Talk:Interpretation (logic)

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[edit] NEWCOMERS START HERE (5 May 2008)

Those who visited this talk page for the first time on or after, say, 3 May will hardly be able to read this amount of information and to understand what the whole discussion is about and where it started. But reading the whole talk page in not necessary. To form your own opinion, look at the version of the article of 29 April, which was the object of the initial dispute, http://en.wikipedia.org/w/index.php?title=Interpretation_%28logic%29&oldid=209108477, then, if you wish, look at the present version, and decide yourself. --Cokaban (talk) 14:21, 5 May 2008 (UTC)

[edit] Trying to find a consensus

Philogo asked if we have consensus about the definition. I think after all this discussion that's a complicated question, so I try to break it down into several small points that I hope are uncontroversial. Please reply whether you agree, listing any points that you doubt or disagree with.

1a) There are several similar but slightly different definitions of "interpretation" in the literature. Mendelson's definition is the most typical among them, and the obvious candidate for presenting in an article called "interpretation (logic)".

I have not seen the definition of Mendelson, or i do not remember it. In any case, no objections. --Cokaban (talk) 06:26, 6 May 2008 (UTC)
Mendelson's definition is definition of interpreation no 6 above.--Philogo (talk) 22:11, 6 May 2008 (UTC)
Modulo trivial differences, I think Mendelson's definition is the same as is presented in all mathematical logic texts. — Carl (CBM · talk) 11:16, 9 May 2008 (UTC)
I would support support the use of this definition no. 6 but would suggest a fuller presentation such as Mate's nos. 5 and 7 above. Mendelson's is defintion is rather too terse to stand alone for the non-speacialist non-mathematican reader. Mendelson book was written for mathematic students; Mates for non-mathematical Logic students .--Philogo (talk) 20:21, 6 May 2008 (UTC)
I support the Mates formulation. Pontiff Greg Bard (talk) 16:42, 7 May 2008 (UTC)

1b) Many mathematicians are not familiar with the term "interpretation", because (at least in model theory) it is obsolete.

I did not know about this. Though it seems that indeed in model theory it is more customary to talk about interpretations in the sense of interpretable structures. It is true that many mathematicians are not familiar with the term "interpretation", simply because they are not familiar with model theory. --Cokaban (talk) 06:26, 6 May 2008 (UTC)
Every mathematician is familiar with the idea that "one person has a different interpretation than another." That's what this article was intended to be. Pontiff Greg Bard (talk) 16:42, 7 May 2008 (UTC)
This makes sense to me as an opinion, but i am not sure if the article interpretation (logic) is really supposed to be about this (sounds a bit like psychology to me). It may be reasonable to start a new section and ask what the others think about Gregbard's interpretation of the subject of the article. I would be very interested to know how many people share this POV. --Cokaban (talk) 13:08, 8 May 2008 (UTC)
The difference between an descriptive interpretation and a model is made clear below Pontiff Greg Bard (talk) 07:49, 6 May 2008 (UTC)
So if mathematicans read this article then they will become clear. --Philogo (talk) 22:12, 6 May 2008 (UTC)
Wrong. "Interpretation" in model theory is not obsolete. And the article Greg wants should be at interpretation (rhetoric) or possibly interpretation (philosophy), not interpretation (logic). — Arthur Rubin (talk) 14:49, 12 May 2008 (UTC)

1c) Mendelson's technical definition of "interpretation" is much more precise and rigid than the natural language meaning of the word.

Should be so. --Cokaban (talk) 06:26, 6 May 2008 (UTC)
Mathematicians will always see it that way. However, a natural language philosopher will say that natural language is actually more precise. Both are intended to follow the patterns in reason. I think the mathematicians really don't care anything about mirroring reason, etc. Math is set up to be convenient, not true or reasonable. That's why you guys think its so important to be able to assign non-unique names, when reasonable people don't do that. Pontiff Greg Bard (talk) 16:42, 7 May 2008 (UTC)
Sweeping generalisation. Please define the term natural language philosopher, an then provide quation from one where he or she says that "natural language is actually more precise" than xxx.
Gregbard, can you name a "reasonable person" other that yourself, mathematician or not, who also thinks that it matters whether an object has a unique name or not? Who are these other "reasonable people" who are comfortable with names which do not name unique objects? (i am just curious whether i've missed something.) --Cokaban (talk) 13:20, 8 May 2008 (UTC)
Even philosophers recognize that natural language may be ambiguous. I doubt very much that any "natural language philosopher" fails to recognize the need for a speciaized formal language in some context. — Arthur Rubin (talk) 14:49, 12 May 2008 (UTC)

2a) An interpretation in Mendelson's sense is the same thing as a structure (mathematical logic).

Cannot comment, but should be so. --Cokaban (talk) 06:26, 6 May 2008 (UTC)
If so, article should say it is a synonym--Philogo (talk) 20:21, 6 May 2008 (UTC)
Be careful. I'll bet there is a subtle difference. Pontiff Greg Bard (talk) 16:42, 7 May 2008 (UTC)
On second thought i agree with Gregbard. --Cokaban (talk) 13:22, 8 May 2008 (UTC)
There is no difference. Gregbard, please explain what you are thinking, if you don't see they are the same. — Carl (CBM · talk) 11:16, 9 May 2008 (UTC)
Carl, maybe you meant that model and structure are the same? Still, even though models and structures are in a sense equivalent, i would not say that they are the same. Models are used my model theorists, structures --- by universal algebraists, and the formal definitions are probably slightly different. Interpretation (or model), in my opinion, includes the data about all constant and relational symbols used (and hence about the whole language), while in a structure (in the sense of universal algebra) one usually keeps track only of their arities. See also my comment about these in New Lede. --Cokaban (talk) 10:21, 10 May 2008 (UTC)

2b) Many philosophical logicians are not familiar with the term "structure", because it is relatively recent.

Quite likely, so article should say structure is a synonym for interpretation and not use structure to defeine interpretation--Philogo (talk) 22:14, 6 May 2008 (UTC)
Agreed. Pontiff Greg Bard (talk) 16:42, 7 May 2008 (UTC)
There is huge variation in terminology between different texts even in the same field. — Carl (CBM · talk) 11:16, 9 May 2008 (UTC)

3a) A model of a language is the same thing as an interpretation (Mendelson) of the language.

I thought that "models" are only used for "theories", but i do not mind using the term this way too. --Cokaban (talk) 06:26, 6 May 2008 (UTC)
Agreed. That why the thing about Peano arithmetic which was removed belongs in there. Pontiff Greg Bard (talk) 16:42, 7 May 2008 (UTC)
Even if it is the case, the article is called "Interpretation (logic)", not "Model (logic)", and hence it is about "models" of languages, not of theories. This is why i thought the Peano Arithmetic was not relevant. Even if one thinks that models of theories are relevant here, Peano arithmetic is just an arbitrary and not so elementary example, though a well-known one. --Cokaban (talk) 13:30, 8 May 2008 (UTC)
This is a different meaning of "model". The more common one refers to theories. — Carl (CBM · talk) 11:16, 9 May 2008 (UTC)

3b) A model of a sentence is the same thing as an interpretation (Mendelson) of the language of the sentence, under which the sentence is true.

There is a subtle point here. What is the language of a sentence? Is it always the minimal language containing all the symbols from the sentence, or is it specified as a part of the structure of the sentence, and so is allowed to contain other symbols as well? --Cokaban (talk) 06:26, 6 May 2008 (UTC)
Be careful. Pontiff Greg Bard (talk) 16:42, 7 May 2008 (UTC)
Yes; the sentence is treated as a theory. — Carl (CBM · talk) 11:16, 9 May 2008 (UTC)

3c) All logicians, whether mathematicians or philosophers, are familiar and comfortable with the term "model".

