Talk:Proposition

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Contents 1 comment 2 New lead paragraph 3 Propositional logic 4 Street Philosopher 5 Sentence (philosophy) vs. Sentence (mathematical logic) 6 Difference? 7 In philosophy and logic, a proposition is a string of sounds or symbols that have a meaning. 8 Philogo's edit

[edit] comment

This entry is very dictionary-ish... --k.lee

I agree. But it could become a decent disambiguation page in the future. --mav

---

I've tried to rewrite the article into something managable (unfortunately I'm finding a lot of older Wikipedia philosophy articles read like bad lecture notes). I don't think it needs to be a disambiguation page yet, because the non-philosophical uses of proposition are (I think) fully explained in the short space they're given.

I'm worried I came out sounding a little too pro-proposition; it's difficult to cover a subject that some people claim don't exist without asserting its existence more often than not. If a better writer or someone more familiar with the arguments against propositions would like to extend that section or touch up the rest of the entry, please do. piman 04:30, 2005 Feb 27 (UTC)

[edit] New lead paragraph

The old lead paragraph read:

In modern philosophy, logic and linguistics, a proposition is the meaning of a sentence, rather than the sentence itself. In ordinary usage, a proposition is like an offer, a request, or a suggestion: it is something which is proposed. (Will you marry me? proposes matrimony.) This article is concerned with a related technical sense, in which any sentence, when asserted, proposes that a certain claim is true.

I deleted this paragraph and replaced it by:

Propositions are a term used in logic to describe the content of assertions, content which may be taken as being true or false, and which are a non-linguistic abstraction from the linguistic sentence that constitutes an assertion. The nature of propositions are highly controversial amongst pohilosophers, many of whom are skeptical about the existence of propositions, and many logicians prefer to avoid use of the term proposition in favour of using sentences.

Points:

1. The nature of propositions is highly controversial, and there is no consensus claiming that propositions are meanings of sentences. The term content is used to mean more or less the whatever it is of sentences that propositions are.
2. The old attempt to explain proposition in terms of proposing something are unconvincing: the normal analysis of propositions is as assertions (as opposed to questions, commands, etc.). I changed this languages.
3. It's worth highlighting the controversy and skepticism about propositions in the lead paragraph, I think. --- Charles Stewart 17:45, 19 May 2005 (UTC)

[edit] Propositional logic

"Propositional logic is so named because its atomic elements the expressions of complete propositions"

"Propositional logic is so named because its atomic elements are the expressions of complete propositions"? --Memenen 19:02, 24 July 2005 (UTC)

[edit] Street Philosopher

I wanted to insert the following change, but then I realized this material really only deserves, at best, to be in the discussion section here. I am just learning how to use Wikipedia. I apologize for the confusion. If there is way to undo the edits I submitted to the article, I will be glad to do so. The first change consisted of some thoughts below. The 2nd change was to take the thoughts out from the article. I apologize if I messed anything up.

To my comments, for what they are worth...

When I read, For example, Tiny crystals of frozen water precipitation are white is in English, but is said to be the same proposition as snow is white by virtue of the definition of snow.

I inserted...

Noam Chomsky (http://en.wikipedia.org/wiki/Noam_chomsky put all this kind of discussion to rest with the system for sentences, prescriptive vs. descriptive etc., called Generative Grammer (http://en.wikipedia.org/wiki/Generative_grammar. Generative grammer is new technology, superceding the discussion of this paragraph, and the next.

Lengthy, tortured strings of philosopohical discussion often indicate the wrong language being used to express ideas. Yes, there is a way to state the relationships between propositions and assertions in English, but they flow more easily in math. That is what Chomsky laid out.

I realize that is cocky of me to say, especially since I know jack sh!t about this stuff. I am just trying to contribute, in case what I said made sense. If it didn't, then I am sorry to have distracted you.

I want people already working on this material to know, I very much appreciate your efforts to make this information available to lay people, such as myself. This is a treasure you are building here. I am very very grateful. Peace.

