Talk:Proposition

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comment[edit]

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)

New lead paragraph[edit]

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 philosophers, 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)

Propositional logic[edit]

"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)


Street Philosopher[edit]

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.

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

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.

Difference?[edit]

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)

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

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)

References

  1. ^ Undergraduate texts include Boolos, Burgess, and Jeffrey (2002), Enderton (2002), and Mendelson (1997). A classic graduate text by Shoenfield (2001) first appeared in 1967.

Philogo's edit[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)

I'm going to indulge myself in a brief off-topic response here, almost five years late; while this is not what talk pages are for, it would be somewhat unfortunate to have people read the above without a response.
You have to interpret what Per Martin-Löf says here in the light of intuitionism, or at least his school of intuitionism (which is presumably the one I'm most familiar with, having studied it from Giovanni Sambin). In this view, "proof" does not mean exactly what (say) Hilbert meant by it — start with a fixed collection of formal axioms and apply a fixed collection of rules of production. Rather, it's something like "I can prove ∃xP(x) if I can name a particular a and demonstrate to you why P(a) must be true", where the meaning of "demonstrate" is never formalized. That sounds open-ended, and is, but in practice what they accept as a "demonstration" is generally narrower than what classical mathematicians accept.
So take a Gōdel-like example: Let S assert that there is no formalized Hilbert-style proof of 0=1 starting with the axioms of Peano arithmetic. Then S is presumably true, and presumably not provable in Peano arithmetic. What Martin-Löf is saying is that, if you succeed in proving S to him in his sense of the word "prove", he will accept it as true. Such a proof need not (or at least need not a priori) be formalizable in Peano arithmetic — he'll know it when he sees it. If you can't, then he doesn't accept S as true (which is not the same as saying he considers it false).
It's a very different paradigm from the one most mathematicians use so it's a little hard to follow when you look at such a lecture without warning that words are used differently from what you're used to, but (while I don't actually buy it) it's not as crazy as you might think. I do agree that Martin-Löf probably should have said something here about why the Gödel theorems are not a counterexample. By the way, Philogo's link is broken by now — you can find the lectures at docenti.lett.unisi.it/files/4/1/1/6/martinlof4.pdf. Any further discussion should probably happen on someone's user talk page, but I thought it was worth breaking the rules here just this one time. --Trovatore (talk) 19:33, 13 February 2013 (UTC)

Philogo's new edit[edit]

In mathematics, the statement "I am Sparticus," is not a proposition, but a predicate. The singular personal pronoun "I" is clearly a variable, and the truth value of the statement depends on the value of the variable. To a mathematician, there doesn't seem to be any difference between "I am Sparticus." and "'x' is 7". To obtain a truth value, we would quantify the predicate. Either there exists a person named Sparticus, which is true, or all people are named Sparticus, which is false.

This seems so obvious to me that I hope you will clarify its status in philosophical disciplines.

Also, you have deleted the discussion of the relationship between a proposition's explicit and implicit content. Is this no longer of interest in philosophy?

I am not sure what you mean by "in mathematics". "I am Sparticus," is surely not a predicate. The word "I" in English, refers to the speaker, or the writer. Hence if Tom Smith says "I am Spartacus" he is saying "Tom Smith is Spartacus"; the former like the latter is meaningful declarative sentence which can be used to express a proposition. If you do not believe that "I am Sparticus," is or expresses a proposition, then try saying it on oath in a court of law, or when passing through customs, or giving your name to a policeman, or opening a bank account. If your ID shows you are Rick then you would be accused of being a liar; then try the defence "I made/expressed no proposition, I merely uttered a predicate, so I cannot be a liar". Best of luck, let us know what happens!--Philogo 12:37, 17 June 2008 (UTC)
NB The article is clearly headed
This article is about the word "proposition" as it is used in logic and philosophy. For other uses, see Proposition (disambiguation).
not mathematics. (mathematical logic, symbolic logic, formal logic, elementary logic are all covered by the term logic)

--Philogo 12:40, 17 June 2008 (UTC)

But this leaves you with the problem you discuss in the article, of the "same" proposition having different truth values. If you accept that "I" is a variable, the problem goes away. I'm not trying to make the article about mathematics. Rather, I'm asking for a reference that in philosophy "I am Sparticus," is consider a proposition, rather than a predicate.