Not too sure about that, I see some dounts above. Therefore do not use the term model in defintion of intepretation, but instead describe it in body or article.--Philogo (talk) 22:14, 6 May 2008 (UTC)
Thanks. --Hans Adler (talk) 22:28, 5 May 2008 (UTC)

I list below some more statements for comment or to build bridges and spread mutual understanding:

I agree that an interpretation is the same as a model. I've always heard that. The article on structure (which model redirects to) did not look like the same concept at all. The whole thing looks like that now though, so we have the same problem that caused me to create this article in the first place. Pontiff Greg Bard (talk) 16:42, 7 May 2008 (UTC)

4 Logic, Philosophical Logic and Philosophy of Logic are distinct branches of Philosophy.

I wouldn't say that strictly speaking, but I'm easy, so I'll go along with it. Pontiff Greg Bard (talk) 16:42, 7 May 2008 (UTC)
I have no idea, so I am prepared to believe it. --Hans Adler (talk) 21:36, 7 May 2008 (UTC) – I agree with CBM: The word "logic" is ambiguous. When philosophers say "logic" they usually mean a branch of philosophy, when mathematicians say "logic" the mean a branch of mathematics. They are not the same thing. --Hans Adler (talk) 10:20, 12 May 2008 (UTC)
No clue. --Cokaban (talk) 14:00, 8 May 2008 (UTC)
Seems dubious that "Logic" is a branch of philosophy. Certainly Philosophical Logic is. — Carl (CBM · talk) 11:16, 9 May 2008 (UTC)
This seems to imply that either mathematical logic is not a branch of philosophy (hence not a branch of logic), or mathematics is a branch of philosophy. — Arthur Rubin (talk) 14:49, 12 May 2008 (UTC)

5 The majority of philosophy students at universities in the English speaking world study Elementary Logic, by which I mean Sentential (formerly Propositional) Logic and First Order Predicate Logic (usually just called Predicate Logic). This Elementary Logic is usually called just Logic, but used to be called Symbolic Logic and is often called Mathematical Logic.

Agreed. Pontiff Greg Bard (talk) 16:42, 7 May 2008 (UTC)
Sounds plausible, not my business, and I am prepared to believe it. --Hans Adler (talk) 21:36, 7 May 2008 (UTC) – CBM is right. This defines "mathematical logic" as "elementary logic". This may be correct for the term "mathematical logic" as used by philosophers (which isn't my business). It's not surprising that people who only get exposed to a leisurely introduction to elementary logic, the basics of mathematical logic, confuse the two. But when mathematicians say "mathematical logic" they mean a large part of mathematics including a lot of algebra, and even some topology and differential equations. It makes no sense at all to call this "elementary logic". --Hans Adler (talk) 10:20, 12 May 2008 (UTC)
Do not know. --Cokaban (talk) 14:00, 8 May 2008 (UTC)
Yes. However, Mathematical Logic extends far beyond the elementary definitions and results, as does Philosophical Logic. — Carl (CBM · talk) 11:16, 9 May 2008 (UTC)
There's definitely a problem here. What Greg calls "logic" is not "Mathematical Logic", "Symbolic Logic", "French Logic", or any other form of Logic that I've seen. Whether it's the form "majority of philosophy students at universities in the English speaking world study" is another question. — Arthur Rubin (talk) 14:49, 12 May 2008 (UTC)

6 The majority of philosophers, and probably of philosophy students in the English Speaking world routinely use this Elementary Logic as part of their every day tools.

Agreed, Pontiff Greg Bard (talk) 16:42, 7 May 2008 (UTC)
Doesn't sound plausible to me, but it's not my business, so I am prepared to believe it. --Hans Adler (talk) 21:36, 7 May 2008 (UTC)
Hard to believe. (What does it mean to use this Elementary Logic, whatever it is, as a tool? An example, maybe?) --Cokaban (talk) 14:00, 8 May 2008 (UTC)
see Analytic philosophy--Philogo 19:59, 11 May 2008 (UTC)

7 the majority of philosophers and philosophy students are not mathematicians

Agreed. Pontiff Greg Bard (talk) 16:42, 7 May 2008 (UTC)
Obvious. --Hans Adler (talk) 21:36, 7 May 2008 (UTC)
Depends on what you mean by a "mathematician". Usually i use "mathematician" as "professional mathematician", but in this kind of a discussion, by a mathematician i would mean anybody who runs this sort of a mathematical engine in his head, and understands at least the natural numbers and the sets. So i would prefer that in this last sense the majority of philosophers were mathematicians, otherwise they are likely to experience big difficulties in philosophy of mathematics, whatever it is. --Cokaban (talk) 14:00, 8 May 2008 (UTC)
When they are studying topics in elementary mathematical logic, they act like mathematicians, in the same way that mathematicians who study foundations sometimes act like philosophers. — Carl (CBM · talk) 11:16, 9 May 2008 (UTC)

8 The majority of philosophers and philosophy students would be interested in developments in the world of mathematic logic especially if they might be of philosophical interest , and would be keen to be told of any variations in terminology.

Amen. Pontiff Greg Bard (talk) 16:42, 7 May 2008 (UTC)
"Majority"? I doubt it, but not enough to disagree when it doesn't concern me. (As an aside to Gregbard: If you are not interested in learning the basics of a field (such as the culture in which it lives), then you are not interested in it at all.) --Hans Adler (talk) 21:36, 7 May 2008 (UTC) – This is probably another instance of the "elementary logic"/"mathematical logic" confusion. One of the greatest breakthroughs in pure mathematical logic in the second half of the 20th century was Morley's categoricity theorem. I am not aware of any philosophers who are interested in this, other than those who are really (also) mathematicians. The qualification "especially if they might be of philosophical interest" is key: Almost nothing in mathematical logic is of philosophical interest. --Hans Adler (talk) 10:20, 12 May 2008 (UTC)
Do not know. --Cokaban (talk) 14:00, 8 May 2008 (UTC)
Not if Greg is the one explaining it. </sarcasm> Seriously, if I can't understand Greg, it's not likely the "target audiance" can. — Arthur Rubin (talk) 14:49, 12 May 2008 (UTC)

9 This article should be written in such a way as to be easily understandable by its target audience.

Amen. Pontiff Greg Bard (talk) 16:42, 7 May 2008 (UTC)
Yes. And it should be written in such a way as not to be easily misunderstood by its target audience. Philosophers seem to have an inclination to read exact definitions in a fuzzy way. If this article is to present mathematical definitions, then it must not contribute to this kind of misreading. --Hans Adler (talk) 21:36, 7 May 2008 (UTC)
Sweeping genalisations. Please provide some quotes some eminent philosophers demonstrating their inclination to read exact definitions in a fuzzy way.
No opinion. I have no clear understanding neither about who the target audience is, nor what Logic is, nor what this article is supposed to be about. --Cokaban (talk) 14:00, 8 May 2008 (UTC)
What is this target audience? — Carl (CBM · talk) 11:16, 9 May 2008 (UTC)
see 10 below

10 The target audience is not professional philosophers or mathematicians

Agreed, it should be targeted at reasoners. Pontiff Greg Bard (talk) 16:42, 7 May 2008 (UTC)
"reasonesrs" appears a wooly ill-defined term; who are you minded to include and exclude?
With the current title, students of mathematics and professional mathematicians will be among the readers. I don't know about philosophers or "reasoners", but I doubt that there will be a large general audience for this kind of article. Page view numbers for such articles are notoriously small. --Hans Adler (talk) 21:36, 7 May 2008 (UTC)
No opinion, see above. --Cokaban (talk) 14:00, 8 May 2008 (UTC)

11 The article structure (mathematical logic) would not be easily understandable by the majority of the target audience or professional philosophers or philosophy students and it would not therefore assist them much in understanding the concept of interpretation.