[edit] Sentence (philosophy) vs. Sentence (mathematical logic)

This article ends with a redlink to Sentence (philosophy). There is an article at Sentence (mathematical logic). My small knowledge of logic suggests they may be the same thing, but I'm not sure enough to replace the link. --User:Taejo|대조 22:31, 29 April 2007 (UTC)

No, they are not the same. The second of the two has a much more technical meaning. Rick Norwood (talk) 20:05, 27 May 2008 (UTC)

I am not personally aware of a the word sentence being a technical word in philosophy any more than the term combustion engine. If the word senence were used in a philosphy text it would therefore refer to either (a) the common usage (as this is the middle of a sentence) or (b) as used in Logic meaning, either meaningful declarative utterance or well formed formula containing no variables. or (c) some other technocal us in some other discipline.

Philosphy however has emphased the importance of the type/token distinction including. but not exclusivly, between a sentence-type and a sentence-toke. The following paragraph containing three sentence-tokens, one sentence type, six token-words, two word-types, twenty-four token-letters and (coincidentally) twenty-four token-letters. So if you said "This book contain 50,000 words" you might be asked if you meant word-types or word-tokens, since the word word is ambiguous.

Jack wept. Jack wept. Jack wept.

[edit] Difference?

What is the difference between a proposition/statement and a predicate? --Abdull (talk) 16:10, 22 February 2008 (UTC)

Simply put: If and only if something is either true or false then it a proposition/statement/delarative utterance/declarative sentence: they are is a truth-bearers. Eg It is raining. I will uses the term statement here. A statement is to be distingusied from an imperative "Look out!" or a question Who are you? for they are neither true nor fase. A predicate eg is wise applied to a name e.g Socrates results in a statement Socrates is wise. The word predicate in Logic is thefore analogous (but not the same as) the term predicate in grammar: remember subject + predicate = sentence? You can find this better explained in the introdution to any good book on elementary logic; meanwhile I hope this helps.--Philogo (talk) 22:36, 22 February 2008 (UTC)

This needed to be explained in Wikipedia before any of the logic articles made sense. I've made an attempt at statement (logic). Rick Norwood (talk) 20:07, 27 May 2008 (UTC)

[edit] In philosophy and logic, a proposition is a string of sounds or symbols that have a meaning.

I say this is simply wrong. All the words in this sentence, and all the words in the OED have a meaning but that does not make them propostions. Many strings of words have a meaning but are not prosotions eg "strings of words" and "the evening star". Many strings of words make up a sentence but they are not thereby propositions, not even declariatve utterances e.g. the following sentence. Do you not agree? Finally normally propositions are not considered to be strings of sounds (or letters) or symbols at all, but what some strings of symbols - delartive uttereances - express. The version of Charles Stewart from 2005 was more accurate:-

"Propositions are a term used in logic to describe the content of assertions, content which may be taken as being true or false, and which are a non-linguistic abstraction from the linguistic sentence that constitutes an assertion. The nature of propositions are highly controversial amongst pohilosophers, many of whom are skeptical about the existence of propositions, and many logicians prefer to avoid use of the term proposition in favour of using sentences."

.--Philogo 12:43, 28 May 2008 (UTC)

My attempt at the first sentence was simply a rewrite of the previous first sentence, which said the same thing but mentioned grunts as kinds of propositions. I agree with everything you say, but I'm currently in the process of trying to separate a) logic in philosophy, b) introductory articles on mathematical logic, and c) technical articles on mathematical logic. Mixing the three topics has resulted in a hodge-podge of links, many to the wrong topic, and a collection of articles that range from the murky to the abstruse.

This article is mostly about the idea of a "proposition" in philosophy, while Charles Stewart's definition begins with what Hamilton, for example, in Logic for Mathematicians, calls "statements". I'm not wedded to Hamilton, but it is mathematically correct, and for me it has the advantage that I taught a course out of it a few years ago. So, in my attempt to sort the articles into the three classes above, I've left this one mostly to the philosophers, and only tried to paraphrase what they say in less muddled English, leaving out the grunts. I've written a new article, statement (logic), based on Chapter One in Hamilton, which provides a very elementary introduction to mathematical logic. The advanced article on this subject as it is understood in mathematical logic is sentence (mathematical logic). Yes, any permutation of the three titles could be argued for, but we have to start somewhere. Rick Norwood (talk) 13:27, 28 May 2008 (UTC)

I share your concerns. Promise not to be offended if I edit or question your edits? The term "statement" became fashionable to avoid the using the term "proposition". See my message to you at User_talk:Philogo#propositions. A distinction to be borne in mind is between Logic and Philosophy of Logic. The term Logic as used by philosophers (unless discusssuing history) since Frege is one and the as what was called symbolic logic and alter called mathematical logic. It would appear that the term mathematical logic has now expanded in connotation.--Philogo 13:40, 28 May 2008 (UTC)

