User talk:Trovatore

Previous discussions:

CH

In response to

By the way, CH actually *is* an open question.

Is that really the way people see it? I'm accustomed to it being treated like the parallel postulate: it depends on what you're doing. The 'existence' of hyperbolic space is not a challenge to the parallel postulate any more than the 'existence' of rectangles is to ~(parallel postulate).

I don't think it's generally accepted that either CH or not-CH is inconsistent (indeed, with Cohen's proof, it's not clear in what sense it could be without much of modern set theory falling apart). Are you suggesting a philosophical position?

(Not an attack, just curious.)

CRGreathouse (t | c) 01:15, 11 June 2011 (UTC)[reply]

My philosophical position is that there is no clear line between philosophy and mathematics (or between mathematics and science), so sure, you can call it a philosophical position if you like.

Of course there are models of ZFC satisfying CH, and others satisfying ~CH; up to here you're fine.

But you know, there are also models of ZFC satisfying Con(ZFC), and others satisfying ~Con(ZFC), and we don't treat those on an equal basis. We think Con(ZFC) is true (if it isn't, then there aren't any models of ZFC at all), so the models satisfying Con(ZFC) are right, and the other ones are wrong.

Now, you could make a distinction here on the grounds that both CH and ~CH have wellfounded models, whereas all models of ~Con(ZFC) are illfounded (in fact, they're not even ω-models).

But are the opinions of all wellfounded models equally correct? Surely not. For example, there are wellfounded models that think that 0# does not exist. But if it does exist, which seems like the reasonable thing to believe at this point, then those models are wrong.

I think I'll stop here for the moment; I'm interested to see what you do with the above. --Trovatore (talk) 09:03, 11 June 2011 (UTC)[reply]

Frankly I'm not a fan of Regularity (seems like too much assumption for too little 'bang'), so I'm not convinced by the ill-foundedness of ~Con(ZF) models though it supports my feelings in this matter.

It just seems like the claim that CH is open relies on either ZF being false or the system under which the question is to be interpreted changing. The former case seems unlikely; the latter seems unrelated to CH itself.

CRGreathouse (t | c)

The axiom of foundation (that's the more usual name than "regularity") is really not an assumption at all. All it says is that we're restricting attention to the wellfounded sets. Note that illfounded models still satisfy foundation. That is to say, they think they're wellfounded. They just happen to be wrong about that.

I'm sorry, I don't understand your second paragraph at all. --Trovatore (talk) 22:21, 13 June 2011 (UTC)[reply]

There is one way in which ~Con(ZF) is different from ~CH — if ~Con(ZF) were true, then we could write down an actual proof of a contradiction from ZF, a complete finitary object. While the best one can do with CH or ~CH is to construct (small) finitary fragments of models of ZFC+CH or of ZFC+~CH. JRSpriggs (talk) 11:44, 14 June 2011 (UTC)[reply]

That's a difference, certainly, but I don't see that it's relevant in context. If you take the position that the truth of statements of set theory is relative to models of ZFC, then you have to come to terms with the fact that there are models of ZFC that disagree on the truth value of Con(ZFC). --Trovatore (talk) 16:15, 14 June 2011 (UTC)[reply]

Re: LivingBot edit summaries

It is a reference to the preceding sentence ("Revert if in doubt.") Say, for example, you're watching the talk page for "Stretcher" (medical apparatus). Now, LivingBot tags it for a book about woodworking. Clearly, what was meant was Stretcher (piece of wood). The comparison with Georgia is used to imply that LivingBot may actually not be wrong, and you should stop and think before reverting it. - Jarry1250 ^{[Weasel? Discuss.]} 22:02, 19 June 2011 (UTC)[reply]

Your indent style

Regarding this change. Your preferred style makes no sense whatsoever. We both replied to the same comment, I replied before you, and you replied after me. Your method is as follows: if someone replies before you, then you insert your reply above their earlier reply with an extra level of indentation. That has two main flaws:

Your extra level of indentation adds to confusion. (Indent level n is a reply to indent level n–1. Using three indents, when there's only a level zero and level one indent means that you are replying to no-one!)
You imply that your comment is somehow more important than other people's by "cutting in line".