Agreed Pontiff Greg Bard (talk) 16:42, 7 May 2008 (UTC)
I agree absolutely. The intended target audience for that article is mathematicians who click on the link from one of several other articles (especially model theory, universal algebra, signature (logic)) in order to get more information on something that is already discussed in those other articles. This is approximately a last year undergraduate / first-year graduate topic, because it is not covered earlier. Getting the basics of the field covered using consistent terminology is currently more important than explaining unlikely topics to hypothetical non-technical readers. --Hans Adler (talk) 21:36, 7 May 2008 (UTC)
The article structure (mathematical logic) has nothing to do with philosophy, it is about mathematical logic. So i might agree, but cannot be sure. --Cokaban (talk) 14:00, 8 May 2008 (UTC)
So fix it. I agree it can use some work to be more accessible. — Carl (CBM · talk) 11:16, 9 May 2008 (UTC)
What is meant by "nothing to do with philosophy"; what is an what is not "to do with philosophy"; spounds a very fuzzy concept to me.
Philogo, i meant had nothing to do with that part of philosophy which is not a part of mathematics (assuming there is a part of philosophy which is a part of mathematics). I understand that it is not clear what it means "to have something to do with". I meant more or less in the same sense, in which the real world (beer, women, etc.) has nothing to do with mathematics (even though some constructions in mathematics are motivated by the real world). --Cokaban (talk) 20:59, 11 May 2008 (UTC)

12 The majority of philosophers and philosophy students are not especially interested in the standard interpretation, or consider Mathematical Logic particularly applicable to mathematical objects but would agree with Mates, ibid p. 56 where he says …the student must bear in mind that any non-empty set may be chosen as the domain of an interpretation, and that all n-ary relations among the elements of the domain are candidates for assignment to any predicate of degree n. They would feel free to have a domain of “human beings” or “all persons that wrote The Daffodils" or “all characters in David Copperfield” (e.g.s from Mates, ibid).
Thanks--Philogo (talk) 22:00, 6 May 2008 (UTC)

I agree with this in general. Pontiff Greg Bard (talk) 16:42, 7 May 2008 (UTC)
I agree. This is not the point about which I disagree with Philogo, not at all. Examples should be taken from the real world. However, they need to be chosen so they don't accidentally teach something that is not true. ("The truth value of an interpretation depends on the state of the world." Wrong. For different states of the world there are different interpretations.) --Hans Adler (talk) 21:36, 7 May 2008 (UTC)
Of course I agree that "Examples should be taken from the real world. However, they need to be chosen so they don't accidentally teach something that is not true." - its obvius isn't it? what ever makes you think I might not agree? I not recall ever saying "The truth value of an interpretation depends on the state of the world." Where or when did I say it? I am not sure that I agree with "For different states of the world there are different interpretations", sounds a bit wooly to me, if I might be so bold. I am more likely to say something like "A sentence is true or false under an interpretation" in fact I think I have, in the new lede. Perhaps you are confusing me with another editor? I have joined this discussion page relatively recently. I am the one who keeps saying we must be clear and precise and understandable to the intended audience.--Philogo 14:05, 8 May 2008 (UTC) PS In fact I said in new lede:

A sentence of a formal language is either true under an interpretation in that language or it is false under that interpretation in that language

just to set the record straight. --Philogo 14:09, 8 May 2008 (UTC)

I see we are still disagreeing. If "interpretation" is defined so that for one interpretation a sentential letter S must be assigned a constant truth-value, then "S means 'It is raining'" cannot be an interpretation. If we fix a state of the world where it is raining, then it becomes an interpretation. If we fix another state of the world where it is not raining, then it becomes a different interpretation. That's the entire point of defining "interpretation" formally. If we get that wrong in the example, then it's better to skip either the formal definition of interpretation and work with an informal one, adapt the formal definition (provided there are reliable sources), or drop the example completely. But there is no reason to get it wrong, because we can make a correct example instead. But I am under the impression that you insist on the misleading aspect of the example because you don't understand the full impact of the formal definition. --Hans Adler (talk) 10:20, 12 May 2008 (UTC)
Do you mean the standard model of the theory of natural numbers with addition and multiplication, which is mentioned in in the article? I agree that it is not really relevant, and probably should be removed altogether. --Cokaban (talk) 14:00, 8 May 2008 (UTC)
I meant the stadard model - as explained in Mendelson, I took this be a term in common use. To be clear, when I suggested that philosphers were not especailly intereted in the standard interpretatoin I was not saying that they were uninterested in it. I though that, in contrast, perhpaps mathermaticians WERE especaiily intersted in the standard interpretation or interpretatons where the domain is some set of mathematical objects.
I do not know what standard models was Mendelson about. You did not answer the question: are they the same (standard models), as currently defined in this article? In mathematics, all interpretations have sets of mathematical objects as domain, so i do not understand your last sentence. What is standard interpretation? It has been mentioned several times already, but no meaningful definition was ever given. I am only familiar with standard/non-standard models of the arithmetic, or, one may say, of natural numbers. Please sigh your comments. --Cokaban (talk) 21:09, 11 May 2008 (UTC)
There exist also standard/non-standard (models of the theories of) reals, etc. --Cokaban (talk) 07:50, 12 May 2008 (UTC)
The distinction between "standard models" = models with elements in the world of mathematics ("the set-theoretic universe") and more general models is not one that mathematicians usually make, so don't expect any expert opinions from mathematicians on this, or any mathematical definitions that make clear whether one or the other is meant. For mathematicians this is a non-issue. --Hans Adler (talk) 10:20, 12 May 2008 (UTC)

[edit] Some clarification

I think the following will help us clarify some of the issues we are facing...

“ When an axiomatic system is stated, the basic language used is assumed to be understood. Usually its interpretation is tacitly presupposed. Only in special cases is it explicitly specified, for example by semantical rules. On the other hand, the interpretation of the axiomatic constants is not supposed to be fixed. The author of an axiomatic system often specifies a certain interpretation, that is, an assignment of meanings to the axiomatic primitives, based on a specified domain D of individuals. He usually does this informally, it may also be done in a semantical system of rules of designation. In either case, the statement of the interpretation is not to be regarded as part of the description of the axiomatic system. When an interpretation of the primitives is given, the remaining axiomatic constants straightaway receive an interpretation through their definitions, and thereupon all sentences of L' have an interpretation, including the axioms and theorems. An interpretation of an axiomatic system is called a true interpretation if under it all axioms are true; and, moreover, a logically true interpretation if all its axioms are logical truths. One of the essential characteristics of axiomatization in the modern sense consists in the fact that the deduction of the theorems makes no use of any interpretation of the axiomatic constants. Each theorem is logically implied by the axioms. Therefore under any true interpretation all theorems are true; and under any logically true interpretation they are logically true. In this way, the same axiomatic system may serve as a representation of many different theories.

We say an interpretation of an axiomatic system is a logical interpretation provided all axiomatic primitive constants are interpreted as logical constants, otherwise it is a descriptive interpretation. Thus an interpretation of an axiomatic system is a descriptive interpretation provided at least one axiomatic primitive is interpreted as a descriptive constant.

By a model (more specifically, a logical model or mathematical model) for the axiomatic primitive constants of a given axiomatic system with respect to a given domain D of individuals we mean a value assignment VA to these primitives such that both D and VA are specified without the use of descriptive constants. A model is said to be a model of the axiomatic system provided it satisfies all the axioms. D may for example, be the class of numbers of a certain kind, or of order k-tuples of such numbers, or the like. VA assigns to each primitive an extension of the corresponding type with respect to D, for example, to an individual constant an element of D, etc. The study of models is simpler than that of interpretations, since it deals with extensions, not intentions; for example, with classes not properties. Logical interpretations are essentially the same as models. Therefore, if we are only interested in possible applications of a given axiomatic system within the field of mathematics, the investigation of models is sufficient. For this reason, some mathematical books use terms interpretation and model as synonyms. However, if we are interested in the use of a given axiomatic system in fields of empirical science, for example, physics, economics, etc, or in the construction of an axiomatic system as a formal representation of a given scientific theory, then we have to consider descriptive interpretations.

According to our definition of logical implication the following holds:

  1. The sentence Ii is logically implied by one or more other sentences if and only if every model satisfying these sentences satisfies Ii also.
  2. If we can construct a model satisfying the other sentences but not Ii, we have shown that Ii is not logically implied by those sentences.”