The examples you give are examples where, by speaking the phrase, I assign a value to the variable. I see no difference between that and pointing to a number 7 and saying "This number is 7." The act of pointing assigns a value to the variable.

If I say, "I am Sparticus," then the truth value is "false". But if I say, "Consider the sentence, 'I am Sparticus,'" then the truth value is unassigned.

If "I am Sparticus," is considered a proposition rather than a predicate in modern philosophy, then it should be easy to give a reference. (Need I say that the reference need not mention Sparticus, but only the assertion that a pronoun is not a variable.)

I'll see if I can find somewhere that discusses this point as I see what puzzles you. Usually in Logic books the first thing you learn is "transalting/representing" sentences in natural language into symbolic logic, be it sentential or predicate. You usually start with the sentential. In "transalting/representing" natural to sentential, we might translate/represent

If Socrates is wise, then Plato is envious. Socrates is Wise. Plato is envious

with

P->Q,P, Q.

. We would translate just the same

If I am Spartacus then I will die. I am Spartacus. I will die.

with

P->Q,P, Q.

. [more later (dinner time!)] Best wishes, --Philogo 18:25, 17 June 2008 (UTC)

Interesting. A mathematician would symbolize, "Socrates is wise" by P, but would symbolize "I am Sparticus" by P(x), indicating the presence of a variable.
I still wonder about the deletion of the paragraphs on the difference between denotation and connotation. Rick Norwood (talk) 12:56, 17 June 2008 (UTC)
I do not remember such a passage. When did it go?

--Philogo 18:25, 17 June 2008 (UTC) A logicain or mathematical logiciann would more likely symbolize, "Socrates is wise" by P(a), and would symbolize "I am Sparticus" by b=c, with an interpreation assigning to Socrates to a, who ever is the speaker to b and Spartacus to c.--Philogo 23:47, 13 October 2008 (UTC)

deleted passage[edit]

Here is the deleted passage, which you deleted on June 15 without an explanation.

A philosopher might observe that "snow" is a softer word than the German "schnee", and therefore produces a different reaction in the person who hears the word, while "tiny crystals of frosen water" suggests an entirely different context, and therefore a subtly different meaning. In fact, some philosophers have claimed that "meaning" occurs in the mind of the person hearing or reading the statement, and therefore changes from person to person, and within the same person from time to time.
Further, a philosopher might observe that snow reflecting the setting sun appears red, that snow at night may appear blue, and remind the reader of the common advice, "Never eat yellow snow." This "philosopher" might naively conclude that the proposition "Snow is white," has no universally agreed upon truth value, and some would go so far as to say that no proposition has a universally agreed upon truth value. It would be pointed out that the term "is white" normally means "appears white when illuminated by white light", and that different sentence-tokens of the same sentence-type (e.g "Today is Wednesday" "I am in London") have different truth-values depending on when and where the sentence-tokens occurred, and that to say that the sentence-type "Today is Wednesday" has no universally agreed upon truth value is just a confusing way of making this obvious observation.

I certainly agree it needs a rewrite, and references. I'm not sure deletion is the answer.

Rick Norwood (talk) 13:44, 18 June 2008 (UTC)

I don't thionk it says much of any imporance, epsieaclly with it weasel words 'A philosopher might...'

Its not explaining any theory or concept or presenting the views of any philosopher or movement. --Philogo 18:01, 18 June 2008 (UTC)

rename[edit]

Renamed article from Proposition to Proposition (philosophy) since title better reflects content--Philogo (talk) 00:47, 19 February 2009 (UTC)

Philogo do you realize that people use those titles to link to. There is no article named "Proposition" and you see a need to tag this thing "philosophy" as if it is some highly technical term. The prevailing use is this one. Please move this to the appropriate place "Proposition" and stop with the parentheses. You are moving this material father away from the reader practically and in principle. ?!?!? Pontiff Greg Bard (talk) 01:04, 19 February 2009 (UTC)

I agree. Please undo what you have done, Philogo. The article is already in the Category Philosophy.Rick Norwood (talk) 15:14, 19 February 2009 (UTC)

Proposition called a claim?[edit]

Page currently says

In logic and philosophy, the term proposition (also often simply called a claim)....