I promise not to be offended; I am the most reasonable of men. Just keep in mind that modern philosophers, while they are aware of Frege and Russell, have followed some very twisted trails into postmodernism. Take a look at the Wikipedia article truth, for example, where I fought a loosing battle to have the article begin "Truth is correspondence between what is said or written and reality." Rick Norwood (talk) 13:57, 28 May 2008 (UTC)

You do not approve of:

In philosophy and logic, proposition is used to refer to either (a) the content or meaning of an assertion or (b) the string of symbols marks or grunts that make up a written or spoken declarative sentence. In either usage, propositions are meant to be the truth-bearers, i.e they are what is either true or false. ?

Do you thing we should really be attemting to descibe the use of the term in linguistics?--Philogo 21:01, 28 May 2008 (UTC)

I don't really object to the content of the sentence -- for all I know, I may have written it. Coming upon it cold a few days ago, it struck me as badly written, and I tried to craft a better written sentence that said the same thing. Then I did a little research, and discovered that while mathematicians require propositions to be either true or false, not all philosophers do. So, I reported what I found and cited some references. If you think you can do better, feel free. I'm a mathematician. Philosophy is only a hobby.

I'm not sure I understand how your quote of the old intro relates to the question of whether or not we want to get into linguistics. I would be happy to leave that up to the poor linguists, who probably have to deal with the philosophical view of their specialty just like mathematicians do. Rick Norwood (talk) 21:20, 28 May 2008 (UTC)

I am not sure that your three categories: a) logic in philosophy, b) introductory articles on mathematical logic, and c) technical articles on mathematical logic. are way-to-go. IMHO the prinicipal division is beween Logic and Philosophy of Logic, just like there is Science and Philopshy of Science and Maths and Philopsophy of Maths. (It is just confusings that Logic is consider to be "part of" Philosophy and "part of" Maths. It is also confusing that the term Philosophical Logic is sometimes used synonymously with Philosophy of Logic and sometimes as something different.) It used to be the case that Logic books covered both Logic and Philosophy of Logic without carefully differentiating the two. I think we should follow current trends and keep them seperate. Where there is an associated topic, thats what links are for! In each field there is the need for great precision.

What was the course you taught?

Re lingistics: I was referring to the opener which said the article described the use of the term in liguistics. I propose we delete that and stick with the term as used in Logic and if you insist Philosophy but I would be happier if it was discussed under philosophy of logic.

--Philogo 21:42, 28 May 2008 (UTC)

PS as I said in my message to you on my talk page:

Re your recent postings re propositions and statements Untangling and clarification of these and similar terms falls within the province of philosophy of logic rather than Logic. It would be better to set out these issues in the nascent article philosophy of logic discussion at Talk:Philosophy of logic#Truth, Propositions and Meaning. If you would be interested in this topic join me there.--Philogo 21:40, 27 May 2008 (UTC)

--Philogo 21:48, 28 May 2008 (UTC)

The problem is essentially a turf war. Members of philosophy departments are not going to let members of mathematics departments take over their articles, and members of mathematics departments are not going to let members of philosophy departments take over their articles. Two separate sets of articles are the only solution, IMHO, in this case this article for the philosophers, the article statement (logic) for the beginner in mathematical logic, and the article sentence (mathematical logic) for the upper division mathematics student or the professional mathematician. All three discuss the same type of object, but for a different audience. I suppose there is a fourth article declarative sentence for the linguist, but I haven't looked at it.

The problem with references is that, as things currently stand, a person reading a math article will click on a link and find themselves in a philosophy article, and vice versa. I'm working on fixing that. (A related problem is that a person reading a math article for the layman will click on a link and find themselves in a highly technical article, and vice versa.)

There is a big difference between logic as one of the five major areas of philosophy, and the philosophy of logic, as you can see by comparing the articles. Neither is about logic (mathematics), thank goodness.