Rudolf Carnap, Introduction to Symbolic Logic and its Applications


Pontiff Greg Bard (talk) 05:22, 6 May 2008 (UTC)


Gregbard refers to:
Introduction to Symbolic Logic with Applications, Dover, 1958.
Perhaps the distictions made and terminology introduced by Carnap in 1958 have not been preserved in the literature in the subsequent fifty years. Can anybody cite more recent usage of this terminology, and is it suffiently main-stream to be usefully used or mentioned in this article?--Philogo 22:48, 12 May 2008 (UTC)
Thanks a lot, you are making me very happy. So model = logical interpretation (what I called mathematical or formal interpretation), as opposed to descriptive interpretation (what I called philosophical interpretation or informal interpretation). Carnap says logical interpretations are essentially the same as models; the only thing he says about differences refers to "interpretations", not "logical interpretations". --Hans Adler (talk) 10:07, 6 May 2008 (UTC)
What is the definition of "logical constant" and "descriptive constant" in this context? If the axiomatic system contains a symbol "1" and I interpret it as "the natural number that is the successor of zero", is the latter constant a logical constant?  --Lambiam 16:39, 6 May 2008 (UTC)
The logical constant (or mathematical constant) is a symbol that is designated to stand for a mathematical entity like a number, a set, or a theorem. A descriptive constant is designated to stand for an object. You question is an excellent one about naming a number in a non mathematical way :"The smallest number only namable with nine or more syllables." I would suppose that it should be treated as descriptive (it is a phrase), however, we will need some support to be confident of that. Pontiff Greg Bard (talk) 16:42, 7 May 2008 (UTC)

--Philogo 23:08, 7 May 2008 (UTC)

A small correction: a theorem is not a mathematical entity. Not in its usual meaning at least.
I apologise to Gregbard, but can you please give some references for the terminology like "logical constant" and "descriptive constant"?
(Another thing: my favourite number is in fact not the one suggested by Gregbard, but the one that is the smallest among all the natural numbers not namable in less than 100 words. :) ) --Cokaban (talk) 14:27, 8 May 2008 (UTC)
I ACTUALLY AGREE 100%, however, I am talking to mathematicians. I am so glad that you are CORRECTING ME on it!! If you take a look at the discussion at the article on theorem, there was a big discussion getting at the essence of a theorem (and I was apparently a bit of a pain there too, but never uncivil). Let's not let this be a big aside --its a can of worms... (also see Berry paradox for material on such numbers as your favorite one.)
Also interestingly the question of distinguishing between a logical and descriptive constant is apparently not a straightforward one. As of the earlier part of the 20th C, they were still grapling with the analysis, the metaphysics, etc. However, I do have some material on it. I will post it here soon. Be well, Pontiff Greg Bard (talk) 17:30, 8 May 2008 (UTC)
Where when and by whom is the term "descriptive constant" used and how is it there defined? Is helful in this article to use or provide a history of terminology from the earlier part of the 20th C? Should this not rather appear under an History of Logic article--Philogo 22:48, 12 May 2008 (UTC)

[edit] Merge proposals

Given the above clarification, we should move much of this material. Whatever is left should evolve into an article about descriptive interpretations. If we could please give full coverage in either Mathematical model, or Structure (mathematical logic) I would appreciate it. Pontiff Greg Bard (talk) 21:58, 6 May 2008 (UTC)

Please define "descriptive interpretation" and how it differs from interpretation as described by Mates and Mendelson. Pending that, oppose merger.--Philogo (talk) 22:19, 6 May 2008 (UTC)
I can find no account of interpretation at [First Order Logic], and it should surely have one. When we are content that the material here is clear precise and helpful we might more sensibly merge it there, but not before it is here clear precise and helpful. --Philogo (talk) 22:35, 6 May 2008 (UTC)
Yes, this is a bad defect of the first-order logic article, which only discusses it as a "formal deductive system". I am not sure about the exact definition of that, but it seems it doesn't include any semantics at all. There are a few advanced passages about semantics at the end, but they are built on air and make no sense in the current article. Tizio is currently working on the article, and if he doesn't fix the problem I will do it in a couple of weeks.
A descriptive interpretation is contrasted with a logico-mathematical interpretation simply in that the domain of discourse of a logico-mathematical interpretation is something like the natural numbers or Zermelo’s hierarchy of sets, whereas a descriptive interpretation has a domain of discourse consisting of, for instance, the set of U.S. Presidents (or any other physical objects). There also exists a logico-empirical interpretation apparently. There is some material on it here.Pontiff Greg Bard (talk) 00:16, 7 May 2008 (UTC)
You mean a descriptive interpretation is an interpretion other than interpretation such as the so-called standard interpretation in which the domain is mathematical objects? If so then a descritive intepretation falls within the defenition of interpretation provided by e.g. Mates and Mendelson as above.--Philogo (talk) 12:19, 7 May 2008 (UTC)
I still do not understand the term standard interpretation, and do not understand where it could have come from. Shouldn't it be rather intended interpretation? (see the comment of Carl in It seems you guys play fast and lose with the term "wrong".) --Cokaban (talk) 14:37, 8 May 2008 (UTC)
Do you agree with statement 12 above i.e.:-

12 The majority of philosophers and philosophy students are not especially interested in the standard interpretation, or consider Mathematical Logic particularly applicable to mathematical objects but would agree with Mates, ibid p. 56 where he says …the student must bear in mind that any non-empty set may be chosen as the domain of an interpretation, and that all n-ary relations among the elements of the domain are candidates for assignment to any predicate of degree n. They would feel free to have a domain of “human beings” or “all persons that wrote The Daffodils" or “all characters in David Copperfield” (e.g.s from Mates, ibid). --Philogo (talk) 12:21, 7 May 2008 (UTC)

It depends on what you mean by interested. My my mind I am thinking the article should have been primarily about how reasoners have different interpretations of things, how an interpretation consists of these 4 (or 5) parts, and Oh, BY THE WAY, you can also use this set up to have a domain with numbers, so you can do some math. The Mates formulation was the basis for my original formulation. It is my favorite of the formulations presented. As far as the standard interpretation, I was interested in having that in the article, however, the math people have gone overboard taking over this article (which was tagged for phil, not math btw). We are probably better off setting up interpretation (critical thinking) just to try to discourage them from gunking it up. Be well, Pontiff Greg Bard (talk) 16:42, 7 May 2008 (UTC)
Your tone is completely unacceptable per WP:CIVIL. Please stop it. Zero sharp (talk) 23:41, 7 May 2008 (UTC)
You are over-reacting. I mean it. If I want to describe things as gunked up you can cry about it. Stop dramatizing. I'm not getting personal about anything. I hope you reconsider your sensitivity level. I would like to think we can all be forthright. I have no problem with apologizing for my offenses, but really I think you are ramping up the sensitivity level. I will continue my measured contributions. Than you. Be well. Pontiff Greg Bard (talk) 04:01, 8 May 2008 (UTC)
I said especially interested, not interested. As in I am not especially interested in Beethoven, I am interested in Bach as well! --Philogo (talk) 17:09, 7 May 2008 (UTC)

PS Gregbar your are being rude again: our collegues I am sure are not trying to gunk it up. Speak softly like the Clerk of Oxennforde gladly would he lerne and glady teche. I noticed that one of the professional mathematical logicans mentioned that they had neither taught nor studed Logic at university. Those of us who have taught and or studeid Logic in philosophy departments are aware I think of the way these issues need to be explained to students in such courses. In my expereince had I tried to explain the concept of interpretion as part of such a course on 1st order logic using the article on structure, the room would have been emptied immediateley and I would have been out of a job.--Philogo 23:24, 7 May 2008 (UTC)

Gregbard, if you have proposed the merger with mathematical model under the impression that that's the article for things like models of a first order theory, then I strongly suggest that you withdraw that particular proposal. The disambiguation notice "The term model has a different meaning in model theory, a branch of mathematical logic" is there for a reason. This is applied mathematics, and while it is vaguely related to the word interpretation, discussing this merger along with the disputes that we already have must lead into chaos.

If you want to close the discussion and remove the tag for that merger, that would be fine with me. I'm not going to be doing the work to do any merge like that. However, my advice, and strategy would be to accumulate all of these formulations, including several in "see also", into one big article with sections. Then shorten each section to a summary and a link to a main article on particular types interpretation/models etcetera.