I don't think this is right. A proposition may be something that you consider flat false; a claim is usually something that you believe, or at least are assuming for the nonce. --Trovatore (talk) 00:19, 2 September 2009 (UTC)

I am a mathematician who has published in the area of mathematical logic, and I have never heard a proposition called a claim. Rick Norwood (talk) 12:41, 14 October 2009 (UTC)

1) One person calling a proposition a "claim" does not mean that it is "often" called a claim.

2) In "All men are mortal." the subject is "men", not "all men". "All" is a quantifier. A full statement would be "For all x, if x is a man, then x is mortal."

Rick Norwood (talk) 20:59, 29 October 2009 (UTC)

I did provide a reference, Parker and Moore (which is two people btw). These guys wrote a very popular textbook on the subject (which means more than two people agreed since it is in like its tenth edition.) Yes, it is correct for at least two reasons. The meaning of "claim" clearly involves both that it be a statement, and that it be either true or false. The term "claim" redirects to this article. I am not sure what the point of #2 is supposed to be. Is "full statement" some kind of term because it looks like you are making a universal instantiation of a propositional function there.

Furthermore, all critical thinkers call propositions "claims". Pontiff Greg Bard (talk) 21:12, 29 October 2009 (UTC)

Parker and Moore is a wonderful book. It is, however, an attempt to explain logic in natural language to college students. Parker and Moore never say "a proposition is often called a claim", they just use the word "claim" as a common word that is easier for beginning students to understand than "proposition". Everything in that book is aimed at beginning students, and it is not a good reference for an encyclopedia. Rick Norwood (talk) 21:26, 29 October 2009 (UTC)

Insofar as logic and critical thinking and Wikipedia is concerned, it is a RS. Your characterization of the book and Wikipedia are your POV. This is a general reference encyclopedia for a wide readership... this includes non-mathematicians. I think what is happening here is that some people just insist on mathematical jargon to the exception of other terminology used. That's not appropriate for this article, nor Wikipedia. In the interest of people searching that term, please relent. Always include alternate terms. Pontiff Greg Bard (talk) 21:37, 29 October 2009 (UTC)

Propositions are NOT sentences[edit]

Why are we defining propositions as sentences, when philosophers have consistently distinguished between sentences as units of language and propositions as what sentences express? I'm not sure I know of any prominent philosopher who thinks propositions just are sentences. Parableman (talk) 12:57, 12 June 2010 (UTC)

I am not sure what's going on, but I am pretty sure that most practising mathematical logicians don't make this kind of distinction. Propositions in the sense you describe aren't of much use as mathematical objects. Some time ago I learned on Wikipedia that some people argue for renaming propositional logic to "sentential logic" based on this philosophical definition lf "proposition". That's the first I ever heard of it. A small number of mathematical textbook authors seem to have followed this proposal, but the majority still use the standard term.
Could it be that the second sentence is intended to explain how philosophical terminology differs from the plain language meaning of "proposition" and the way the term is used in mathematics? Hans Adler 13:14, 12 June 2010 (UTC)
Parableman is right that the article here shouldn't define a proposition as a sentence. But let me explain first what I think is going on. Mathematicians (I am one) don't really use the word "proposition" except in vestigial forms such as "propositional variable" or "Proposition 1.32". However, philosophers have different ideas. They like to distinguish between "sentences" and "propositions", particularly in the (metaphysical) study of truth. From the SEP article "Propositions":
"Propositions are also commonly treated as the meanings or, to use the more standard terminology, the semantic contents of sentences, and so are commonly taken to be central to semantics and the philosophy of language. "


