fdrake

Aah, so I can stipulate {alcontail is wrong about the significance of axioms to justifications in natural language} and derive that and have it be tru...

The example in the last post of "eats" is a blueprint of how functions and predicates are formally constructed and assigned on a domain. Properties ar...

How do you decide what goes into an "axiom pack"? @"alcontali"

Let's look at an example, this will contain how we assign predicates meanings (what predicates formally mean) in a simple example, and how we specify ...

We're going to start talking about the semantics of first order predicate logic now, and relate it to the syntax. In propositional logic, the semantic...

Fixed, thank you.

Statistics! This is all very pure for me.

The bare bones rules of propositional logic and first order predicate logic are quite similar; first order predicate logic just expands on or rewrites...

Let's stop to consider the richness of the language of first order logic, the kind of things that we can express with it. (1)"Every number has a prime...

I'm a mathematician who studied a decent amount of logic. The material I've presented here is recapitulating stuff from 2 undergraduate courses in log...

The rules of the formal language of first order logic tell us how we can build up well formed formulae out of symbols, and what symbols there are. So ...

One of the major reasons we need to add quantifiers to a formal basis of mathematics is that we need to be able to deal with infinite domains of objec...

The thing in itself isn't generated by our faculties limits, or anything to do with us, rather it's that which generates whatever appears to us; in or...

In CoPR the noumenon's aligned with what we can experience. But what we can experience isn't coextensive with what is. The noumenon marks the limit of...

So far we built a system of deduction - the rules of inference of propositional logic - on top of a way of writing down grammatical statements within ...

Fair. Would you be interested in doing the more detailed version I had in mind? It is likely that we imagine different things by rigorous proof. To me...

Yes, that's well put. Weak/strong is a silly way of saying nothing relevant. Whose interests would be facilitated by an armed conflict between America...

If it happens, it's probably imagined as being to the benefit of some of them and not others? Can't say to who though. Weakening Iran through military...

If/when it happens; Saudi ruling class might gain from destabilised Iranian economy, Israeli ruling class might gain as Iran and Israel have been prox...

Feel free to intervene in the bits I've written to add further detail if you like. Define the hand wave operator H as a function on the cartesian prod...

I think it's a fetish for parsimony. I vaguely recall that having a single logical connective simplifies proofs and the well formed formulae definitio...

Thanks, fixed. The presentation is very non-standard. If and when you've read it I'd appreciate you pointing out flaws and errors as I'm mostly wingin...

The previous post gave a sketch of how a formal language; a grammar of well formed formulae; can be augmented with more structure (inference rules) to...

The kind of discussion that distinguishes a mind from a subject is already a more interesting idea than the usual elision of reason which joins them. ...

I don't give much weight to the distinction, at least whenever I think it's relevant. I think that it generates intractable access problems (how does ...

The subject object distinction is a metaphysical distinction; it makes sense when you have an account of souls separated from objects, or minds separa...

Now that we've set up how to specify a formal system to produce strings given a set of production rules and symbol primitives; a formal language; we n...

Don't know enough about type theory to comment. Might as well start then. I'm largely going to assume that we can have a classical logic in the backgr...

You need logical symbols to state set axioms. You also need them for Peano arithmetic (and the Von Neumann version you presented in the OP). You don't...

I think there's a big difference between expecting to show how the entire universe works mathematically (what some people seem to be reading the threa...

We should put the logic in the background then, except where it's completely necessary to go into it. I'm guessing that we'll need to set it up so tha...

I don't think you realise how big a project just getting to differential equations of real variables would be. It's a lot of work.

Interested in filling out parts of the story that I know. I was thinking about this issue. If we want to arrive at a general description of... well, e...

I guess it comes down to whether you require that the application of a function to an input necessarily produces a distinct output (IE, no fixed point...

A function can have fixed points. These are when you get the same thing out as what you get in. The operation "take a sequence, delete every second el...

I'm thinking of them as sequences. The first sequence, the one in your OP, is the sequence "the constant sequence where every element is b". The secon...

So you mean they're identical collections, but their elements aren't equal? :S

Assume what you're saying is true. Then {1} = {2}, then 1=2, contradiction, then what you're saying is false.

There are two miscomprehensions in your post. The first is based on how sets are defined. The second is based on a conflation of an equivalence (of se...

Sexual preference, no matter strength, no make babby, no exclude babby. Sometimes babby come from gay man or woman and partner because like partner an...

Bijections between sets only show they're of equivalent cardinality, not that they're identical sets. Sets are identical when and only when they share...

Even if you make the assumption that individuals which are homosexual are exclusively homosexual in sexual interest, that doesn't mean they don't repr...

A rough guideline is that your posts should stand alone without their references. Certainly, central parts of arguments or posts in general should usu...

You don't need to demonise the Orange staff to demonstrate that what they did was wrong. Demonstration of empathy: I'm sure there were heated boardroo...

I had no idea that pointing out unsupported assumptions, equivocations and falsehoods was sophistry. Posting arguments in premise-entailment form as a...

Equivocating between a cause and a predisposition doesn't help much. Let's grant that mental illnesses do not occur without genetic predisposition, ge...

Whatever causes the sickness and death doesn't really matter, does it? It just changes what should be done to address the issue, and the laws which ma...

If you need a structural argument for why workplace safety should have laws attached, consider that sickness has huge social costs; it decreases workp...

Can you spell out for me how that relates to workplace conditions that lead to unhealthy workers - exposed to conditions that are not necessary for th...

Are you arguing that it is necessary for people to be harassed into suicide in every workplace because if it doesn't happen civilisation will collapse...