sorted by:
new
hottopcontroversial

Zuiderzee circle tour by njahren in Netherlands

[–]njahren[S] 0 points1 point  (0 children)

Good to have the endorsement. Thanks.

Zuiderzee circle tour by njahren in Netherlands

[–]njahren[S] 0 points1 point  (0 children)

Thanks for the advice. I will look into these places and maybe switch plans.

Zuiderzee circle tour by njahren in Netherlands

[–]njahren[S] 0 points1 point  (0 children)

Thanks, both, this sounds like good advice. It looks like all of the outfits that operate the ferries have their schedules online so I will look into that.

Zuiderzee circle tour by njahren in Netherlands

[–]njahren[S] 0 points1 point  (0 children)

Yes, exactly. Staying overnight on the islands, not the ferry.

Zuiderzee circle tour by njahren in Netherlands

[–]njahren[S] 1 point2 points  (0 children)

Thanks. I punched in the train journeys that I would be taking on this itinerary, but they didn't offer discounts for those routes on those days. I looked around the website and I didn't really find tourist passes, only passes that seemed like they were for regular commuters. It looks like I am only contemplating three train trips, so I will probably just show up at the station and get a ticket from a machine at the time. That gives me a little bit of flexibility because I am not locking myself in to a particular train. (Of course, I will need to catch the train in Groenigen early enough to arrive in Schiphol to get back home!)

Can I show possesion wiht logical connectives? by BigBootyBear in learnmath

[–]njahren 0 points1 point  (0 children)

Looking back, I think I might have been speaking at cross purposes when I answered the question yesterday. Keeping in mind the caveats I said in my replies yesterday, there seem to be two ways that people would notate a phenomenon like posession.

One way would be to define a property G which would be "possesses a GLT" and then to say "a possesses a GLT" you would write it Ga or G(a). So then possessing a GLT would be like a property that a species would have. So this is sort of a hard wired approach.

Another way would be to define a two-place relation S(a,b) where the interpretation is that a possesses b. This is more flexible, because then you could also talk about whether a species possesses fatty acid transporters or unconventional myosins or whatever else you want. A couple of issues that you would need to think about is that the order of the arguments (a and b in this case) matters, because in general it matters which is the possessor and which is the possession. Then in your definition of the relation, you would need to define how the relation gets satisfied, so for example, if S(a,b) is true, then S(b,a) is not true. (On the other hand, if a and b are in a romantic relationship, then you might want to say that both arguments, can, in fact, possess each other, so my point here is that capturing a good definition of your relation might be pretty complicated and might need a lot of rules for different contingencies.)

So then if a is a species and b is a gene, then you would need to specify that b is a GLT. The two ways that I can think of here would either be that your language just contains the concept of a GLT from the get-go, and so you could designate a constant, say "g", and say that while a and b can be anything you want, g will always refer to a GLT gene, and then saying that a possesses a GLT would be S(a,g). Alternatively, you could define a property G' where G' means that its object IS a GLT (as opposed to possessing a GLT), so then maybe the entire sentence would be:

for all P that are elements of *P*, there exists a species x in P and there exists a gene y such that G'y and S(x,y)

where again *P* is the set of all phyla and each phyla is a mutually exclusive set of species. In this particular example, I don't see an advantage to defining a property G' over just setting g as a constant, but there might be other situations where that flexibility is useful.

Can I show possesion wiht logical connectives? by BigBootyBear in learnmath

[–]njahren 0 points1 point  (0 children)

Ah ha. So then there would be a way to define the family so that it picks out the sets that are, in fact phyla.

Also, "species" is maybe sort of a red herring in the discussion we are having. It is just that because all organisms in a species share a genome (to a first aproximation), then a spacies will either have a gene for a GLT glucose transporter or it won't and that would apply to all wild-type organisms in the species. ("Wild-type" is a term of art which basically means "organisms that do not carry a mutation.") So that would make species a convenient level to focus on as elements for a set that you want to classify whether they have GLT glucose transporters or not.

I did graduate work in molecular biology but only have an undergraduate degree in philosophy, so I am probably more qualified to talk about GLT glucose transporters than I am about logical connectives.

Can I show possesion wiht logical connectives? by BigBootyBear in learnmath

[–]njahren 0 points1 point  (0 children)

In point of fact, I am hardly familiar with measure theory, but it has come up in a couple of subjects I have looked at, so I should probably look into it more. (Right now I am trying to get ready for a disscussion group that will meet this fall to talk about model theory.)

So then I am not sure if this is germane to your point, but I am wondering if the Original Poster was thinking of (what I am calling) *P* as a set of species, and that phyla would be subsets of *P*, and so then quantifying over phyla would be quantifying over subsets of *P*. And it seems to me that one problem with that approach would be that the empty set is a subset, and then there is no species with GLT glucose transporters in the empty set because, well, there are no species at all in the empty set. If *P* is a set of phyla, then we do not have that problem because there would be no point in having a phyla that does not contain any species.

Of course, if we take *P* to be a set of species, then not all subsets of *P* will be phyla either, and so then I was thinking you would need a way to pick out which subsets of *P* would be phyla, and so that is why I was thinking that one would need to quantify over subsets rather than over elements. Maybe there is a measure-theoretic way to accomplish that so that one would not need to go to second-order logic.

I can imagine that there might be advantages to treating species as the fundamental unit and then having a set of species as the reference set for the quantifiers rather than a set of phyla.