The course I taught was just called "Logic" but it was for upper division math majors. Now I teach "Logic, Problem solving, and Geometry" to freshman education majors, and my upper division courses for our majors are such subjects as "Topology", "Complex Analysis", and "Abstract Algebra". Rick Norwood (talk) 22:02, 28 May 2008 (UTC)

re difference between Logic as one of the five major areas of philosophy, and Mathemathetical Logic. The latter term was origiannly snonymous with Symbolic Logic, which (leaving aside so-called "Informal Logic") was Logic as taught as a "branch of" Philosophy, up to FOPC. However I note that the desrciption in Wiki of the latter as :

Mathematical logic is a subfield of logic and mathematics.^[1] It consists both of the mathematical study of logic and the application of this study to other areas of mathematics. Mathematical logic has close connections to computer science and philosophical logic, as well. Unifying themes in mathematical logic include the expressive power of formal logics and the deductive power of formal proof systems.

I do not think that "the application of this study to other areas of mathematics." or "close connections to computer science" would be considered a "part of" Logic as one of the five major areas of philosophy. That sounds like "applied logic" or "applications of Logic" really. However Mendelson 1964 was the text book used to teach Logic to advanced Philopsohy students I took in a Philosphy department.

Would you be content, as a fellow WikiPojectLogic member to the division of articles between (a) Logic/Classical Logic/Sentential Logic + First Order Predicate Logic
(b) Philosophy of Logic
(c) "the application of this mathematical logic to other areas of mathematics." and its "close connections to computer science" etc.
(d) Misc eg History of Logic, Aristotlelean Logic etc.?
In particular we should not have material beloging to (b) mixed in with articles of category (a).

Re links. Suppose we have a (b) type article on, say Interpretations (logic), and Validity (Logic). After the articles have explained these as a technical terms in Logic, the links might say e.g.

For more on the philosophical issues raised see Naming and Referring(Philosophy of Logic), and The analytic/Synthetic Distinction (Philosophy of Logic).
For more on the mathematical treatement of these issues see Whatever(Mathematics).

Pedagodically, and (humorously), you learn to walk in category (a) you run in (c) and you question the nature of walking and whter there is such a thing in (b).

--Philogo 22:48, 28 May 2008 (UTC)

Your last comment sounds like The Hitchhiker's Guide to the Galaxy.

I prefer my categories to yours. (Why does that not surprise me.) But I don't want to get into a revert war over it. Let me just talk a bit about logic as I see it.

Logic is a natural function of the human brain. Aristotle wrote down some rules that capture the function of the brain pretty well (except for the cat/mouse or as it is sometimes cast the horse/stable problem). Symbolic logic does an even better job, but does not attempt to deal with problems which arise in natural language. (In the compound statement "She got married and she got pregnant" the "and" is not a commutative operation.)

Mathematical logic, which I know more about, is a well organized body of mathematical knowledge which most mathematicians agree on. In fact, most mathematicians mutter the magic words "ZF plus Choice" and get on with their work.

Philosophical logic, in contrast, is an area in which there are many schools and strong disagreement. See, for example, the article on Truth. I do not want to mix the mathematical articles on logic, which tend to be stable, with the philosophy articles, which tend to change rapidly. So, turning to your categories, I would not want to mix in category 1 Logic and Classical Logic (which tend to an historical and philosophical approach) with Sentential Logic and First Order Predicate Logic (which tend to a more mathematical approach). I do agree that b) should be a separate category, or maybe two separate categories. I don't want philosophy of logic in the article on free and bound variables. And your category c) would include applications of logic to not only mathematics, but also philosophy, science, linguistics, etc.

So, maybe we don't disagree as much as I originally thought. Let's just keep plugging away and see what happens.

Rick Norwood (talk) 12:48, 29 May 2008 (UTC)

We seem to be agreed (coorect me if I am wrong) that

• we should classify the articles.
• one class should be Philosophy of Logic
• one class shold be History of Logic, biographies of Logicians etc.
• one class should include Sentential Logic and First Order Predicate Logic, and exclude matter belongon to the above two classes. This class is what I call Formal Logic, Symbolic Logic, Classical Logic or just plain Logic: i.e. Logic post-Frege. They are as you say mathematical articles on logic, which tend to be stable, (As Chemistry to me means Chemistry as now taught and accepted, and excludes reference to Earth, Air , Fire and Water as elements, or phlogiston so Logic to me means Logic as now taught, in Mates and Mendelson and pretty much ignores (accept as a historic footnote) the sylogism, the law of the excluded middle and so on).

