Talk:Type–token distinction

Difficult example

Can someone provide a more accessible example of a type having no tokens than a formulation of Goldbach's conjecture? I had not even been exposed to Goldbach's conjecture before reading this article and asking my roommate about that sentence.

I hesitate to change it to a simpler example for fear of obliterating some distinction I fail to grasp. —Christian Campbell 04:16, 1 May 2009 (UTC)

Let N be the total number of tokens of the type '0' created in the history of literacy. The type that is a concatenation of N occurrences of '0'has no type as of this moment--and almost certainly never will. BOOLE1847 (talk) 22:26, 18 November 2013 (UTC)

Whether a line of prose contains tokens.

A disputed edit. The offending statement:

"There are, in fact, three word types in the sentence: "rose", "is" and "a". However, although there are eight word tokens in a token copy of the line, there aren't any tokens at all in the line itself."

Later it states, "There are not eight word types in the line. It contains (as stated) only the three word types...," which demonstrates the sentence and the line are used as synonyms, and that the following applies to both the sentence and the line:

If it's true that there are types of word in the line, it's true the line contains things, and it's true the line contains those things. Those things - types of words - are tokens of what we call types (they are tokens of the type of types), therefore "the line contains three types of word" implies "the line contains tokens."

user:Gregbard writes,

"Undid / the point here is that the "line" is a concept, not a physical object. Therefore the token instance of the line consist of token words, but the line itself is a type, not a token."

It doesn't matter whether the line is supposed to conceptual and nonphysical. The contradiction only depends on whether the line can contain things. It's possible, if the terms are separated and the distinction between terms is defined, this can be turned into a consistent distinction. For example, the line is not the same as the concept that a rose is a rose is a rose, that equality is reflexive. If that's what's meant, it would not be the line you are claiming contains no tokens, but the meaning of the line. ᛭ LokiClock (talk) 18:09, 7 June 2013 (UTC)

I think you are unclear on the over-arching point of the whole article. Types are concepts, tokens are physical objects. So the "line" to which the sentence is referring is the concept of a line, which is commonly called a "line." The "things" to which you are referring are concepts. So just because a thing is contained in another thing, doesn't make the thing a physical object if the things you are talking about are concepts. As a mathematician (who presumably understands geometry) just ask yourself what is the difference between a "line" and an "imaginary line?" When mathematicians and logicians are talking about things like lines and theorems, they are always talking about the concepts, not the chalk marks, or marks of ink on the page, unless it is specifically stated as such. The material quoted is faithful to the material in the literature by Quine. I'm going to revert your revert based on this understanding. Greg Bard (talk) 19:40, 7 June 2013 (UTC)

Please don't re-establish a disputed edit while the dispute is unresolved. If it's faithful to a statement in the literature, it should be referenced in the article. It would be a different thing if it said "the concept of a line contains no tokens." It doesn't, it says the line does not contain tokens. In the mathematical analogue, this would be saying a line contains no tokens of points, as opposed to saying while each line contains points, the concept of a line doesn't contain points. It's not a matter of the difference between an abstract or formal line and a line drawn on paper. What about my argument makes you think that's where the issue lies? ᛭ LokiClock (talk) 20:57, 7 June 2013 (UTC)

As I stated, when mathematicians talk about their various objects of study (lines, points, theorems, etcetera) they are always talking about the concepts (i.e. types), not the physical marks (tokens). So saying the "line contains no tokens" is tantamount to saying the "concept of a line contains no tokens." Furthermore, it would render useless the language used to communicate this concept if we were to replace the disputed sentence with language such as "the concept of a line contains no tokens", because then a reader would mistakenly be lead to believe that somehow this is different than saying the "line contains no tokens." I'm sorry, but, again, it seems that you are unclear of what is being communicated here. I am open to suggestions for finding a way to reword it in such a way that would clear up your confusion, but that will not be a simple matter if a) the clarification deletes the concept being expressed just because you haven't grasped it, and b) the concept is reworded so as to obliterate the very distinctions which it is trying to clarify. This looks like a case of Mathematosis. Greg Bard (talk) 21:35, 7 June 2013 (UTC)