Another nice place to start in the SEP is Correspondence theory of truth:
"Confusingly, there is little agreement as to which entities are properly taken to be primary truthbearers. Nowadays, the main contenders are public language sentences, sentences of the language of thought (sentential mental representations), and propositions. Popular earlier contenders, viz. beliefs, judgments, statements, and assertions have fallen out of favor primarily because of the problem of "logically complex truthbearers".
The thing that is amazing to mathematicians is that anyone has found it relevant to make a distinction between language-sentences, thought-sentences, propositions, judgments, statements, and assertions. However, if you reflect for a moment about the problems that would arise if you tried to defend a metaphysical theory of truth, it does make sense that these distinctions might be relevant.
Personally, I try to avoid editing these sorts of things, because as a mathematician I think I am not sufficiently sensitive to the area to get it right. However, I dug up the edit that changed the lede to its present form [1]. I think that going back to the previous lede would be an improvement. — Carl (CBM · talk) 14:33, 12 June 2010 (UTC)
I changed it back to the previous lede from the diff I posted. — Carl (CBM · talk) 14:48, 15 June 2010 (UTC)
I have to agree, claiming that propositions are sentences is far from uncontroversial; while it may well be that the distinction is meaningless in mathematics it is certainly a valid and very important area of contention in philosophy, at least in theories of truth. Many different sentences (utterances, what have you) can express the same proposition -- I have never heard anyone claim that they are the same entity, and even if a source could be produced attesting to this equivalence it certainly shouldn't be presented in the lede as if it were the only possibility. BrideOfKripkenstein (talk) 23:12, 15 June 2010 (UTC)
The article Truthbearer explores the various usages of the terms sentence, proposition statement &c. and sets out the various philosophical issues involved. As the article Truthbearer says Many authors use the term proposition as truthbearers. There is no single definition or usage. Sometimes it is used to mean a meaningful declarative sentence itself; sometimes it is used to mean the meaning of a meaningful declarative sentence. This provides two possible definitions for the purposes of discussion as below (wherein mds is written as shorthand for meaningful declarative sentence).Philogo (talk) 15:29, 14 November 2010 (UTC)

References[edit]

If I'm understanding him correctly, User:Gregbard has elsewhere conceded that propositions are not sentences; nonetheless I would offer the following two sources I was able to find right off the bat that support my contention (that propositions are not uncontroversially assimilated to sentences, either sentence types or sentence tokens):

  • Soames, Scott (1999). Understanding truth. New York: Oxford University Press. pp. 13–19. ISBN 0-19-512335-2.
  • Lycan, William G. (2000). Philosophy of language: a contemporary introduction. London: Routledge. pp. 80–87. ISBN 0-415-17116-4.

And, not to flagellate a deceased equine, I concur with User:CBM above. BrideOfKripkenstein (talk) 18:56, 16 June 2010 (UTC)

I think it's nonetheless fairly common to define propositions are either sentences or something like the meaning of sentences. While there is undoubtedly some philosophical debate on this, I find that introductory logic and critical thinking texts usually define propositions as sentences and texts which are somewhat more philosophically sophisticated go for the meaning definition (or something similar). I really don't think that this issue should bother us too much in the lede. I'd be happy if readers came away with an introduction to the subject similar to that found in elementary texts. Phiwum (talk) 02:39, 17 June 2010 (UTC)
And again, some quotations that might be of help:  User:Morton Shumway/Proposition (Quotes) --Morton Shumway (talk) 11:35, 3 August 2010 (UTC).

Related Concepts[edit]

Under thus section the article says 'Facts are verifiable information.' I have not see this definition before and a citation would improve the article, but I doubt if it is the only account of the concept of 'fact' (see eg/ http://plato.stanford.edu/entries/facts/) Philogo (talk) 19:07, 30 November 2010 (UTC)so the article should say perhaps 'Some authors says that Facts are verifiable' information.Philogo (talk) 19:02, 30 November 2010 (UTC)

Section is too confusing, self-contradictory and off-topic to be useful therefore deleting — Philogos (talk) 01:47, 13 October 2014 (UTC)

Anyone working on this?[edit]

Is anyone actively editing this page? I notice several things that I think should be changed, so if someone else is working on it, it might be easier to coordinate or plan changes. Also, I am fairly familiar with mathematical logic, linguistics, and, to a lesser extent, philosophy of language, but I am not familiar with how propositions are treated in philosophy generally. So if there is a philosopher around, I could use some help in that area.

For starters, I think it would be helpful to either focus the article on things that can be assigned truth-values or else institute at the beginning a distinction between the syntactic and semantic concepts relating to propositions. Other uses can be handled by pointing to the disambiguation page (or such). Perhaps an outline of the linguistic objects and distinctions associated with propositions would also be helpful.

