Talk:Atomic sentence

message: Edited all accept the examples: --Philogo 12:23, 3 September 2007 (UTC)
thread_title: edits

message: Carl (CBM · talk)  says I think that a more nontechnical definition (one that attempts to capture what an atomic sentence would be in natural language) would improve the article.  Is this a good idea or should the article stay with dealing with the term Atomic Sentence as used in Symbolic Logic? Problem 1. It would be on what an atomic sentence would be in natural language, as used in Logic (see article title) not what is. If the term is not used in Logic in connection with natural language then this would be the proscribed original reseach and or not to do wuth Logic, more perhaps Philosophy of Logic of Philosophy of Language.  Great topic, but is this the place fot it?  If you look up Wittgenstein. TLP para 4.21 to 4.24 you will see that whatever W. used in Germn is transalted as elementary proposition not atomic sentence.  He said:  4.24 The simplest kind of proposition, an elementary proposition, asserts the existence of a state of affairs   
but then  says:
4.24 ..I write elementary propositions as functions of names, so that they have the form 'fx', ψ(x,y) etc. or I indicate them by the letters 'p', 'q', 'r'. so HE was referring to an artificial language,  but beleives - I understand - that there are facts which are what is the case  and the latter is the existence of a state of affairs (2) and with 4.24 he must believe that there are elementary facts which correspond to (are pictured by) elementary propositions.  But W. said Russell and Moore would never understand TLP so what hope have I? And is this article the place to discuss these issues, or should they not better come under a Phil o Logic Article?--Philogo (talk) 20:47, 20 February 2008 (UTC)
thread_title: Proposals for this article

message: Kaustuv Chaudhuri said, 13:14, 26 September 2007 (UTC)
replies: text: Is it that bad?  —Preceding unsigned comment added by Philogo (talk • contribs) 13:57, 31 January 2008 (UTC)

text: No merge. They are very closely related, however, that justifies keeping them separate, so that the distinction is clear. Pontiff Greg Bard (talk) 19:40, 31 January 2008 (UTC)
replies: text: At some point I have been planning to work on all these split- up articles on formulas, sentences, etc. "Atomic sentences" are a strange concept to emphasize, as they are simply the sentences of propositional logic. Eigenvector is a nice example of how intimately-related topics can be covered in a single article. — Carl (CBM · talk) 22:21, 31 January 2008 (UTC)
replies: text: ...as long as it is presented in such a way that one gets confused. People may be looking up one or the other so as to be able to distinguish them from each other, etc. I think having a separate article helps, but then it will always be a short one. I am very supportive of the goals of WP:INT. Pontiff Greg Bard (talk) 22:32, 31 January 2008 (UTC)

text: Are not 'Fa', 'Gab', 'Habc' etc. atomic sentences although not sentences of propositional logic?
--Philogo (talk) 14:17, 11 February 2008 (UTC)

text: One issue is that atomic sentence is a virtually unknown term in the literature. It makes sense as a term, but only a a corner case of atomic formula when there are some 0-ary relations in the language. Since ordinarily one doesn't work with 0-ary relations in the context of first-order logic (as a matter of practice), the term really isn't particularly important. It's right up there with putting an atomic formula in prenex form - it has one, but prenex form is only interesting for formulas with quantifiers. Similarly, the idea of sentence is only interesting for formulas with variables. — Carl (CBM · talk) 02:22, 9 February 2008 (UTC)

text: In the context of propositional (sentential) logic, perhaps. But this article uses the definition of sentence from first-order logic, in terms of free variables. Perhaps the issue is that the article is simply confused. — Carl (CBM · talk) 03:08, 9 February 2008 (UTC)
replies: text:  The definition 'In (sentential logic and predicate logic), an atomic sentence is an atomic formula in which no variable occurs free.' would appear to define the term atomic sentence for both sentential and first order logic.  Since there ARE no variables in the former, it would follow that in the former (but not the latter) an atomic sentence is the same as an atomic formula.  If the definition does not hold for higher order logics then it should be amended to say 'In (sentential logic and first order predicate logic),...'--Philogo (talk) 14:24, 11 February 2008 (UTC)

text: No, those aren't atomic sentences, since they are not even atomic formulas. — Carl (CBM · talk) 15:14, 11 February 2008 (UTC)
replies: text: 
As I said if they are not then their examples should be removed from the articel, but...
If they are not atomic formulae then Mendelson, Introduction to Mathermatical Logic, 1964,  Chapter 1 page 46 is wrong when he writes:
The predicate letters applied to terms yield the atomic formulae, i.e. if A is a predicate letter and t1..tn are terms, then A(t1..tn) is an atomic forumula.
[Terms are previously defined as just variables, individual constants and functions]
Also see:
Formal Logic/Predicate Logic/Formal Syntax
i. A sentence letter (a zero-place predicate letter) is a well-formed formula. 
ii. If A is an n-place predicate letter (n greater than 0) and a1..an are terms, then A(a1..an)is a well-formed formula. 
An atomic formula is one formed solely by formula formation clause {i} or {ii}. Put another way, an atomic formula is one in which no sentential connectives or quantifiers occur.  —Preceding unsigned comment added by Philogo (talk • contribs) 14:18, 12 February 2008 (UTC)