In my opinion it would be best if this article discussed all aspects of interpretation that relevant to logic. This will lead to duplication of the discussion of "interpretation" (Mendelson) = "structure" (mathematical logic), but this seems to be one of the few cases where it's justified. One reason is that a merged article would have to have one of the two titles, and there seems to be a clear divide in usage. The other reason is that the "structure" article is already doing a balancing act to accommodate both logicians and algebraists.

I propose a new article model (logic) (currently a slightly unfortunate redirect to model theory). Interpretation (logic) can discuss mainly the philosophical side, mention that there is a more restrictive formal definition of an interpretation, and link to model (logic) for details. The term "model" is familiar to philosophical and mathematical logicians. Mendelson says that a model of a sentence is an interpretation which satisfies the sentence. Modern model theorists say that a model of a sentence is a structure which satisfies the sentence. So model (logic) is the natural place to describe the mathematical concept of an interpretation/structure rigorously, but for a target audience that includes philosophically minded readers. --Hans Adler (talk) 22:02, 7 May 2008 (UTC)

My suggestion is that if an article called intepretation (logic) is not suitable for stand alone, then it should be merged into First order logic since it is absurd that the latter article does not explain interpretation. But first can we finish this article as is stands so it is a clear and precise article about the term intepretation as used in first order pred logic as wideley taught to thousands by philopshy departments using books of complexity up to and including Mates and Mendelson. (For your interest Mates was used as the text for a 5000 level course at the Universtity Of Minnesota, Philosphy Dpt, for use by those who had already completed at least a 1000 level course Logic course, mainly seniors and grad students. Mendelson was used for an 8000 level (phil grads only) compulsory course for all philosophy graduate students at the same university. (Study of Logc is compulsory in most Philopshy deaperemtns; is that true of maths departments?)—Preceding unsigned comment added by Philogo (talk • contribs)

I don't know what the numbers mean; I come from a culture that doesn't number university courses in this way. I think most German mathematics departments either don't teach logic at all, or it's optional. I believe a large number of mathematics students leave university with not much more background in set theory than the minimal amount of informal set theory which they learned (sometimes explicitly, sometimes only by example) during their first two weeks or so. British universities are generally much stronger in mathematical logic than German universities, but for all I know my description might apply even to them. I don't know about the US situation.
As I said, I am perfectly happy with having this article, and I think it shouldn't be merged into anything. --Hans Adler (talk) 08:28, 8 May 2008 (UTC)
In the US, most math undergraduates learn very little mathematical logic, although of course they learn natural language reasoning skills. It is sometimes available as an elective course. On the other hand, a course in symbolic logic is a common requirement for philosophy undergrads. Sometimes that course is taught in the math department, sometimes in the philosophy department, sometimes both. — Carl (CBM · talk) 15:14, 9 May 2008 (UTC)

[edit] New Lede

I have put a new account of the term interpretation at the top of the article, based on the definitions we have discusssed. It is not verbatum from either Mates or Mendelson, but based on their definitions and explantions. The target audience I have in mind has the knowledge of having studied some Logic at university, is probably not a mathematician, and is now studying first order predicate logic: about the same audience as for the article First order logic. Hans: is it sufficiently precise? Gregbar: Is it understandable for our hypothetical undergrad majoring in say History doing a course in Logic as part of his/her minor in Philosophy? Hans : look under Notes: where I suggest certain terms being synonmous. Are the suggestions correct? Am I right about models (readers may want to know a bit about model theory, I suggest a link to somewhere saying what its all about and why it might be of interest to someone who finds 1st order logic of interest.) Heads together, common purpose, forwards and upwards? I apologise if I have pushed my way in on this 50 page debate, but I was invited by Gregbar who was arguing with 'a mathematician'. I'll push off again if I am not helping, and return to reading Frege.

Constructive reasoned comments only please. Thank you (in advance) for no slanging matches, appeals to self-authority or discussions about any part of the article other than the new lede I have inserted in this section. This section is reserved for logical logicians that gladly wolde lerne, and glady teche.

Remember:-
| ||Wikipedia has a code of conduct: Respect your fellow Wikipedians even when you may not agree with them. Be civil. Avoid conflicts of interest, personal attacks or sweeping generalizations. Find consensus, avoid edit wars, follow the three-revert rule, and remember that there are 2,408,089 articles on the English Wikipedia to work on and discuss. Act in good faith, never disrupt Wikipedia to illustrate a point, and assume good faith on the part of others. Be open and welcoming. |- | 

--Philogo 23:08, 7 May 2008 (UTC)

