Ars combinatoria universalis (fragments of talk) / discussion: S Awodey, P Ehrlich & G Hellman (& others) (contd.)

0:00 There will be a whole power cell in such totalities. That's a different condition. It won't be much stronger. In fact, it might even imply booleans, because, you know, typically what this Piotrowski definition does is it picks out things that are not only finite, but these transition maps are epic, and that's not true. So, it still may not be enough. The p sub-finite included in p will still be not... So, there's a whole conjectural theory here, which is all these combinatorial computers. So, now the question, what does all that have to do with the axiom of infinity, in some sense? I don't know. I think there's some there's some swindle you see there's okay what's this yeah sorry I talk too much The first sort of predicate-less logic is a primitive predicate on an axiomatized structure involving a set of operations. We add the properties of this model to the standard notion. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you.

2:30 Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. So with natural numbers, there's going to be another object in the same world, which is some kind of weak set theory. It is a weak set theory which has a notion of finiteness. And given that, it's not going to be a single object. But more of it can construct a lot of new forms. Yeah, that's not exactly clear. I don't know if it's correct, but it's simply the observation that if you have a set with a successor operation, it has, not through this background, with a successor operation, it has a property, but as we argument, the collection of all its predecessors into the successor operation is infinite and gives, in a sense, a finite. And that set of answers is uniquely characterized by that set of answers. I guess at some point you're saying you have a rather ordinary set of answers. Linearly ordinary sets of answers. So my objection is that to get that notion of antecedents out in a finite number of chemical ways is going to involve some kind of... All of this is based on localised impredicativity of the description to that notion of finance. That's the psychological question. Localised. Well, that wasn't his claim. That was my claim, that there is some amount of impredicativity of all these descriptions specifying that notion of finance. It's not a single final set. It's an arbitrary final set. Thank you for your attention.

5:00 That was his plan? Yeah. Oh, his physics. He gave me the initial plan. He gave me the initial plan. From... Not their language. From everyday practice. From everyday practice, etc. Your mom was like, you didn't do anything like that. Well, at least they know that. Well, that doesn't even make sense. I like that. Characterization there. That's beautiful. Yeah. Yeah. Yeah. I'm talking to you. Instead of having to go to the computer, you can go to the lab. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. It is very difficult to prove the double natural numbers of the two, you know, the Vedic and so-called Pyongyang conditions, even given in the end of math anywhere within your test period, given any setting in the end of math, and then starting from the new math from your natural numbers, which is compatible. Thank you for your attention.

7:30 Special operations? No, surely not. It would again be a democratic program. I mean, it's going to be a very strong program. I mean, it's going to be a very different program. I mean, it's going to be a very different program. I mean, it's going to be a very different program. I mean, it's going to be a very different program. I mean, it's going to be a very different program. I mean, it's going to be a very different program. I mean, it's going to be a very different program. I mean, it's going to be a very different program. I mean, it's going to be a very different program. I mean, it's going to be a very different program. I mean, it's going to be a very different program. I mean, it's going to be a very different program. If the finalist condition suffices for the definition of quantum function, then, yes, we can, if we know this or not, find precisely what the definition of quantum function is. Right. But we don't know what they're given as a definition of quantum function. Exactly. This is the point. This is the point. This is the point. This is the point. This is the point. This is the point. This is the point. This is the point. This is the point. This is the point. This is the point. This is the point. This is the point. This is the point. This is the point. This is the point. This is the point. This is the point. This is the point. This is the point. This is the point. This is the point. I was just trying to re-formulate it, but I don't think we can make a good amount of sense. Well, there are also a couple of categories of finite objects and another object. So let's try to prove that that other object is actually finite. Let's give them a notion of finiteness. So we'll give them a function of time. So now we've got a partial object which has one hundred, probably a million years. At any point during the down segment of our time, I'm saying we need to postulate a sub-chapter of our time, and let's see what we need. Maybe we can just say that all the negative and finite lines are my sense. That might be one thing. We might just postulate on properties, but then, as you say, the better of it is that the segments have to be... We've never actually brought in finite equipment in an external way. Can we prove that this object really isn't actually an object from the Big Bang? I'll say it. I think they'd rather not have a subject like that. Yes, I'd like to prove the piano axioms. That's what they think they are. But I think that's not the answer. Thank you very much for your time, and I look forward to seeing you again next time.