Talk:Symbol (formal)

Why do we need a separate page for this?

Right after I created the page, user Hans Adler wrote this on my talk:

I don't understand what you are trying to do with your new article Symbol (formal). Symbols are just elements of the alphabet. They can be virtually anything, although we tend to think of them as things we can write on paper. They are, however, not usually strings of elements of alphabet. In other words: A symbol is not usually a string of symbols, and claiming it is certainly doesn't contribute to an understanding of the concept. Whenever this is done, it is best thought of as encoding the symbols of one alphabet into strings of symbols of another.

I don't think we need an article for this term at all. It is defined in formal language. That seems to be enough. Hans Adler 10:19, 18 August 2009 (UTC)

---

In my response on his page:

The word symbol as used in formal languages needs a definition. It is not sufficient to leave it to another article.

Having said that, I think the state of my efforts (which I have edited ten times because I am rather unhappy with it) were not very clear.

But let's not throw out formal symbols altogether. They deserve a wiki page. mukerjee (talk) 10:28, 18 August 2009 (UTC)

My reason for creating this page was that I felt we needed it to distinguish the formal use of the word, "symbol", from the linguistic or traditional use (representing something else).mukerjee (talk) 10:31, 18 August 2009 (UTC)

There is no definition for symbols. They can be anything! They only become symbols if we use them as such. You can't discuss them in isolation, only in combination with alphabets and formal languages. We are writing an encyclopedia, not a dictionary. Readers shouldn't have to go on a treasure hunt (game) before they can put the snippets together and get a full picture. In a formal context, the question "what is a symbol" is simply the wrong question, and readers asking it need to be redirected to the article that answers the right questions ("what is an alphabet?", "what is a language?"). Hans Adler 10:33, 18 August 2009 (UTC)

This edit introduced a real problem. Formal language was a self-contained article. It explained all the necessary terms. Letters and symbols were in italics and without a link, making it clear that these are undefined, atomic terms. Now you have made one of them a link. This suggests to readers that symbols have some special quality about them or that they are not actually atomic. You might cause thoughts such as: "I need symbols to represent the stars in the universe. It would be convenient if I could somehow just use the stars themselves, but are they symbols? I will have to follow the link to find out." Hans Adler 10:40, 18 August 2009 (UTC)

I agree that we are writing an encyclopedia, but that is exactly why we need such an article. If all we were talking was models of computation, I would agree with you. But here, there are other pieces of knowledge, such as another kind of symbol, which needs to be distinguished from a formal symbol. In fact, that is how I started this page. As for the edit in question, I have linked both letter and symbol to the new page. mukerjee (talk) 12:30, 18 August 2009 (UTC)

Is { 1, 2, { 0, 1 }} a symbol? Hans Adler 12:45, 18 August 2009 (UTC)

The point of my question was: In the context of the article Formal language, the set { 1, 2, { 0, 1 }} is a symbol. That was implicit in the article until you linked the word symbol to the present article, which seems to imply that it is not a symbol. Please fix this problem. Hans Adler 09:23, 20 August 2009 (UTC)

This article is pretty OR-ish and I don't understand the purpose of it either. 207.241.229.56 (talk) 23:28, 15 September 2009 (UTC)

Greg Bard's "clarification"

Greg Bard has put in no small amount of work on this page, but I must say that I am not certain it is an improvement. Perhaps we should discuss whether or not it really is helpful to declare that a formal symbol is an idea, concept or abstraction. See this diff. Phiwum (talk) 03:27, 16 June 2010 (UTC)

Diagram

The diagram File:Formal languages.png is not adequately sourced (it refers to Godel, Escher, Bach, but without supplying an edition, chapter, or page number), is clearly off-topic in this article, and most interpretations made of it are incorrect, so it's misleading. — Arthur Rubin (talk) 21:57, 21 October 2010 (UTC)

Definition Ambiguity

This article is kind of a mess. It uses "symbol" and "formal symbol" in some places interchangeably, and in other places asserts that they are mutually exclusive abstractions. Here is a short list of things that seem to contradict themselves or contradict other logic articles:

1. Symbols of a formal language need not be symbols of anything. For instance there are logical constants which do not refer to any idea, but rather serve as a form of punctuation in the language (e.g. parentheses). Symbols of a formal language must be capable of being specified without any reference to any interpretation of them. This directly contradicts the text below which says logical constants aren't formal symbols.
2. Symbols such as ∧ or ¬ or are not formal symbols, in that their semantics is fixed - they are logical constants. This suggests that formal symbol is another word for variable and/or non-logical symbol, but I can't find this usage anywhere else. Is this accurate?
3. I guess a term like non-formal symbol would fairly refer to logical constants, then? Because the text repeatedly calls these symbols, even as it excludes them from being formal symbols.
4. A symbol or string of symbols may comprise a well-formed formula if it is consistent with the formation rules of the language. This and the diagram to the right seem to be using the word symbol to mean formal symbol or non-formal symbol, because wff's in almost any syntax may contain variables and logical constants.
5. Formal symbols are usually thought of as purely syntactic structures...tl;dr. In this case, the exclusion of logical constants doesn't make a whole lot of sense since these are closer to 'pure syntax' given their universal interpretation. (This may be my under-trained bias speaking, though.)
6. The set of formal symbols in a formal language is referred to as an alphabet (hence each symbol may be referred to as a "letter"). So this means logical constants aren't part of a formal language...?