I beleive another class should be

• the parts of what may be called mathematic logic which do not fit under either of the above classes eg. "the application of this mathematical logic to other areas of mathematics." and its "close connections to computer science"

I am wondering why you would not be surprised if we disagreed. --Philogo 13:28, 29 May 2008 (UTC)

[edit] Philogo's edit

I don't understand your "fact" flags on the mathematics section. I cite a standard textbook in the area. Do you want me to cite more textbooks? What is it that you doubt? Rick Norwood (talk) 12:53, 7 June 2008 (UTC)

Hi Rick. regards

In mathematical logic, however, a proposition is usually a statement and is therefore necessarily either true or false. In the absence of qualifying remarks, in mathematics the word "proposition" is usually used to mean "true proposition", or as a synonym for theorem.[4]

The term proposition is of some vintage and there are a variety of accounts of what a proposition is, if anything, and whether there are any such things and whether we can avoid pre-supposing their existence. The term statement (in logic) was introduced by P F Strawson in the 1950s see in particular Strawson 1952: Introduction to Logical Theory. To avoid the term proposition and any of its pre-suppositions, some texts substituted the term statement. But statements too are not without there pre-suppositions. (Pun intended!) To avoid the term proposition and any of its pre-suppositions AND the term statement and its pre-suppositions, many texts refer simply to sentences and e.g. in particular refer to sentential logic rather than propositional logic.

In that context it is not clear what a proposition is a statement would mean, and the more weasel a proposition is usually a statement no less so, and I would be interested to see a full quote from a text in which this was said. Perhaps your sources are using the term statement in the vernacular (rather than the Strawson sense) as a meaningful declarative sentence (e.g. "I am hungry") (as opposed to say a meaningful interrogative sentence ("e.g. "Are you hungry", or a meaningless declarative sentence (e.g. "Greenness perambulates"). The words "necessarily either true or false" in the context are puzzling. Is it saying that propositions are "necessarily either true or false" BECAUSE they are "usually a statement" or WHEN they are a statement? And what is the force of the word "necessarily" in “necessarily either true or false". Does it mean by definition? Consider a proposition is usually a statement[citation needed] and is therefore necessarily either true or false and a proposition is usually a statement[citation needed] and is therefore necessarily either true or false . What is the first saying over and above the second?

Even more strangely now consider
A: In mathematical logic, however, a proposition is usually a statement and is therefore necessarily either true or false.
B In the absence of qualifying , in mathematics the word "proposition" is usually used to mean "true proposition", or as a synonym for theorem

A appears to entail:
C: a proposition is either true or false.
B appear to entail
D: a proposition is true
Consider more closely
E: in mathematics the word "proposition" is usually used to mean "true proposition"
This appears to entail
F: in mathematics the word "proposition" sometimes means "true proposition" and sometimes something else
Now the word proposition appears twice in F and I think to make sense the two uses must differ in meaning, so lets distinguish by tagging so we have:
G: in mathematics the word "proposition1" sometimes means "true proposition2" and sometimes something else
Now does proposition2 mean proposition as defined in the first sentence
H: In mathematical logic, however, a proposition is usually a statement and is therefore necessarily either true or false
which can be construed as:
I: a proposition is either true or false
If we take proposition2 in G to be proposition as defined in I, then we can substitute the latter for the former and obtain:
J: in mathematics the word "proposition1" sometimes means "true proposition2 something that is either true or false" and sometimes something else
in other words
K: In mathematics the term proposition sometimes means something which is either true or false and is true, and sometimes it means something else

Being puzzled by these two sentences and what they are saying, I thought it would be helpful were the actual text be cited so that the sense became clearer.--Philogo 12:14, 8 June 2008 (UTC)

To find the quote you request, you need only follow the link from "statement" to get the definition in Hamilton, "A statement is a declarative sentence that is either true or false."

Keep in mind that I'm not talking philosophy here, only mathematics.

In mathematics -- in Hamilton in particular -- we have (parapharse, because it is Sunday and my Hamilton is out at school):

Proposition 3.5: If a group is cyclic, then it is abelian.

Proof:

Clearly, in this usage, which is common, "proposition" means "true proposition".