After a first, hasty reading: Everything is correct. The main thing I could criticise is having so many one-line notes at the end, but I am sure you didn't intend the lede to stay in this form anyway. Clearly our misunderstandings were due to the cultural gap between mathematicians and philosophers more than anything else. I am very happy that you are taking part in this discussion.
For some reason it's much more irritating to argue with a very intelligent and well-educated person who uses language in a slightly different way, than with an idiot. So please, everyone, take it as a compliment that I became a bit aggressive. But I promise to calm down now anyway. --Hans Adler (talk) 08:56, 8 May 2008 (UTC)
Correct the one-liners I imagined would be reacast in one way or another. Also the redundant parts of the old lede would be removed and the non-redundant parts re-cast.
One cultural difference I think is that people with training in philosophy enjoy talking to intelligent people even if they get irritated. Unfortunately the result is often irritating to the other person, especailly if assumptions are challenged. Simlilary an appeal to authority is like a red-rag to a bull to anybody with a philosophy background. That explains why Gregbar goes beserk at any "we mathematicans say..". It's like saying "I am the pope and I say the sun goes round the earth, I am infallible so if you don't agree I will have you burnt".
If you read Plato you will find Soctrates the personification of the irritatating philosopher, which characteristic he claimed as a merit, being the gad-fly on the Athenian state. Oh mathematicans, pr-eminent in logic, prepare for stings from gad-flies. The assumption is that by the clash of thesis and counter-thesis, the close examination of all arguments, the challendging of all assumptionsn and by reason and not authority, shall we arise at the truth. Bet you found that irritating! Never mind, you can explain to the ignorant why the term model seems to have different meaning when applied to a sentence from to a language, and why it is a better term than interpretation. I actually want to know. And what is the advantege of the term stucture if its synonymous with interpreation. And why signature as well. If those not familiar with these terms could see their use and application we could converse more easliy and the ignorant might learn from the wise. The church communated better when it adopted the vernacular rather than Latin when addressing the peasantry. Regarding homonyms and how intelligent people can argue for hours debating whether an X is A Y whithout realizing they are using X and Y in different senses, consider whther you assent to the proposition "Men find bums attractive" and whether it depends upon whether expressed in British or American English. --Philogo 13:22, 8 May 2008 (UTC)
You seem to be interpreting what I said as something stupid that I didn't (want to) say, even though later you seem to imply that you did get my main point ("using language in a slightly different way"). The only way I can read this as anything but condescending is if I interpret you as saying that philosophers enjoy talking past each other. Is that what you mean?
For the record, I have said elsewhere that I was being light-heated above and no offence was intended.--Philogo 20:55, 12 May 2008 (UTC)
Signature is not a synonym for structure/interpretation at all. The signature is just the collection of non-logical symbols (plus what we obviously need to know about them: whether a symbol is a constant symbol or binary function symbol etc.) I missed that error, but Cokaban has pointed it out already and so it's irritating that you repeat it here. (Did I claim this somewhere? Sometimes I type the wrong word, and I should certainly correct it if that's the case.)
Advantages of the term "structure"? Easy, and I think I explained it already. The Hungarian Wikipedia has an article hu:ásványvíz, but no article mineral water. If Hungarian were sharing its wiki with English, then there would still be one article ásványvíz and one article mineral water, each in the appropriate language. Getting philosophical and mathematical aspects into one article is a bit easier than Hungarian and English, but it still leads to bad articles unless done very carefully by someone who is an expert in both fields. We don't have such an expert. And we would still have to decide about the name. What will you say if all discussion of interpretations in logic is moved to structure (mathematical logic)? Approximately what the universal algebraist will say if what he knows as algebras is discussed only under interpretation (logic), I would bet. And titles such as interpretation/structure are unencyclopedic. If you want a more intrinsic reason for calling interpretations structures: The word captures the counterintuitive arbitrariness of the mathematical definition, which is necessary so that mathematicians can work with it. And with this word it is much more intuitive that an interpretation is not an interpretation in the formal sense if the truth-values of sentences depend on the state of the world. But we can't discuss these things in an article because mathematicians feel these things, they don't (normally) talk about them, and so there are no reliable sources. --Hans Adler (talk) 10:11, 9 May 2008 (UTC)
About Philogo's comment: I am glad to learn that philosophers share the same neglect for authorities as mathematicians. I thought before that this was unique to mathematics as a field. --Cokaban (talk) 13:02, 9 May 2008 (UTC)
First of all, please see a short disclaimer on my user talk page under Interpretation (logic).
1. What is formal logic in the first sentence? Is this a way to leave aside the common-sense logic, or does it mean here non-mathematical interpretation of mathematical logic? Is the term "formal logic" an original invention? Anyway, i cannot propose anything better.
Any logic that is in some formal language. -GB
2. Formal language is a very general concept, see the article where it is linking. For example, the set of all words using only the letter "a" ("a", "aa", "aaa", "aaaa",...) is a formal language. It seems that here a formal first-order language is meant. However, sentential letters, i think, are not used in first-order languages.
The article on formal language should suffice. It is symbols and strings of symbols without any meaning, which we can move around (yes it's almost that basic) using rules. However, first-order languages may include sentential letters, and indeed subsume whole sentential languages as a part of themselves.-GB
3. Be aware that sometimes (in mathematical logic at least) the empty domain is allowed. For example, the sentence (\forall x)(x=x) is satisfied even if the domain is empty, and the sentence (\forall x)(x\ne x) is satisfied only if the domain is empty.
Until we can intelligently say when it is allowed or not allowed, we should just be inclusive and say that sometimes there is a restriction.-GB
4. It is not good to say that "The term interpretation is synonymous with the term structure". I would suggest a milder formulation: "In mathematical context, the term interpretation may be thought of as a synonym of the term structure". Or better, to remove this altogether. First of all, structure is linking to a mathematical notion, while the context of this article is supposed to be more general than mathematical logic. Second, i do not believe that interpretations of sentential letters are ever used in structures. Third, in any case, interpretation is no more synonymous to structure, than relation is synonymous to subset of Cartesian power, which some people prefer to treat differently.
I think Carnap clarified the whole issue nicely between model and interpretation. I don't know about structure. It seems to me that a signature is a part of an interpretation. -GB
5. The term interpretation is definitely not a synonym of signature, i am removing this.
consistent with what I was thinking --GB
6. I do not understand the sentence about model for languages being synonymous to interpretation for formal languages. What are these non-formal languages anyway?
?-GB
A formal language is as opposed to a natural language, desined to have a very simple grammar and syntax to enable us to anlsysmre eacily teh underlying logical structure. Really derfeived from Frege, developed by Russel and enabled he devlopemtn of both symbnolic logic (later called matematicaa logic) and moden analytical philosophy. A non-formal languagee would be English e.g. although that term is not used, we say natural language--86.0.105.175 (talk) 23:13, 8 May 2008 (UTC)
7. I do not understand the sentence about predicate/property and extensional/intensional. I am simply not familiar with the terms.
All in all, it seems that the introduction deals now with propositional and first-order logics in mathematical sense (and with their non-mathematical interpretations :0 ), while mixing them together.
Phew, you open a can of worms there. Well the denotation/connotation intention/extension sense/reference distinction started way back. Mention of it at denotation. Deserves an article really. Briefly off top of my head: take a word like, say wise. Wisdom is the property and the things which are wise are it denotation, what it denotes. The property can be used to define a set. The members of the set are the set's extension, which is the same as the denotation of the property. The conation of the word yellow is its meaning, or its intention or its sense. The extension is things that have it or belong to its set. Now two terms can have the same den notation but different connotation. Egs. Is pres of USA/is head of US armed forces; is an equilateral triangle/is an equiangular triangle; is a creature with a heart/is a creature with a kidney. The pairs of terms are "co-extensional", but do they have the same sense? If we say two terms have the same meaning if they are co-extensional then the pairs of terms have the same meaning, which is counter-intuitive; having a heart does not MEAN having a kidney, surely, it just happens to be. The fact that they are co-extensional is contingent, not necessary, could have been otherwise, and the assertion that they have the same extnesion is sythetic truth, known a posterior, not anytically true known priori. All SORTS of problems and paradoxes arise if we equate meaning and denotation. But the whole of set theory is based on extensionality (two sets with same members are the same set). And as mentioned in this article, meanings are given to predicates by way of denotation, i.e extensionally. Therefore there is the danger that these problems and paradoxes may touch set theory and predicate logic, and then we are really up a gum tree. Some of us realy worry about such things

Russell’s paradox famously put set theory and Frege's prject up a gum tree back at the beginning of the last century. Nominalists fight shy of senses, meaning, and generally giving ontological status to anything corresponding to an abstract noun. They wish to avoid the problem of the universal, for fear we will finish up with Plato's realm of Ideas or Forms. Realists on the other hand cheerfully accept the existence of abstract objects, like Wisdom, the Number five, and the Truth and so on. Mathematicians tend to be realists - they believe there really is a number four and there are really mathematical objects and truths to be “discovered”. Nominalists perish the thought, and would like to say there are only concrete objects that exist in time and space, everything else is baloney, smoke and mirrors, and the prodcuat of confused thinbking at best.

Realism is also feared as giving succour to right wing ideology, e.g. if there are really abstract thinks like the number three and wisdom, then there could really exist something like the Will Of The People or Germany’s Destiny, and then you need a Fuhrer or Superman who can tell you what it is, who know the real Will of The People (as opposed to what the people say they want) and you know what happens next. See how it might make an article (in philosophy of logic) all by itself. I'd much rather write such an article then mess around with this one, but there it goes. Roughy drafted off the top of my head. --Philogo 23:15, 8 May 2008 (UTC)

Hope my comments are helpful. --Cokaban (talk) 11:22, 8 May 2008 (UTC)
I hope that we can eventually get some context by addressing the whole descriptive v logico-math interpretation. Pontiff Greg Bard (talk) 21:21, 8 May 2008 (UTC)
Perhaps you could explain your meaning of the whole descriptive v logico-math interpretation; sounds a bit wooly to me--Philogo 21:00, 12 May 2008 (UTC)

[edit] Lack of structure

My main issue with the new lede is that it seems to duplicate the sections lower down. I would rather see these merged. At the moment the lede is overly long, and the entire article seems ill-stuctured. The "notes" section, for example, should be integrated into the rest of the article, rather than standing as a list of staccato sentences.

I don't mind doing this merging, except that I am still waiting to hear whether there is material other than the definitions of first-order stuctures and propositional valuations that should go here. — Carl (CBM · talk) 10:57, 9 May 2008 (UTC)

The notes are intended for merging, and gradually doing so. I have proposed new material below.--Philogo 21:01, 12 May 2008 (UTC)

[edit] new section in formal system

I have added a section to the article formal system (on interpretations) so as to frame the topic. I will be adding more information in the future. Feel free to integrate material to or from there. I just wanted people to be aware of it. Pontiff Greg Bard (talk) 20:13, 8 May 2008 (UTC)

[edit] Four merge tags

I see there are three merge tags at the top of the article:

  • Mathematical model is a completely different topic; the only similarity is the same word is employed
  • Structure (mathematical logic) is the article on first-order interpretations. This would be a reasonable merge if the goal of this article turns out to be only to discuss the mathematical side of things - I cannot tell whether that is the goal of not. All the material that is being added seems to suggest that the goal is only to discuss the mathematical side of things.
  • First-order logic needs a lot of work, but since there is another article specifically about structures, I think that would be a better choice.