In the meantime, the following paragraph jumps out as particularly bad:

In mathematical logic, propositions, also called "propositional formulas" or "statement forms", are statements that do not contain quantifiers. They are composed of well-formed formulas consisting entirely of atomic formulas, the five logical connectives, and symbols of grouping (parentheses etc.). Propositional logic is one of the few areas of mathematics that is totally solved, in the sense that it has been proven internally consistent, every theorem is true, and every true statement can be proved.[2] (From this fact, and Gödel's Theorem, it is easy to see that propositional logic is not sufficient to construct the set of integers.) The most common extension of propositional logic is called predicate logic, which adds variables and quantifiers.

I don't recall seeing the term "proposition" used often in mathematical logic, only perhaps in introductions to logic aimed at non-mathematicians. Instead, I see terms like "string", "formula", "well-formed formula", "expression", and "sentence" for the syntactic notions, and for semantic notions, "interpretation" or "value" of some kind. (I have, though, seen "atomic formula" defined to include some strings with quantifiers.) Also, propositional logic (including its atomic formulas) is also called sentential or statement logic. Since there are objects in predicate logics that can be assigned truth-values, this whole section seems misleading in the context of the article. Anyway, since usage isn't consistent across authors, more explanation seems in order. Also, there are not only five logical connectives (think not only of the Sheffer strokes but all other n-ary connectives). The "totally solved" remark is bad for many reasons. The reference to Gödel's first incompleteness theorem seems irrelevant besides being poorly stated. The last comment also seems unmotivated, but at least "extension" should be clarified (it has specific meanings in logic and model theory), and predicate logic adds predicate and function symbols in addition to quantifiers and variables.

Cheers, Honestrosewater (talk) 09:12, 15 January 2012 (UTC)

The section you quote as particularly bad is based on Hamilton's Logic for Mathematicians. Of course, there are other ways of developing symbolic logic and other terms used. Improvement is always welcome, especially from people who are active researchers in this area. Rick Norwood (talk) 13:57, 15 January 2012 (UTC)
Well, I can see it being clearer in context. I can add some to the logic and linguistic aspects, but I wouldn't know where to begin with the philosophy stuff. Some of the claims seem suspicious, though. For example,
The existence of propositions in sense (a) above, as well as the existence of "meanings", is disputed by some philosophers
What philosopher -- serious, professional philosopher -- disputes the existence of meanings? Unless they are using some uncommon meaning of "meaning", it doesn't seem tenable. How would such a person explain language use? Perhaps what was meant is that philosophers dispute particular theories of meaning, reference, and such, e.g., Fregean senses.? Cheers, Honestrosewater (talk) 14:57, 15 January 2012 (UTC)

I added a bit to the Logic section and deleted the references to consistency and completeness. I'd appreciate any feedback so I know if or how to continue. Cheers, Honestrosewater (talk) 19:04, 15 January 2012 (UTC)

There is a very good article in the January 2012 issue of the Notices by Frank Quinn about the different understanding of "truth" in mathematics and in philosophy. I don't know if any part of it applies here, though. Rick Norwood (talk) 20:39, 15 January 2012 (UTC)
I hate to say it, Honestrosewater, but I think now you have gone into much more detail than this article needs. For example, the idea that a proposition can be viewed as a string of symbols is important, but a catalog of the kinds of symbols that can be used (variables, quantifiers, etc.) is too much to go into at this level. I think what the reader needs to know in this article is that the word "proposition" is often used in mathematical logic, that it is sometimes distinguished from the word "predicate", and that it is assumed to have a truth value. In other words, I found the previous version not too short, but too long.
I also note that the paragraph on Logical Positivism, which has been part of the article for a long time, doen't make beans for sense. What is the truth value of a STOP sign?
And it occurs to me that the article should mention "The King and I".