text: Notice the explanation you quoted: "Put another way, an atomic formula is one in which no sentential connectives or quantifiers occur."  That is exactly the normal definition of an atomic formula.  So since there are no quantifiers, and no free variables, there must be no variables whatsoever in an "atomic sentence".  I looked at three references quickly this morning, and none of them even included in the definition the possibility of 0-ary relation symbols in a first-order language. So while it would be possible to define an atomic sentence in first-order logic as a sentence consisting of a single 0-ary relation symbol and nothing else, this definition is essentially unheard of, because it has little practical interest in first-order logic. — Carl (CBM · talk) 14:40, 12 February 2008 (UTC)
replies: text:  I see the source of some confusion here.  The article says:
"
the following wfs are atomic sentences:
* p
* F(a)
* H(b,a,c)
*
The following wfs are  atomic formulae but not atomic sentences because they include free variables:
* F(x)
* G(a,z)
* H(x,y,z)
"
I MEANT to say above:
"
If the following examples given are indeed NOT atomic sentences:
* x(F(x))
* z(G(a,z))
* F(a)
* H(b,a,c)
then parts of the article above need revision
"
--Philogo (talk) 13:26, 13 February 2008 (UTC)

text: Things like F(a) are atomic sentences, yes, in the sense that they are atomic formulas and sentences. Now the question is the extent to which this topic is covered in logic texts. My experience is that it is not a topic of much interest, and rarely covered. — Carl (CBM · talk) 13:41, 13 February 2008 (UTC)

text: Please note that the topic of this section is about merging this with the article on atomic formulas. I'm glad that you've figured out the definitions, so that we can get back to talking about that. — Carl (CBM · talk) 14:42, 13 February 2008 (UTC)
thread_title: Merge with Atomic formula

message: I propose the following REVISED new introduction (that is (a) independent of the article on atomic formula and (b) addresses the issue of the equivalents of atomic sentences in natural languages):--Philogo (talk) 13:16, 22 February 2008 (UTC)
replies: text: I like that, modulo some minor copyediting. The last paragraph is redundant with the next-to-last paragraph, though; they could be merged or the last paragraph removed. — Carl (CBM · talk) 14:47, 21 February 2008 (UTC)
thread_title: Proposed New Introduction

message: Someone mentioned it above, but I thought it deserved its own section.  Sentences are often mentioned as being either atomic or molecular, but there's no mention of the word molecular in the entire article (not even the 'see also' section).  DavidRF (talk) 23:25, 20 July 2008 (UTC)
replies: text: Sorted! See "A sentence consisting of one or or more sentences and a logical connective is a compound (or molecular sentence)." in lede.  For details see logical connective. I don'tthink it needs a whole article to itself, but logical connective could note molecular and compund are synonymous.  Note you can have sentences which are not simple sentences that are not compound (molecular) sentences either on this defeinition, i.e. those which are not simple because they contain quantifiers, eg (x)Fx.  It makes sense that (x)Fx is not a simple sentence because it can be seen as equivalent to Fa & Fb & Fc. & .. for all elements in the domain.  A characteristic of an atomic sentence is that it can be joined by conjuction with any other atomic sentence without contradition.  Moreover no atomic sentence can be deduced from (is not entailed by) any other atomic sentence.  Wittgenstein made much of this in his Tractatus Logico-Philosopicus. If there are such atomic sentences then there must be "atomic facts" which correspond to them, and the conjuction of all true atomic sentences woould say all that that was the case, and that of course is "the world" (according to Wittegenstein: "The world is all that is the case", T L-P, 1.0. Enjoy!--Philogo 00:07, 21 July 2008 (UTC)
thread_title:  request article for [[molecular sentence]] 

message: I have to object to Philogo's latest unexplained editing. Furthermore, I feel I have to say something about this whole "truthbearer" obsession. Perhaps we can take things a little bit at a time and see if we can come to an agreement about things. I also feel that some of the best material was taken out, and I am astonished by that. Greg Bard (talk) 21:19, 5 December 2010 (UTC)
replies: text: Could you say which were the "best bits" you refer to/or suggest how the article could be improved?  I note you have not waited to "take things a little bit at a time and see if we can come to an agreement about things".  I will copy below the two latest  versions for comparison and comment by others.
Philogo (talk) 18:47, 6 December 2010 (UTC)

text: For one thing, when you say "atomic sentence" to me, that makes me think that we're concentrating on the syntactic aspects, saying that an atomic sentence is one that is true or false (a truthbearer) seems suspect to me as illicitly applying a semantic concept.  What if I'm in a non-classical sentential logic with a semantics that allows for truth-value gaps? Can't I still define an "atomic sentence"?  Similarly for first-order-like logics with free variables/quantifiers. BrideOfKripkenstein (talk) 00:48, 8 December 2010 (UTC)
replies: text: I think these matters were resolved to the satisfaction of editors as discussed in the section above "Proposed New Introduction" and prior.  The agreed lede remained substantially unchanged (so far as I can see) until May 27 2010 22:02 when it was changed without discussion on this talk page. I reverted to the previous agreed lede, with the note "revert degradation".  The lede was subsequently changed again without further discussion on this talk page. I feel that if a lede has been agreed by consensus among a number of editors then non-minor changes should be proposed and discussed on the talk page prior to implementation.  Therefore I propose that we revert to the lede agreed by consensus, immediately prior to the edit of May 27 2010 22:02, and then non-minor changes should be proposed and discussed on the talk page prior to implementation. (We could discuss the particular point you raise in a new section of this page).    Philogo (talk) 15:03, 8 December 2010 (UTC)
replies: text:  Which version of the three below are you proposing for the lede? Sorry if I'm being dim. As to your outside-the-box, maverick proposal that we discuss changes on the talk page . . . it just might work.BrideOfKripkenstein (talk) 16:34, 8 December 2010 (UTC)

text: Version (b): 5/12/2010 17:47 (because it looks much like the consensus version a, with just some links  added)Philogo (talk) 16:49, 8 December 2010 (UTC)
thread_title:  degradation