Why should you insert your reply above mine? I replied first, you replied second, ergo, my reply is placed before yours. Following your reasoning, the person to reply after you, i.e. third, should put their reply above both mine and yours, and with an indent level of four (again, replying to no-one). I'll leave you to think about this. Even though you prefer your anachronistic style, it goes against WP:INDENT, and it's quite simply rude. — Fly by Night (talk) 05:46, 10 July 2011 (UTC)[reply]

Come on, FBN, you're making way too much of this. I'm not going to apologize because I don't think I did anything wrong. But I am distressed that it strikes you this way, which I never intended.

To my eye, responses to the same person, indented the same, have a tendency to blend together; the first person's comments get attributed to the second person. I don't have a fixed "style" to solve this problem, but deal with it ad hoc, either with the way I did it, or sometimes by putting an extra newline before my comment. It's silly to extrapolate what would happen if it were iterated; common sense comes into play. --Trovatore (talk) 07:07, 10 July 2011 (UTC)[reply]

Boiled Lamb?

In the discussion on Wholemeal starchy food you refer to boiled lamb with mint jelly as, I think, an English food. I'm intrigued and have never come across any method of cooking lamb that involved boiling it. Are you sure you're not thinking of roasted lamb? I'm asking here rather than extend an off-topic conversation on the refdesk. Thanks. --Frumpo (talk) 08:33, 25 July 2011 (UTC)[reply]

Could be roasted, don't know. --Trovatore (talk) 10:01, 25 July 2011 (UTC)[reply]

The old testament of the Bible mentions "You shall not boil a young goat in its mother’s milk." in Deuteronomy 14:21. I presume that this would not have been mentioned unless that method of preparation was common-place back then. JRSpriggs (talk) 10:46, 25 July 2011 (UTC)[reply]

I suppose a lamb stew (typically with carrots and other vegetables) is sort-of boiled lamb but this wouldn't be normally served with mint sauce. Mint sauce (with a vinegar base) is traditionally served with slices of roast lamb. I haven't seen the sweeter mint jelly for several years. I don't much fancy the idea of lamb boiled in milk but it sounds like an interesting preparation. --Frumpo (talk) 20:52, 25 July 2011 (UTC)[reply]

Julius Caesar

I've seen many interesting opinions on the chap, but never that he was a "thug".

What makes you think that of him? --Dweller (talk) 09:09, 28 July 2011 (UTC)[reply]

He took over Rome by military force, and installed himself as military dictator. I don't know what else you need. --Trovatore (talk) 09:36, 28 July 2011 (UTC)[reply]

Dictator in those days doesn't quite mean the same as these. You can't divorce Caesar from the times he lived in... the traditional senatorial system of the Republic was falling apart and someone had to get a grip. It was him, though not for long. if he hadn't, one of the other triumvirs (or someone else) would have dealt with him rather unfavourably. And what followed him was a path into far greater dissolution of senatorial power. I don't think there's much thuggish about his behaviour though - he believed in the rule of law. To me, he comes across as a powerful man, who was a masterful general, perhaps the most masterful of all time, who couldn't quite make the leap to the imperium. His mistake was that he alienated people and perhaps wasn't thuggish enough to deal with them like a real thug, say Saddam Hussein or Stalin, would have done. --Dweller (talk) 10:10, 28 July 2011 (UTC)[reply]

I am not an expert on the times, but I have a very low opinion of Julius Caesar. I see him as a mob-pandering military ruler, something like the Hugo Chavez of his day (though of course even Chavez in the current day doesn't use the brutal tactics Caesar did). -Trovatore (talk) 10:26, 28 July 2011 (UTC)[reply]

Mob-pandering = popular with the masses? He does seem to have been, but that's not usually a trait of a thug. Caesar's tactics in Rome were spectacularly unbrutal - our article on him notes how he pardoned and spared his opponents. Although he was indeed brutal in warfare against the Gauls and other non-Roman tribes, but you'd expect that of any warrior of his day, and Rome's survival probably depended on it. He also tried to refuse some of the honours the Senate bestowed on him. Give him another look - he's a fascinating and complex character. --Dweller (talk) 11:01, 28 July 2011 (UTC)[reply]

The word "dictator" referred originally to an official appointed by the Senate to exercise unlimited powers ("he was not legally liable for official actions") for (up to) one year during an emergency. The word got the bad connotation it has today because of the frequent abuse of that power.
Gaius Julius Caesar was a left-wing military dictator, similar to Hugo Chavez as you say. JRSpriggs (talk) 14:20, 28 July 2011 (UTC)[reply]