Rick Norwood (talk) 21:17, 15 January 2012 (UTC)


Yes, I agree with you mostly about the level of detail. I had more detail about symbols originally but trimmed it down. I could perhaps trim more. The point was mainly to show that propositions, as syntactic objects, can be built up in different ways, and this affects what propositions, as semantic objects, can be expressed or proven in the system or something along those lines. I don't think these distinctions have been made quite clear enough yet, though.
Quinn's article so far is amusing and right, I think. I can't stand most philosophy, and most people hate math. :^) It's interesting because I am doing an independent study in nonstandard analysis this semester and so have been reading and thinking about this period in mathematical logic (~1850-1931), model theory, and the back-and-forth between intuition and formalism. It ended up being a strange (and nonconstructive) formalism from math logic and model theory (nonstandard models via compactness, nonprincipal ultrafilters, and such) that allowed an infinitesimal approach to reemerge (and Leibniz himself anticipated (and hoped for) much of the formalization). Anywho... good stuff.
I notice that you guys seemed to want to make this article mainly about philosophy? But the articles that Philogo mentions, declarative sentences in linguistics and statement and sentence in logic, are not about the same thing. In linguistics, you have an even more complicated situation because, in addition to the more complicated language, you have to also consider pragmatics. Consider "A couple was hit by a bus. The driver called for help." The second sentence expresses the proposition (grant, for argument) that the driver of the bus called for help. Or the discourse as a whole conveys this, at least. But neither sentence expresses this explicitly. It is an inference that the hearer is expected to and does make (called a bridging inference). In a similar vein, "Q: Did you finish your homework? A: I finished most of it." conveys that not all of the homework was finished, though this is not explicitly stated (this is a scalar implicature). There are many more things to untangle: utterance, locutionary act, physical signal, linguistic signal, conceptual signal, sentence, statement, propositional content, assertion and other illocutionary acts, meaning, intended (speaker) meaning, received/inferred (hearer) meaning, truth-functional/semantic meaning, pragmatic meaning, inference, presupposition, implicature, ambiguity, reported speech, etc. It's rather hairy. :^|
I think the linked SEP article starts in a good way, by noting the many meanings of the term. Would it be a bad idea to try to organize this article by how the different fields that address propositions (logic, linguistics, philosophy) deal with it, perhaps with some indication of the scope of meanings given in the intro? The historical usage section now only includes philosophical uses, so this could be a start to the philosophy section. The logic section also is started. I can start a linguistics section.
Perhaps a better option would be to organize by the different meanings or relationships of the term. E.g., how propositions are related to speech acts, to formulas in formal languages, to truth-values, sentences, mental states, etc. Then the approaches, if any, of different fields can be treated in the appropriate section.
I do not know how traffic signs are true or false, though. I suppose it depends on the type of sign. (We could add a bit about semiotics, the more general theory of signs (in a technical sense of the word).) A stop sign has more of a directive meaning, I think, as I presume you meant; it tells you to do something. Something like a street sign (with the name of a street) could maybe be interpreted as asserting that some street has some name or perhaps it is declarative in that the sign actually makes a street have a name by virtue of its being there. It is perhaps more important to explain the issues than to pronounce verdicts anyway. People can interpret things in different ways, so it's hard (maybe impossible?) to find perfect consensus, though some overlap of interpretations must exist for the system to work.
I have to plead ignorance about The King and I.
Cheers, Rachel / Honestrosewater (talk) 22:47, 15 January 2012 (UTC)

The King and I is a Broadway musical in which the King of Siam begins many of his speeches with the word, "Proposition". Rick Norwood (talk) 23:54, 15 January 2012 (UTC)

Merge "Statement (logic)" proposal[edit]

I am proposing that the article Statement (logic) be merged here to "Proposition". This is a continuation of the suggestion at Talk:Statement_(logic)#Merge_with_proposition.3F. Generally speaking — although I'd guess some particular authors differentiate (although probably also inconsistently) — I believe that "statements" and "propositions" are synonymous and are used interchangeably. The "Statement (logic)" article is short and less-well developed, hence it seems to make better sense to merge here (even though I have a slight personal preference for "statement"). If you believe there are separate concepts, please detail as succinctly and accurately as possible what you believe the difference is (preferably with some sources). Jason Quinn (talk) 22:20, 12 February 2013 (UTC)

From the other discussion, User:Gregbard has raised concern about what this means for categories using the names. I have responded briefly about that at the old discussion. Jason Quinn (talk) 22:38, 12 February 2013 (UTC)
"Proposition" is the older usage, "statement" the more recent, but in most mathematical contexts they are synonyms, and we don't need two articles. Rick Norwood (talk) 22:55, 12 February 2013 (UTC)

From a mathematical point of view these are just synonyms, although some people might want to permit general truth values for statements and reserve the term proposition for statements that are always true or false. In philosophy there are, as usual, no uniform definitions. The meanings still seem to significantly overlap there, as in mathematics with a tendency for statement to be the slightly more general term.