Saying the line contains no tokens is entirely different from saying the concept of the line contains no tokens, and I'm proving that to you: If you say "the line contains something" and then say "the concept of the line contains no tokens," those statements can be consistent. If you say "the line contains something" and then "the line contains no tokens," there's a contradiction, simply that something is a thing token. It reads like the article's trying to use two definitions of the abstract line at the same time, only one of which equipped with the ability to contain words. Any term could have this problem, it has nothing to do with the mechanics of the concept, like what it has to do with intensional vs. extensional definitions or platonic ideals vs. physical manifestations, it's a simple contradiction in what's attributed to the object under definition - first that it is unable to do something, second that is does that very thing. You're blaming my character in stereotype for this problem and getting sidetracked with expositions on the nature of proof instead of addressing my actual argument. If you are the only one of us who has reason to believe I'm unclear of what's being communicated, you're the only one who can reword the explanation to clear up the confusion. ᛭ LokiClock (talk) 01:31, 8 June 2013 (UTC)

-sigh- Saying "the line contains something" and then "the line contains no tokens," isn't a contradiction. It may contain things other than tokens. In fact the idea of using the analogy of a "container" when referring to ideas is extremely common, and well known. I will attempt to work on the language to your satisfaction tomorrow. Greg Bard (talk) 01:46, 8 June 2013 (UTC)

Goodnight, sleep tight. I don't see how there's anything that isn't a token of any type. In fact, already it would be a token of "things which have no type", which is a type. All I'm doing is recursing the type/token distinction so that types are themselves tokens of a different type - the type whose tokens are types. I agree with you that the material suggests that the line and the concept of a line are the same thing, by the way. Recall, what I deleted was the statement that the line contained no tokens. ᛭ LokiClock (talk) 02:13, 8 June 2013 (UTC)

Current photo/video illustration

The current photo/video illustration (or its caption), which involves image(s) of birds in Rome airspace, is confusing for this article because the type-token distinction can be mistaken for the class-member distinction. It says that each bird (of the set of birds in the flock) is a token of a type (presumably of the type, *birds that flock in Rome*, or the type, *species of [pigeons, etc.]*). The concept-type for which these birds are saliently tokens is not clear at all, and makes the caption ambiguous at best, as currently stated.

Current photo/video illustration

The current photo/video illustration (or its caption), which involves image(s) of birds in Rome airspace, is confusing for this article because the type-token distinction can be mistaken for the class-member distinction. It says that each bird (of the set of birds in the flock) is a token of a type (presumably of the type, *birds that flock in Rome*, or the type, *species of [pigeons, etc.]*). The concept-type for which these birds are saliently tokens is not clear at all, and makes the caption ambiguous at best, as currently stated.Dylan Hunt (talk) 04:36, 22 July 2013 (UTC)

Implausible and unsubstantiated claim

Quine discovered this distinction. — Precedingunsigned comment added by BOOLE1847 (talk • contribs) 17:59, 8 November 2013 (UTC)

Quine states in his book Quiddities that he identified this distinction.Greg Bard (talk) 21:26, 8 November 2013 (UTC)

Quine never said he discovered the this distinction, which had been in use in logic before Quine was born. Anyone claiming to discover this distinction would be ridiculed. — Preceding unsignedcomment added by POLY1956 (talk •contribs) 14:05, 11 November 2013 (UTC)

The claim is that he discovered the distinction between types, tokens, and occurances, and yes, he states it quite clearly. Please sign your posts with a "~~~~" Greg Bard (talk) 22:39, 12 November 2013 (UTC)

Incorrect reddening?

Why is "Peirce’s type-token distinction' in red? http://en.wikipedia.org/wiki/Pierce%27s_type-token_distinction — Preceding unsigned comment added byPOLY1956 (talk •contribs) 14:12, 11 November 2013 (UTC)

On Wikipedia, links to articles which haven't been written are red. The dash used in most titles is the emdash (i.e. "–"), and perhaps that is the issue. Greg Bard (talk) 22:39, 12 November 2013 (UTC)

Need for two articles?

Is there any advantage to having the article Charles Sanders Peirce's type–token distinction as well as this article Type–token distinction?— Philogos (talk) 01:19, 20 October 2014 (UTC)