Logicism

Hi, this may be an odd thing to post, but I don't come around here often and have always found you insightful, so would like to ask your help. The article on Logicism seems to be in a poor state and I don't think the people editing it know what they are talking about (If I'm wrong, I'm very very sorry) Could you take a look at the page (if interested, and if you have time) and give some sort of opinion or indication of a direction it should go in? Finally, I'm the IP address under the small changes section on the talk page there; I'm not asking you to come and agree with/back up what I'm arguing (you may very strongly disagree) all I want is someone who knows what they're talking about to look at it. 71.195.84.120 (talk) 16:16, 31 July 2011 (UTC)[reply]

From pure historical fact, the intro looks very accurate up to the early 1900's. Thereafter (failure of Logicism and Formalism to reduce all of Mathematics to simple Mechanism) there's little info to criticise: article is not inaccurate, just incomplete. Bill Wvbailey (talk) 03:07, 1 August 2011 (UTC)[reply]

What I was looking for comment on was a debate going on on the talk page about two things I removed. The first, refering to Godel's Theorem being an objection to Logicism:

"However, the basic spirit of logicism remains valid, as that theorem is proved with logic just like other theorems"

The second:

"Today, the bulk of modern mathematics is believed to be reducible to a logical foundation using the axioms of Zermelo-Fraenkel set theory (or one of its extensions, such as ZFC), which has no known inconsistencies (although it remains possible that inconsistencies in it may still be discovered). Thus to some extent Dedekind's project was proved viable, but in the process the theory of sets and mappings came to be regarded as transcending pure logic."

The second removed because, I may be mistaken, I didn't think that mathematics = ZFC was logicism (I'm not asserting this equality) Second, I'm not sure that it is believed that math reduces exactly to ZFC, but more it reduces to Set Theory, which aren't the same. Since what was written didn't seem right, but I wasn't sure exactly what to replace it with, I removed it. I wanted someone else to look at it because some of the comments on the talk page don't seem very informed. I realize that my objections may seem pedantic, but the article seemed to read as pro-logicism to me; and it didn't seem to explain anything about logicism.209.252.235.206 (talk) 03:47, 1 August 2011 (UTC)[reply]

Sorry, I didn't have Logicism on my watchlist so I missed the debate. My (historical) take on it is this: Logicism died in ca 1927 2nd edition of PM (see the introduction to that volume), wherein Russell admitted his inability to axiomitize all of mathematics in particular because of the failure of his axiom of reducibility. At this time Hilbert's Formalism, and various "set theories" were in fairly developed stages, and Russell yielded the floor to these theories (with intuitionism a nettlesome bugbear). Russell's axiom was taken up by Goedel in a ca late 1940's important paper, so it's not at all clear that Logicism is strictly "dead". I'm sitting in an airport writing this and when I have more time I'll look deeper at the debate. BillWvbailey (talk) 16:50, 1 August 2011 (UTC)[reply]

Walking dead 'eh? First of all, there is a theory called "Neo-logicism" which is thriving just fine. I suppose we could get hyper-semantic and just say something like '...neo-logicism isn't anything like logicism ... it's totally different.' Which is exactly the type of response I expect. However, that would be disingenuous. The idea is that everything in mathematics can be reduced to some logical truth. This claim is eminently reasonable as every mathematician always wants to be logical, and every mathematician always wants to express truths. To the degree that mathematicians run away from logicism, they deserve to lose their credibility. The approach that neo-logicism takes is to expand what we mean by "logic." This, is a perfectly legitimate way to deal with things, and is only at most an equally semantic approach to the approach that the mathematicians are taking in running away from logicism. (Um, who was it who said -- ridiculously -- on a WP talk page that "mathematical logic isn't logic?") Interestingly, the "walking dead" came out with something JUST TODAY.

It's my own person understanding that so-called "philosophical" logicians will always reasonably be able to expand what we mean by "logic" as our knowledge increases. Therefore we will always be able to construct a valid interpretation under which some form of logicism is true. This is their proper role. It is also more properly their role to say whether semantic claims such as "mathematical logic isn't logic" are valid or not. It is not the proper role of a mathematician. Who do you ask about soil, a soil scientist or an archeologist? Greg Bard (talk) 23:04, 1 August 2011 (UTC)[reply]

How is that reasonable exactly? You will always be able to expand what you mean by Logic so that some form of Logicism will be true? Assume I'm stupid and need helped through that because it sounds, to me, like you are saying logic can be what ever you need it to be.