I think it's very sensible if not inevitable to discuss the two terms together in one article. For those authors who treat them as synonyms this is a necessity. For those who define both differently, the meaning of both terms will be much clearer if we define them together. This seems to be the only way to prevent major confusion on these terms. Hans Adler 23:22, 12 February 2013 (UTC)

Regarding Category:Statement and Category:Proposition: I agree that they clearly have different flavours. I see no reason why they should immediately be merged just because we merge the articles. In fact, they could just stay as they are; otherwise one or both should be renamed. Unless someone wants closure before the article merge, I think this can be discussed later. (I doubt that I will participate in a discussion on the categories.) Hans Adler 23:29, 12 February 2013 (UTC)

I think it is sensible to merge these two subjects. One practicle reasons is that meta-connections are scattered with some connecting to 'proposition' the other to 'statement (logic)'. I sense that most people would agree to merge these two and discuss the difference (if there is) on the same page. — Preceding unsigned comment added by Timelezz (talk • contribs) 12:35, 8 December 2013 (UTC)

To understand whether these are really two sides of the same coin. A Statement like "I want strawberries", is a Proposition as well? Timelezz (talk) 16:26, 18 December 2013 (UTC)

The distinction is important in philosophy and theoretical linguistics. Consider that, in most cases, many statements express the same proposition (the same underlyimg idea). I.e. there are usually several ways to say the same thing. I can not stress enough how useful the distinction is. — Preceding unsigned comment added by DPhil2002 (talk • contribs) 13:29, 20 May 2014 (UTC)


There is a very important distinction between propositions and statements. Propositions admit multiple representations. Statements are their representations. Consider a mathematical and linguistic example:

Take the statements '2/2=1' and '2*(1/2)=1'. Both statements express the same proposition. Take the statements 'All cats are mammals' and its contrapositive 'No cats are non-mammals'. Both statements express the same proposition.

If propositions are statements then '2/2=1' and '2*(1/2)=1 are two propositions that express the same proposition (or two statements that express the same statement).

Merging statement and proposition is just a bad idea. I suggest this discussion be closed. 174.91.34.251 (talk) 13:48, 2 October 2014 (UTC) MikeZhao

I think you're taking "statement" to mean "sentence". That is indeed one possible usage of the word, but I do not believe it is the majority one. If the merge happens, there will need ot be a hatnote at the top referencing this other sense. --Trovatore (talk) 16:58, 2 October 2014 (UTC)
Opposed to merge. As is clear from the articles statements and propositions are distinct concepts of truth-bearers justifying distinct articles.— Philogos (talk) 01:02, 20 October 2014 (UTC)

Proposition equals implication?[edit]

When I looked up "inverse" in WP, the article begins immediately talking about implications. So I wondered "Are all propositions implications (because it seemed to me that all propositions should have an inverse)? Elsewhere on the web I found propositions being discussed as implications. If philosophy (does it?) commonly uses this equality ("All A are B" is the same as "If something is A then it's B" or "C implies D for some C, D"), or whatever, should that be discussed somewhere here? -lifeform (talk) 05:52, 8 March 2016 (UTC)

Lesser of Two Equals[edit]

Much of this dicussions deals not with a word but more like an anti-statement made by people who find out that they themselves deal with the proposition but are not targeted by the proponent. What you have thus is a antagonist/protagonist article reffering to the discourse of human kind. As a whole people, this is very suspicious and not to the point of fact. A proper way to put it is that the word deals with risk, not value. — Preceding unsigned comment added by 2602:301:7751:160:863:41AF:35BC:9314 (talk) 14:29, 27 January 2017 (UTC)

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