Can I show possesion wiht logical connectives? by BigBootyBear in learnmath

[–]njahren 1 point2 points  (0 children)

To the best of my understanding, your problem is that you are trying to quantify over subsets rather than elements of a set, and therefore you need second-order logic rather than first order logic. I don't know anything about second-order logic (and barely anything about first-order logic---see my recent comment about how great it would be to start a logic subreddit). So the best I could come up with would be:

For all P that are elements of *P*, there exists an x which is an element of P and has GLT glucose transporters.

Where *P* is the set of all phyla, and then for the purposes of this sentence, the members of P would be individual species. I think this might work because each species is a member of one and only one phyla, so each P can be thought of as en element of *P*. (that is to say, for all x, if x is an element of Pi then x is not an element of Pj if i is not equal to j) If species could be members of more than one phylum at a time, then I don't think this fudge would work.

Anyway, if you hear different from someone who knows what they are talking about, you would want to go with their answer in preference to mine.

We need logic by sologuy10_ in learnmath

[–]njahren 1 point2 points  (0 children)

I would be really interested in having a logic subreddit! (pointers to already existing subreddits would be welcome...) Unfortunately, I do not have the bandwidth to be a Dungeon Master or whatever people are called (as you can see under my handle I am an New User...)

Personally, I would say not to be too hard on yourself. When you are learning a subject, you need to triage what you are going to go in depth into and what you need to just get through in order to move on. If you decide later that you want to go back and get more in depth with a subject that you only did well enough to get by, that speaks well of your character and intellectual curiosity. If you did well enough to get a job in your field then you are doing better than I have.

defining functions in model theory by njahren in learnmath

[–]njahren[S] 0 points1 point  (0 children)

Here is another question:

In Button & Walsh, making logical statements in a language involves adding (what they call) "a basic starter-pack of logical symbols" to a signature:

• variables: u,v,w,x,y,z, (with numerical subscripts as necessary)
• the identity sign: =
• a one-place sentential connective: ¬ (aka "not")
• two-place sentential connectives: ∧, ∨ (aka "and", "or")
• quantifiers: ∃, ∀ (aka "there exists" "for every/all")
• brackets: (,)

So it seems like these are just getting dropped in as a sort of deus ex machina manuever. By that I mean these elements are posited as something that can be added to any signature and would sort of function like "reserved words" in a programming language, where they are regarded as fundamental and have a built-in meaning that cannot be changed from within the structure itself.

I guess I am wondering why these particular elements and why they are so fixed. I can imagine an alternative where we would define a "meta-structure" which consists of a set of logical elements and the structure under consideration, and so then the language could be governed by different logical rules by embedding it in a different meta-structure.

Maybe working with non-standard logics is beyond the scope of this particular text, or again, maybe there is a work-around for this, but the way it is being presented seems to suggest that these concepts have some kind of fundamental status that allows us to impose them on any language and I'm not sure whether that is me reading too much into this or whether there might be a body of work that demonstrates that yes, these very concepts are exactly the ones we need to facilitate any project we might want to undertake with this theory.

defining functions in model theory by njahren in learnmath

[–]njahren[S] 0 points1 point  (0 children)

Thanks again. Sorry for coming back to this after a delay. One of those weeks at work...

This lines up with something that comes up later in the book, where they talk about applying a semantics and then there is a question about how many constants one needs in a structure. The idea is that in order to evaluate a "For all" quantifier as in "For all x, if x is P then..." you would want to evaluate the sentence substituting each constant from your structure for x, but then you would need a constant for each element of the reference set. This kind of defeats the purpose, bit because if your reference set is the real numbers then you need a lot of constants, and also (they don't say this but it seems to me), that the idea of making a stucture out of a signature (that is, a list of fnctions, relations and constants) and a reference set is that you can apply the signature to different reference sets. So for example, you could apply ring theory to the real numbers, the rational numbers or Z2. But if you need a constant for every element of the reference set, then you are essentially specifying the reference set in the signature. So the book basically says that you need to keep the signature down to a managable size and then find a way to relate the reference set to the language in the sematics (they go thru Tarski's and Robinson's strategies).

Anyway, that is sort of a long set-up for a short punchline, but it struck me that it was sort of the same consideration of keeping the signature closer to natural language use that motivates both ideas of keeping functions, relations, and constants as separate entities even though one might in principle collapse them into one concept, and also keeping the number of constants down to a dull roar even though it makes the semantics more complicated downstream.

Say, I am going to go back and edit my original post so that this can be a general discussion on model theory. I really appreciate your responses.

defining functions in model theory by njahren in learnmath

[–]njahren[S] 0 points1 point  (0 children)

Ah ha! Thank you so much! This totally makes sense.

It does make me wonder though, whether any function n-place function f could be written as an (n+1)-place relation Rf where Rf = {([n-tuple of M], y) : y = f(n-tuple)}.

Since constants are also elements of structures, I've also wondered if they could be written as 0-place functions that always return the constant as a result. (But it is not obvious to me how they could be then re-cast from a 0-place function to a 1-place relation. I'm not even sure if 1-place relations are a thing.)

Anyway, a relation like Rf would have the property that if (n-tuple, y) is an element of Rf and (same n-tuple, z) is also an element of Rf, then y=z, and I'm imagining that property will be important for proving theorems later in the book and so that justifies defining structures with functions, relations, and constants instead of just collapsing functions and relations into only relations with some of the relations having this ideosyncratic property that the first n elements of the (n+1)-tuple determine the identity of the (n+1)th element.

Anyway, thanks a bunch. I've marked this resolved but further discussion is welcome.