I'll rewrite to make this clear to the reader. If you agree it is now clear, you can remove the "fact" tags. Rick Norwood (talk) 13:07, 8 June 2008 (UTC)

This defeintion of statement is not the usage in Strawson 1952. You could abod the anbiguty by avoiding the term statement

By writing not

In mathematical logic, however, a proposition is usually a statement and is therefore necessarily either true or false. but In mathematical logic, however, a proposition is usually a declarative sentence that is either true or false.
But usually implies not always. So when "in mathematical logic" does the term proposition NOT mean a declarative sentence that is either true or false and what then does it mean, and why does "mathermactcal logoc" use the terem propsition in two different ways, and waht EXACTLY is teh difference bewteen propsition and statement? Bear in mind that this article is the term proposition not statement. If we are going to allude to three terms we need to make crystal clear the difference between (A) propostion (b) statement and (c)declarative sentence. Philosophy and Logic both lay considerable emphasis on the need for precise and careful argument and definitions of terms. Contribitions that do not meet these exacting standards will attract the WW tag.--Philogo 13:27, 8 June 2008 (UTC)

I avoid this in my most recent rewrite, but to make the point clear, you're looking for consistency that does not and never will exist. The "usually" meant that most authors use the word that way, but there will always be some authors who use the word in a different way.

To give a famous example, the word ring "usually" means an abelian group with a second associative operation that distributes over the group operation and has an identity. But some authors omit the requirement of an identity. There is no way to force different authors to use the word the way other authors use it. I wish there were, but there isn't. That is why so many mathematics books have a Chapter Zero in which the author defines his terms. Rick Norwood (talk) 13:50, 8 June 2008 (UTC)

You are assuming that I am looking for consistency, but be that as it mays, you do not answer the questiona

when "in mathematical logic" does the term proposition NOT mean a declarative sentence that is either true or false and what then does it mean. and
what EXACTLY is the difference between proposition and statement?
as before:

we need to make crystal clear the difference between (A) proposition (b) statement and (c)declarative sentence. Philosophy and Logic both lay considerable emphasis on the need for precise and careful argument and definitions of terms. Naturally if a term is used in n different ways, and we are explaining the term in general and not in one particular usage, then we should explain all n usages. If on the other hand we are explaining just one of the useages, then we make that clear and to what or whom the usage belongs. --Philogo 23:41, 8 June 2008 (UTC)

Let me be very specific in answering your question. The term proposition in mathematical logic, if it is not in boldface, means a declarative sentence that is either true or false in all cases of which I am aware. The "usually" in the earlier edit was there because I know there are idiosyncratic mathematicians who use words any damn way they please. The difference between "statement" and "proposition" is this. "Proposition" when used without boldface is a synonym for "statement", but when it is in boldface followed by a number as in Proposition 3.5 it means "true statement" or "theorem". This latter use is a matter of custom rather than definition.

I certainly agree that we need to be careful in our definitions, but in mathematics at least excessive care may result in decreased understanding. For example, a precise and careful statement would be "The number represented by the numeral 2 added to the number represented by the numeral 2 is equal to the number represented by the numeral 4," but "2 + 2 = 4" is easier to understand.

Rick Norwood (talk) 12:57, 9 June 2008 (UTC)

This article is about the word "proposition" as it is used in logic, philosophy, and linguistics= and yet the lede beings with an account of the use of the term in philosophy of language, but suggesting that the usage is in coomon with logic. --Philogo 23:44, 8 June 2008 (UTC)

I do not know how the word "proposition" is used in philosophy or linguistics, or in philosophical logic. I leave it to you to fix that part. I do know how the word is used in mathematics. Mathematicians could do without the word entirely, using "statement" for the non-boldface sense and "Theorem" for the boldface sense. However, in the discussion of the way a word is used in philosophy, it is (for me at least) often helpful to compare and contrast the way the word is used in other contexts.

For example, I gather from recent additions to the article that in philosophy it is considered important to distinguish whether the proposition "is" the idea, or "is" the string of symbols that represent the idea. Mathematicians are aware of this distinction, but there are few mathematicians active in this area (none that I know of). Most working mathematicians I know tend to get impatient with such distinctions, and to consider all possible ramifications of that distinction to have been investigated to exhaustion in the early 19th century. Else, instead of the long example I gave above, we would have to say "The number the idea of which is expressed by the string '2' added to the number the idea of which is expressed by the string '2' is equal to the number the idea of which is expressed by the string '4'." From a pragmatic point of view, once you know the distinction is there, you can go ahead and work with ordinary language (albeit a highly rarefied ordinary language) and ignore the distinction between the idea and the symbol, not because it isn't an important distinction, but because everything that can be said about it (in mathematics) has already been said.