Also, lower down, is a suggestion to merge intended interpretation here. I think that should be postponed until the remainder of the article is sorted out. It may be a reasonable merge depending on the path we take with the article. — Carl (CBM · talk) 11:03, 9 May 2008 (UTC)

oppose merge: intended interpretation has precious little content and what there is lacks citations or references and is largle POV. --Philogo 21:07, 12 May 2008 (UTC)
oppose merge:While there is some overlap, First-order logic is a more general topic, Structure a less general topic, and, as observed above, Mathematical model and Intended interpretation are different topics entirely. Rick Norwood (talk) 15:45, 29 May 2008 (UTC)
Since there is no apparent suppport for any merges I will delete all the merge tags. If anybody still wants to merge they can put a tag back.--Philogo 19:20, 29 May 2008 (UTC)
I have also deleted the "expert wanted" tag, since we appear to have several such involved already--Philogo 19:24, 29 May 2008 (UTC)

[edit] Move to logical interpretation

I have created formal interpretation, and descriptive interpretation. Also I have moved this page to "Logical interpretation" consistent with the Carnap language. I hope people aren't too mad at me, however, I think I have found the right distinctions. I am certainly open to renaming it "mathematical interpretation", because that would be consistent also.

In response to this move all of the Socrates stuff can be moved to descriptive interpretation this way you guys will be able to focus more on this page. I hope this helps. Pontiff Greg Bard (talk) 11:12, 9 May 2008 (UTC)

Formal interpretation has existed since 2004. I don't see the benefit of creating this article and, when issues arise, simply copying those issues to a different new article. It would be better to figure out what is supposed to be in this article first, and create new articles only if (1) they don't already exist and (2) there is a need for them. My question is, what is supposed to be in this article? — Carl (CBM · talk) 11:30, 9 May 2008 (UTC)
Formal interpretation is the more general term for all of the things we are talking about. The main split that I see after that is the distinction between logical/mathematical/logico-math interpretation and descriptive interpretation. I see this organization as making it possible to deal with them separately. The descriptive interpretation can be used for things like physics and economics. This article is for logical interpretation, it has as its domain only math entities like sets, numbers, etc.

Pontiff Greg Bard (talk) 12:50, 9 May 2008 (UTC)

POV--Philogo 21:13, 12 May 2008 (UTC)
I have no idea what is supposed to be in this article. --Cokaban (talk) 12:54, 9 May 2008 (UTC)
I consider Gregbars moving/renaming of the article without prior discussion or agreement an indication of, at best, his inabilty to work as part of a team and worse, plain rudeness.--Philogo 12:59, 9 May 2008 (UTC)
I too no longer know what this article is supposed to be about since its title has been changed; I contributed towards a definition of the term intepretion (logic) as it occurs in carefully cited sourcesm but that is no longer the title of the article. --Philogo 13:05, 9 May 2008 (UTC)
Please be patient with me. If you read the section titled Formal interpretation in the article formal system, it leads into this whole concept. The disambig page presents how there are two types of thing (formal interpretation) we are dealing with. The presentation in formal interpretation is ultimately more a readable and understandable treatment to the average person than previously. Even if you are inclined to move it all back now, please read it and give it a chance. Be well all. I'm still here responding to questions, so don't throw me off the team yet. Pontiff Greg Bard (talk) 13:24, 9 May 2008 (UTC)
IMHO, if Gregbar wishes us to be patient with him then he must learn to be a team player. That means he must persuade his colleagues of his point of view and not impose it unilaterally. If Gregbar reverts then our patience may be restored; if he does not we may conclude that editing an article onece Gregbar is involved is a waste of time. He speaks with passion but does not persuade--Philogo 20:57, 9 May 2008 (UTC)
What exactly do you visualize in each article? Apparently now both Philogo and I don't know what this article is aiming at. Can you make an executive summary for everyone? — Carl (CBM · talk) 14:30, 9 May 2008 (UTC)
I cannot find the term "logical interpreation" (as opposed to "interetation") in Mates, Mendelson or any other books I have. Can anybody else find it?

[edit] Move back, or redirect?

Given that several people here either disagree with the move or think it's confusing, I think it would make sense to move the article back to the other name. But I see that the tag above was changed to "mathematics", which is odd as the stated goal of this article was to be the philosophical logic counterpoint to the mathematics side. If the only goal of this article is to cover the mathematical logic side, I would like to just redirect it to structure (mathematical logic) and work on improving that. — Carl (CBM · talk) 15:16, 9 May 2008 (UTC)

I would keep the article under philosophy, so that Gregbard could work on it. Also, the article would have to be drastically changed to go under mathematics, and it will hardly be useful there. --Cokaban (talk) 15:25, 9 May 2008 (UTC)
The original plan was for it to be more of a philosophy article. At the moment, I am hoping that Gregbard will explain what plan he has in mind. — Carl (CBM · talk) 15:28, 9 May 2008 (UTC)
I have changed it back to philosophy. If Gregbard insists and changes it back to math, the first consequence will be that he will be automatically out of discussion, given his previous posts and edits. --Cokaban (talk) 15:33, 9 May 2008 (UTC)
I am hoping that Gregbar will demonstrate his confidence in his own powers of persuasion by changing the name of the article back to interpretation (logic) an article which seeks to define and explain the term interpretation as it appears in the some seven sources which we carefully documented above. The label will then once more match the contents. From all the sources mentioned it seems to me that there are not two meanings to the term but one. (It may be that the way the term is explained or the way that interpretations are given or presented varies from text to text but that surely is another matter which would be interestingly described in a sub-section. I was intending to do just that from the texts I have to hand and invite others to contibute any alternatives from their sources and then we would have learnt something.) If Gregbar (or others) however intend to impose their POVs without discusssion then contributing to this article is not for me. PS I do not care whether it "comes under" or "tagged" philosophy or mathematics or neither or both. We used to have a tag called "Logic" linked to Wiki-Logic but some divisive powers deleted it. In my view Logic is, well, Logic. If there are reasons to say Logic is "really" Philosophy , or Mathematics, or Linguistics, or Psychology please present in article about under Philosophy of Logic--Philogo 21:27, 9 May 2008 (UTC)
I cannot find the term "logical interpretation" (as opposed to "interpretation") in any Logic books I have, and I have never heard the term before. The article says it is about the term "interpretation" not "logical interpretation". Therefore I can see no purpose to, nor foresee any effect of, re-naming the article to "logical interpretation" from interpretation (logic) other than to create confusion. If there are good reasons for renaming, please share them here for all to see, since glady wolde we lerne and glady teche.--Philogo 10:49, 10 May 2008 (UTC)

I propose, unless the consensus expressed here objects in the next six hours, to restore the status quo by restoring the original name of the article i.e. interpretation (logic) --Philogo 12:07, 10 May 2008 (UTC)
No objections. --Cokaban (talk) 13:49, 10 May 2008 (UTC)
Move Back per Philogo Zero sharp (talk) 14:45, 10 May 2008 (UTC)
Any further views from anybody? I do not want to be involved in what I understand is called a "revert war".--Philogo 18:38, 10 May 2008 (UTC)
Done--Philogo 21:14, 12 May 2008 (UTC)

[edit] math banner

Gregbard has changed the banner at the top back to mathematics. I don't understand this, mostly because I still don't really understand what the intended subject material for this article is. Is it supposed to be an abridged version of structure (mathematical logic)? Is it supposed to be on interpretations in a broader sense than structures? I would be glad to help with the editing if I knew what material to add.

