quantifiers. Where are the additional variables?--CSTAR 03:20, 6 September 2006 (UTC)

[edit] Two meanings of quantification

There need to be two different pages for "quantification", one which is the formal logic definition, the other which is the process of quantifying information. The latter is a very important topic and has really nothing to do with the former that I can see. There are many books on the history of quantification and the "quantitative spirit" in science (starting around the 18th century), ample material for an entire article. --24.147.86.187 01:48, 4 January 2007 (UTC) Insert non-formatted text here

The scientific usage of "quantification" might be a synonym of measurement, and we already have a page on that topic. Tim Vickers (talk) 14:52, 24 August 2008 (UTC)

I don't think 'measurement' is an adequate synonym for quantification even though their meanings do overlap. I propose we create a new page called 'quantification (science)' and remove from this article all the empirical science stuff. Then it might prove ?desirable?? to rename this page as 'quantification (logic)' to reduce any remaining confusion. Any views on this idea? thanks Peter morrell 06:41, 4 September 2008 (UTC)

[edit] Changes made to article undone

I recently changed an erroneous statement in the article which said, "1 is prime" to "1 is not prime." The entry has since been changed back to "1 is prime."

It is widely accepted by mathematicians that 1 is not a prime number. If 1 were to be prime then the fundamental theorem of arithmetic would have to be changed drastically. As it stands, the fundamental theorem of arithmetic holds that every natural number is either prime or can be expressed as a unique, finite product of prime numbers. If 1 were to be prime then every natural number would have an infinite number of prime factors. I am going to change this back. Please, leave the statement "1 is not prime" alone. Eyes down, human. (talk) 01:19, 25 August 2008 (UTC)

The article is not saying 1 is prime. It is using an example:

1 is prime, or 2 is prime, or 3 is prime, ...

as an example of an OR statement. Since it is apparently causing confusion to have an or statement in which one disjunct is "1 is prime", I'll change it to something else. — Carl (CBM · talk) 01:47, 25 August 2008 (UTC)

[edit] is this relevant?

Goldbach's conjecture is that this statement is false, that is, that every natural number greater than 2 is the sum of two primes.

It seemed a bit off-topic to mention Goldbach's conjecture here. It seems sufficient to mention that the example is related to Goldbach's conjecture, but no more.

--Paul (talk) 00:35, 7 March 2009 (UTC)

I think this is fine: first, saying what GC is allows the reader unfamiliar with GC to see that it is the negation of the sentcne above, and secondly, GC is good sort of example, since clicking on the link shows the interesting fact that such a simple sounding sentence is unknown. If we were to further point out that all such undetermined sentences of arithmetic make use of quantifiers, that might be nice in this article, too. — Charles Stewart (talk) 13:07, 8 March 2009 (UTC)

Apart from being relevant or not, Goldbach's conjecture states something different from what is written here. In its present form the statement in the article is just a correct statement. For instance, 11 is not the sum of two primes. —Chris Barista (talk) 15:41, 1 April 2009 (UTC)