Now for the other matter: Most of my complaining on the talk page is from pairs of sentences like these:

"The idea is that everything in mathematics can be reduced to some logical truth. This claim is eminently reasonable as every mathematician always wants to be logical, and every mathematician always wants to express truths."

Those are not saying the same thing! Saying that all of mathematics (again, the philosophical total form of the word, not just all the math we can do now, but literally everything it can ever be) can be reduced to logic is not the same concept as saying that mathematicians want to be logical in their approach and aspire to truth. You know what? Physicists also want to be logical and aspire to truth, is all of empirical science now also reducible to logic? Obviously not. Just because mathematicians use logic does not mean that everything is logic. 209.252.235.206 (talk) 07:34, 2 August 2011 (UTC)[reply]

The problem is that you are confusing philosophy with psychology. When I say that every mathematician wants to always be "logical," I am not meaning 'spock-like' or some other such notion. I mean it in precisely the sense that the context makes obvious. I.e. the actions of the mathematician when he or she scribbles an expression on the chalkboard are the product of reason. More specifically, there always exists some logical system with some interpretation in which the scribbles can be validly constructed. Yes they are saying the same thing. We are able to expand what we mean by logic in the exact same way that every other academic field does exactly the same thing. We make new discoveries and they are published in academic journals. Do not get the wrong idea. I am not talking about a semantic difference of which academic departments choose to focus on which concepts. I am talking about new discoveries in the field of logic which are consistent with the principles of logic in reality.

I am a little surprised by the issues that you have brought up due to what appears to me to be fairly obvious. Please forgive that. Your counter-example of physics I find to be quite off. Obviously, physics involves an empirical component, while logic does not. Therefore there is no "reducing" all of physics to logic, much less "everything." Math however, does not escape that reduction. The degree to which physics "reduces" to logic is in that the scribblings of a physicist are an interpretation (or model) of the physical world we live in. I.e. they are attempts to formalize the principles of the empirical sciences. The aim of these attempts is to construct a formal system that will produce all of the theoretical possibilities (preferably in the end they are in the form of true sentences) and none of the impossibilities. I don't see how math can escape such a treatment, with the notable exception that math has no empirical component, and therefore reduces to logic just fine.

I also wonder what the problem is with logic being 'whatever you need it to be.' I am pretty sure Wittgenstein famously described logic as being like a ladder that you can climb and then throw away. We have non-standard logic, non-classical, etcetera. To say that logic is whatever you need it to be also sounds eminently reasonable. Math also appears to be 'whatever you want it to be...' you have graph theory, arithmetic, game theory, topology. Greg Bard (talk) 22:14, 12 August 2011 (UTC)[reply]

--

I'm unfamiliar with "neologicism". I'm only discussing "logicism" here, as it is used in the literature (see the following quotes). Here's what Kleene wrote:

"The logicistic thesis can be questioned finally on the ground that logic already presupposies mathematical ideas in its formulation. In the intuitionistic view, an essential mathematical kernel is contained in the idea of iteration, which must be used e.g. in describing the hierarchy of types or the notion of a deduction from given premises. || Recent work in the logicistic school is that of Quine 1940. A critical but sympathetic discussion of the logicistic order of ideas is given by Goedel 1944." (Kleene 1952:46)

Here's what Eves wrote (notice that he seems to have borrowed from Kleene !): "Whether or not the logistic thesis has been established seems to be a matter of opinion. Although some accept the program as satisfactory, others have found many objections to it. For one thing the logistic thesis can be questioned on the ground that the systematic development of logic (as of any organized study) presupposes mathematical ideas in its formulation, sucah as the fundamental ideas of iteration that must be used, for example, in describing the theory of types or the idea of deduction from given premises." (Eves 1990:268).

In the latest Scientific American article there's an article by Mario Livio "Why Math Works" wherein he discusses two -isms only: Formalism and Platonism (August 2011:81) and tries to answer the question about whether mathematics is intrinsic to the universe and discovered by mankind (Platonism), or whether it is Formalistic in nature -- i.e. invented by mankind. He concludes both seem to be the case.