If one or more of these seemingly contradictory definitions for "symbol" or "formal symbol" or other related detritus is actually correct, could it be specified in a more straightforward and consistent manner? I'm using Enderton for reference (which may not be the best source), but I'm pretty lost here. At the very least there should be an attempt to line terminology here up with the other logic articles or at least reference alternate naming conventions. TricksterWolf (talk) 06:06, 1 November 2011 (UTC)

Removal of statement that logical constants are not formal symbols

Greg recently blanked a line distinguishing logical constants (whose semantics is fixed from outside the system) with formal symbols (whose semantics depend upon an interpretation), edit reason being "removed false statement". Perhaps we should discuss before editing further? Different books have different conventions for defining formal symbols, but the definition of logical constants as not being formal symbols is common enough that it should not simply be labeled "false". This article needs to be more inclusive with regard to common definitions for the terminology it uses. Wikipedia is not a place to standardize terminology, but rather to supply information on the terminology that exists and is commonly used. TricksterWolf (talk) 17:58, 21 May 2012 (UTC)

That particular removal was a result of an issue brought up at WT:MATH. A formal symbol is (in one sense) the marks of ink on a page, or pattern of pixels on a screen, etc. So the tiny vee shaped thing is a logical constant called "disjunction." The marks on the page can be interpreted as the concept that if at least one of two particular sentences is true then the particular disjunction of the two is also true. So logical constants, including logical connectives are, in fact, formal symbols. They are also abstract concepts. So the statement in the article was, in fact, false and did cause some confusion.Greg Bard (talk) 19:45, 21 May 2012 (UTC)

Title "symbol (formal)"

Does anyone know why this article is not at logical symbol, which redirects here? — Carl (CBM · talk) 20:49, 24 November 2012 (UTC)

First sentence

As far as I can tell, the first sentence has essentially no content:

"A logical symbol is a concept, tokens of which may be marks or a configuration of marks which form a particular pattern."

What exactly is that trying to convey? As far as I can tell the topic of this article is "symbols, as they are used to define formal languages". Is that right? — Carl (CBM · talk) 20:52, 24 November 2012 (UTC)

The sentences after the first one in the lead paragraph seem even more wrong, essentially saying that every mathematical or logical concept is a symbol. Even considering the meme that mathematics is about patterns in nature it seems wrong to say that all such patterns are symbols. Towards the end, the article was asserting that the only meaning which can be assigned to formal symbols is in terms of other formal symbols. I've deleted that because it was clearly wrong. Honestly, this article is Jon Awbery-type material, ripe for AfD. I'll wait a day or so in case someone can produce some philosophy sources for the view advanced here, which is clearly not a view espoused in math or logic. Tijfo098 (talk) 12:12, 25 November 2012 (UTC)

Template with list of symbols

I have several motivations for thinking that the template listing symbols is not a good fit for this article.

• Different typographical symbols are used by different authors for the same logical symbol. For example both ampersand and wedge represent the same logical symbol, which is the symbol that is interpreted as conjunction. Do we want to list every symbol that is used? What about the letters in Polish notation?

• The articles for many of the symbols are just about the typographic symbols, not the logical symbols. For example tilde is about a typographic symbol, not about a logical symbol.

In general, it appears to me that there are two layers of abstraction:

A printed symbol is a token of a typographical symbol is a token of a logical symbol.

Is this article should be about the latter concept (e.g. can a word be a logical symbol) or about the middle one (typographical symbols that are used in logic, as in list of logic symbols)? — Carl (CBM · talk) 20:59, 24 November 2012 (UTC)

sources

There were 5 reversions back and forth today. I see no source upon which they were based, or upon which what was undone is based. ParkSehJik (talk) 01:58, 25 November 2012 (UTC)

Well, the source for Greg's edits is his own imagination, but there doesn't seem to be a source for the previous text. — Arthur Rubin (talk) 04:59, 25 November 2012 (UTC)

Then you should revert your own revert, then revert that, etc. We can all then watch the article shimmer from its lack of sourcing. ParkSehJik (talk) 05:23, 25 November 2012 (UTC)

I've deleted some passages which claimed (without any sources) that the only semantics we can assign to (formal) symbols are in terms of other formal symbols rendering every form of formal reasoning circular. Tijfo098 (talk) 12:04, 25 November 2012 (UTC)

Citation needed tags might work better than deletions to ultimtely improve the article. ParkSehJik (talk) 20:24, 25 November 2012 (UTC)

I don't object to most of your rescission. That large part wasn't my doing. However, I wonder about your deleting this part: "...that define it in terms of other formal symbols." If you read the sentence, it never implies anywhere that it is the "only semantics we can assign to (formal) symbols." In fact the sentence conspicuously used the terms "usually" and "sometimes." Any objection to bringing that back?Greg Bard (talk) 13:53, 25 November 2012 (UTC)