Philogo, I think you have some idea what you would like to see in this article. Could you make an outline or summary of it, to give me a sense of what you;'re thinking? — Carl (CBM · talk) 21:16, 11 May 2008 (UTC)

<some content dup from Gregbard tallpage>

I'm sorry Carl. Thank you for being very patient. Even the couple of days you've given me is certainly more than generous. I have been thinking about what more to tell you about the big picture that I haven't already stated...
  • In my mind, I would like to "tell The Formal Language Story" so that average people have a chance at grasping it if they really wanted to.
  • I have made some recent additions to Formal language, Formal grammar, Formal proof, and Formal system so as to really try to "frame up" the story. I am a little worried that someone is going to say that it's a lot of redundant content, and remove it. I think it helps people understand what is going on. This makes the articles stand on their own.
  • I think wikilinks (in use and in principle) are a good indicator of what content should go in what titled article. In the case of several redirects, they should be mentioned as alternate terminology in the first sentence of the article. This helps avoid duplicate articles/material, organizational issues, etc. In taking a look at what linked to model (abstract), it looked to me like a change was needed.
  • I have replaced the redirect to proof theory to an article that addresses Formal proof. This concept is distinct from mathematical proof, in that a mathematical proof, is a type of formal proof. The absence of this distinction the type of thing I am always talking about: a "logical foundations deficiency". The same type of thing was going on with "algorithm is a type of effective method", and "set is an abstract object." Those seemed to have worked out thanks to your help. I would like to frame up interpretation the same way.
  • I use the template:logic as my guide for "getting the story straight." Recently I changed the links to Proof (mathematics), and Interpretation (logic), to formal proof and formal interpretation.
  • I tend to think of the relevance of the content to be centered around the actual concept, rather than its place within a particular history, field, culture, etc.
Pretty much anything having to do with expressions in formal language is ending up on the mathematical logic worklist, not the philosophical one. The article as it turned out included a lot more of the mathematical content than I originally imagined. Perhaps there is a philosophical interpretation article to be had starting "An interpretation is the giving of meanings to human experience...", and then go from there. This article doesn't really include anything like that. That is why it is under math logic. Those two lists are open and available for anyone to pour over. The formal interpretation is a type of interpretation which is expressed in formal language... I think this over-arching approach helps people really understand things conceptually.
I created the formal interpretation as the over-arching article dealing with all the different models, interpretations, structures, etc. I hope we can use that page to get the story straight, and then the more details go in logical interpretation, and descriptive interpretation. In my view the interpretation (logic) article should focus on the specific logic-mathematical interpretation. There is at least some of material in it which should be moved (or merely copied) over to formal interpretation.

Pontiff Greg Bard (talk) 22:27, 11 May 2008 (UTC)

With regard to banners. I evolved from browsing to editing through responding to invite to help set up WikiProject Logic. We then had our own Logic banner. I thought the project and the banner were great. Logic is important enough to stand on its own without all this "branch of" stuff. Gregbard however said there was a terrible argument between "maths people" and "philosophy people" as a result of which the Logic banner disappeared and all Logic articles were to be badged as either maths of philosophy, to be edited respectively by maths people or philosophy people and hands of each other articles. This makes no more sense to me now than then. Whose articles are validity, entailment, proof, argument and, case in point, interpretation? Which articles would Bertrand Russell be allowed to edit? or Quine, Tarski, Wittgenstein... Is this great argument between mathematicians and philosophers over Logic territory to be found outside of the world of Wikipedia? And within Wikipedia how many people are actually engaged in this warfare, and has it somehow resulted in the idea that philosophers are fuzzy and do not pursue exactness and precision? That is all I have to say about banners...
regarding this article. My view is that if there is a need for an article subject interpretation (logic) (a) it should be both entitled and about interpretation (logic) as defined in our sources, which to my amazement (irony) all amount to the same thing, just as I ventured at the beginning. On this I believe we now all agree (b) it should be suitable for the intended audience (Aside: the article entitled structure is not so suitable) (c) the intended audience is neither professional mathematicians or philosophers, we should not assume that they are students or ex-students of any particular discipline, it would be fair to assume that they have some knowledge or background in Logic, most likely having studied it at university and most likely having been taught it in a philosophy dpt. At the same time it should not be contradictory to what is taught in maths department to maths students. Isuggest it is written more a-la-Mates than a-la-Mendelson. (d) the article should dovetail to the article on first order logic. (e) If there are other interesting and related techniques concepts e.g. signature, structure, model then they should be explained very precisely in the article and/or link to other sources for further reading as appropriate. Case in point. I understood from Medelson and Mates et al that a model of a sentence was an interpretation of a sentence under which that sentence was true. Well either it is or it isn’t. Either Mendelson was wrong or the word has changed its meaning or I mis-read Mendelson. We must be clear precise and readable. If physicists can agree, high and low, that Force = Mass x Acceleration : F-ma) then why cannot we agree on the definition of basic terms like model and interpretation. (f) if there is, as I am sure there is, a variety of ways of providing an interpretation we should describe and give examples of each. I volunteer to describe a method using interpretative functions sourced from L.T.F.Gumut, Logic Language and Meaning, Vol. 1, UoChicago, 1991; ISBN 0-226-28084-5.

I think there IS a need for this article at the moment, that we should extend is as described above, and that this does not prevent its being merged later into say first order logic if that later seems wise. --86.0.105.175 (talk) 23:16, 11 May 2008 (UTC)--Philogo 23:18, 11 May 2008 (UTC)

I am not at all clear what Gregbard is saying or proposing above, either because his remarks are not clear precise and readable or because I am a bit thick. In either case what he says does not appear to be much to with this article. --Philogo 23:24, 11 May 2008 (UTC)

[edit] new content proposal: ways of providing an interpretation

If there is a variety of ways of providing an interpretation we should describe and give examples of each.

I volunteer to describe a method using interpretative functions sourced from L.T.F.Gamut, Logic Language and Meaning, Vol. 1, UoChicago, 1991; ISBN 0-226-28084-5.
Comments?--Philogo 12:47, 12 May 2008 (UTC)

Do you guys (anyone listening out there) believe that discourse, model, and interpretation are the same thing? I hope not, but the article sure sounds that way. A mess has been made I am afraid. Tparameter (talk) 13:51, 12 May 2008 (UTC)
In the terminology of contemporary mathematical logic, an interpretation of a language is a structure, and a model of a theory is a structure for the language of the theory in which the sentences of the theory are all satisfied. There is a different concept of interpretation at interpretation (model theory). We don't use the word discourse much. Can you expand on what you're thinking? — Carl (CBM · talk) 13:58, 12 May 2008 (UTC)
Suggest explain define and clarify these other terms as appropriate under section Nomenclature (for want of a better heading)--Philogo 21:19, 12 May 2008 (UTC)
See math project talk page. Tparameter (talk) 14:22, 12 May 2008 (UTC)
Will do, let's discuss this there. — Carl (CBM · talk) 14:24, 12 May 2008 (UTC)
Nobody has responded to my suggestion at top of this section.--Philogo 21:21, 12 May 2008 (UTC)
Sorry. Yes, your suggestion sounds excellent. Tparameter (talk) 22:05, 12 May 2008 (UTC)

Philogo: let me make sure I am understanding your suggestion:

This article will cover various ways of assigning interpretations, both in the context of symbolic logic and in the context of natural language (e.g. scientific theories).

That seems reasonable to me, and I don't mind editing the content on interpretations of first-order languages via structures. One thing that should be clarified, if I understand the suggestion, is the connection between this article and model (abstract) (which may now be titled formal interpretation). — Carl (CBM · talk) 21:06, 13 May 2008 (UTC)

Let me say what I have in mind. We have agreed I beleive what an interpretation is, and have carefully defined it. So far so good. Now our reader wants to know how to present an interperation, wants to know what they look like. (Article should not just be definitions). Now I look at some various texts, and note that ways of presenting/giving vary. (Thought, maybe thats been the surce of all this argument all along. Perhaps there is no diffenrce about what an interpreatins is or does, but folks from different backgounds are used to different ways of settig them out.) I thought we could give some sample interpretations, showing the variety. I have found and volunteered to present a method using interpretative functions sourced from L.T.F.Gamut, Logic Language and Meaning, to be one of our examples. I'd like to see how Hans e.g. would set one out. It would take me a while so I don't want to do it if it would not be of interest.
--Philogo 21:50, 13 May 2008 (UTC)
PS re "This article will cover various ways of assigning interpretations, both in the context of symbolic logic and in the context of natural language (e.g. scientific theories).". I suggest we stick with the context of symbolic logic; I do not know quite what the "context of natural language (e.g. scientific theories).". would be, and I am "instinctively opposed", danger of mission drift and fity pges rying to agree what we are talking about. We have firm ground staked out in the lede; it took us long enough to get there, lets not wonder off: it makes my head spin--Philogo 23:28, 13 May 2008 (UTC)