This brings me to a final thought (opinion) that what we have in this discussion is of confusion between philosophy of mathematics (Formalism and Platonism) and a particular practice of mathematics (Logicism). I personally am sympathetic to the Kleene-Eves point of view (Logicism is a failure) and I agree with Livio who is also a bit perplexed by this universe of ours: "Why are there universal laws of nature at all? Or equivalently: Why is our universe goverened by certain symmetries and by locality? I truly do not know the answers . . ." (p. 83). At least now we have a few quotes from reputable writers to apply to the issue. I'll keep hunting for more. Bill Wvbailey (talk) 13:37, 2 August 2011 (UTC)[reply]

I found a great quote that corroborates my opinion about Logicism being a "practice" rather than a philosophy. This is from Brouwer's 1907 The Foundations as quoted by Mancosu 1998:9 -- " 'The Foundations' (B1907) defines "theoretical logic" as an application of mathematics, the result of the "mathematical viewing" of a mathematical record, seeing a certain regularity in the symbolic representation: "People who want to view everything mathematically have done this also with the languarge of mathematics . . .the resulting science is theoretical logic . . . an empirical science and an application of mathematics . . . to be classed under ethnography rather than psychology" (p. 129) || The classacial laws or principles of logic are part of this observed regularity; they are derived from the post factum record of mathematical constructions. To interpret an instance of "lawlike behavior" in a genuine mathematical account as an application of logic or logical principles is "like considering the human body to be an application of the cience of anatomy" (p. 130).

(But I ask: why do we humans view the universe's apparently regularity? Is it because of an intrinsic "logical" design of our brains?) There's more to be found in Grattain-Guinness:2000 (about 35 cites in his index). Bill Wvbailey (talk) 14:09, 2 August 2011 (UTC)[reply]

To Gregbard: There are some people who purport to be mathematicians or logicians who are not logical. See "synthetic logic", "fuzzy logic", "Paraconsistent logic", and their ilk.

You said "math has no empirical component". This is false. Mathematics, including logic, is just as empirical as nuclear physics or chemistry. Any calculation or deduction done by a mathematician is actually done in the physical world by some sequence of operations on matter. If these operations did not produce what we consider the proper result, then either that mathematics would not exist or it would be different from what we know it to be. JRSpriggs (talk) 03:57, 13 August 2011 (UTC)[reply]

Aye aye aye. Your characterization of these other mathematicians as "not logical" is just your characterization of them. These people are not setting out to ignore or abandon reason, but rather have constructed a different model of what is reason. Invariably they point to reasons for their constructions. Anyway, the focus should be on the systems, not the people. I think you intend to claim that the systems of logic these people construct are "not logical." Like I said this isn't psychology. Whether or not logic is empirical is a very deep and complex subject, and it is not universally agreed that it is empirical. The prevailing view is the opposite. Your appeal to physicalism has my sympathy, as I am a physicalist as well, however physicalism is a metaphysical theory addressing whether or not there is a dualism between mind and matter. The question of whether logic is empirical is not effected by anyone's metaphysical physicalist or idealist views. Empiricism involves being experienced by the senses. Exactly what sense are you using to sense that a particular truth of mathematics is true? It couldn't be sight, after all, a person could conceivably discover all the truths of logic and mathematics sitting alone with eyes closed. <or>I think more properly that like there is evolution in response to the environment, and so too, the evolution of the brain is a response to the 'logical environment' of this universe.</or> As a physicalist, I would say that the 'logical environment' is only experienced through particular instances of activity involving physical matter. However to say that what I am calling the 'logical environment' itself is physical or in anyway directly sensed through the five senses would need some justification and explanation. You only experience it indirectly which makes the "empirical" logic and mathematics of your view only a soft science. Is that your view? That mathematics is empirical, and that it is a soft science? Who is the psychologist now? In my view, we can call things like a "sense of reason", or a "sense of decency" senses, however, they really are a different category of thing than the five senses, and not empirical. Saying that mathematics is done in the physical world does not make mathematics empirical, otherwise astrology, religion, and "noetic science" would also equally be empirical. Greg Bard (talk) 11:25, 13 August 2011 (UTC)[reply]

Supposition on evenness of zero misunderstanding

Hi Trovatore. As Wikipedia:Reference_desk/Archives/Mathematics/2011 August 10#Is zero really an even number? will soon be archived, I wanted to point out my suppositional response to you question. -- 110.49.248.124 (talk) 15:32, 15 August 2011 (UTC)[reply]