Rick Norwood (talk) 13:15, 9 June 2008 (UTC)

Yopu mean th distinction between a numeral and a number? Clear enough distinction is it not? 2 is a numberal, but 2 is a number. you can add 2 and 2 to make 4. You can concacetenate 2 and 2 to make 22; basic distinction in computer science: data types char, sting, and integer. Even Wikipedia tells you have to use or mention. Easy peasy surely? To state that 2 is an idea however is to make a far reaching - claim read Frege! If your sources have nothing to say about propositions as opposed to statements then there is not a lot of point citing them here, surely, unless you want to compare and contract the terms, but you would have to be very very carful. However many Logic textooks referred to the Propostional Logic/Calculus rather than the Sentencail Logic/Calculus, but I have yet to see one refer to Statement Logic/Calculuss, and the first of these would say that it is proposition that are true or false, the middle sentences, the latter if there were any, statements. The use of the term proposition to mean theorem, as in Euclid, is quite another kettle of fish. If you are interested have a look at http://www.hf.uio.no/ifikk/filosofi/njpl/vol1no1/meaning/node2.html, stuff on proposition starting para 4. Enjoiy!--Philogo 19:49, 9 June 2008 (UTC)

P.S. Your latest fact tag is on something I didn't write and know little about. Why don't you just fix that part yourself.

Rick Norwood (talk) 13:18, 9 June 2008 (UTC)

I care little who wrote it, only if it is true, clear and justififiable. I am not editing this article mainly because it makes me wince.--Philogo 19:49, 9 June 2008 (UTC)

Ok, you don't like to edit and I don't know the facts. If you will tell me, here, what "proposition" means in your own area of expertise, I'll put that in the article. Rick Norwood (talk) 21:07, 9 June 2008 (UTC)

Rick have you had a read of http://www.hf.uio.no/ifikk/filosofi/njpl/vol1no1/meaning/node2.html ? I think you would enjoy it.--Philogo 21:09, 9 June 2008 (UTC)

Rick does your definition here of proposition in mathematics dovetail to the use in Propositional_calculus which claims to be a mathematical article?--Philogo 22:29, 9 June 2008 (UTC)

I have read, with some interest, the first of the three lectures you recommend. I am reminded, at times, of Lewis Carroll's argument that if A implies B, and we know A, then we cannot at once conclude B, but rather must say that A & A implies B imply B. But (according to Carroll), then we still cannot conclude B, but rather must say that A & A implies B & (A & A implies B implies B) are necessary. And so on ad infinitum. Thus, with the lecture, we have a statement A, which is either true or false. In the language of mathematics, A is also called a proposition. But, following Kant, I gather that philosophers want A to be called a "judgment" which affirms or denies a statement. But what is to prevent us from now considering the "judgment" that our judgment that A is true is a true judgment. And so on ad infinitum.

And this does not even get into the problems that arise when you judge that a statement is true, but I judge that your judgment that the statement is true is a false judgment.

If you consider these articles authoritative, then I can report what they say in the article. But more than ever I understand why mathematicians, as the lecture says, took the other road.

To your second comment: The propositional calculus, now more often called propositional logic or the logic of statements, considers statements that are either true or false. Predicate logic considers declarative sentences that contain variables, and are true or false depending on the values taken on by the variables.

I'll say more after I've read the second lecture.

Rick Norwood (talk) 23:49, 9 June 2008 (UTC)

I'm back. I started to read lecture two, then began skimming, and when I came to this in lecture three I gave up. Martin-Lōf writes,

"Are there propositions which are true,

but which cannot be proved to be true?

...there seem to be two possible answers to this question. One is simply,

No,

and the other is,

Perhaps,

although it is of course impossible for anybody to exhibit an example of such a proposition, because, in order to do that, he would already have to know it to be true."

Certainly Martin-Lōf cannot fail to know Gōdel's imcompleteness theorem, and yet knowing that theorem, and so presumably knowing that it is possible to exhibit an example of a proposition which is true but which cannot be proved to be true, how can he go on as he does, never mentioning Gōdel. It is a strange flaw, that casts doubt on the entire work. Rick Norwood (talk) 01:24, 10 June 2008 (UTC)