fdrake

So it looks like there are two thrusts of argument in the paper, and a broad theme. Broad theme; why does "modern moral philosophy" concern itself so ...

Philosophical side note: Different senses of identity can be thought of as equivalence classes under different relations. Numerical identity is like 2...

The previous post talked about equations and how to define the algebra of arithmetic. It turned out that the algebra of arithmetic invokes a notion of...

Here's an argument for the necessity of the empty set. If you want a theory of sets, you want to be able to compare pairs of sets. You want to know if...

You get something really similar to that with any mapping t(k):D\rightarrow M, where M is some manifold in which x is a point. With the constraint tha...

It seems to let you rigorously think of dx as an infinitely small translation/length with the expected connections to calculus and differential geomet...

Page 4. Properties. "However if xd = 8d for all d then x=8". In that link, they are multiplying by d.

All you need to do to turn any non-zero dividing element into a zero dividing element is to multiply it by d. So all elements zero divide. If you quot...

The real numbers \mathbb{R} are a field (without 0). The real numbers augmented with the set of numbers defined in the previous post's link are not.

Ok. Assume d had a multiplicative inverse. Also d^2=0. Then d.d^-1=0.d^-1. Which gives d=0. But d is nonzero. So d does not have a multiplicative inve...

Multiplicative inverses, you have zero divisors from the infinitesimals and that blocks it. It's not, it's just a point of difference. Having a number...

It's not really about the reals and analysis as usually thought of, the construction doesn't satisfy the field axioms. Moreover, every function from t...

I'm only pointing out that if sets can't provide a model for @"aletheist" 's intuition of continuity, since they consist of distinct entities (you can...

Still sets tho. x+db \in R \cup D.

Logical fallacy. It is still possible that all market forces are informed only by moral desires! Praise Xenu!

Think it's about time to convert to Nick Land, the answer is always to make things worse faster.

There's sort of a branching point here, @"Pfhorrest", two ways to tell the same story. Now we've got resources to talk about sets, operations on sets ...

Ideally what is needed, given the equation concept, is a way to manipulate equations so that their solutions can be revealed. What this requires is se...

One important technique is how to construct and solve equations, and we've got the theoretical resources in place to do that for natural numbers arith...

There are other axioms of ZFC. But considering that the story being told is "how to go from formal languages to differential equations", I'm not going...

x+y = x \cup_{i \in y} S^i (x)=S^{x+y}(\emptyset)

Or alternatively "take the thing on the left, and successor function it the number of times required to reach the thing on the right from 0", equivale...

An interesting property of the set N as defined above is the induction property. It allows a kind of proof called inductive proof. This provides a way...

Now onto the axiom of infinity. The axiom of infinity states that: "There is a set N such that \emptyset is in N, and if the set x is in N then S(x) i...

Ok sorry. Now I'm back to no idea of what you're talking about.

>Declares things to be at absolute rest. >Appeals to unspecified sense of anti-realism for claim. "It's like that if we think it's like that".

Ok. A is walking away from B. Find a coordinate system in which they are both stationary.

Relative velocity isn't just "declared". Probably not. But I don't really know what you mean.

Treating the height difference as if it's causing that difference in income is extremely bizarre. Imagine the social programs that would come of it: "...

Just an observation. If one party in a negotiation can always be assumed to compromise without fail and imposes no relevant sanctions when the other p...

Yes. Though nature only affords our societies with some of the differential, or enables/renders possible social costs which leverage distinctions in b...

I think the pictures of metaphysics you get if you immerse yourself in a field differ a lot from field to field, and even subfield. Dive into physics,...

Strictly speaking, none, but the approximation for there being a single sense of time common to all the objects gets better the slower they are moving...

An object at rest is just not moving with respect to its surroundings. That is, its relative velocity to its surroundings would be zero. An object at ...

Immediately reminded me of having sex. If you've had sex, you haven't just had sex, you've also lost your virginity.

A unified "now" only makes sense for collections of objects which are moving sufficiently slowly relative to each other. (Relative) speed changes how ...

I guess the distinction you're looking for is inequalities that derive from features of political organisation with regard to resource access and dist...

Regardless, I think the synthetic differential geometry pdf suggested an intuition closer to it. Roughly, augment the real numbers with some set of sy...

Thanks!

Do you know of any current mathematical objects that behave more like true continuity in your view?

Rejecting (by undermining) the analytic/synthetic divide was a major part of Quine's disagreement with the logical positivists, spelled out in Two Dog...

In the future our unconscious will be used to mine Bitcoin.

This. Also even within the same field but different subfield. "What you're doing isn't history/anthropology/linguistics/psychology..."

In my experience academics involved in any kind of science generally separate themselves from philosophy. "What would make a neural net self aware?" -...

Let's say I have some "True continuity" X. Like a line X=(0,1). Let's say I can take "parts" of it in the above manner; arbitrary subintervals. (0,a),...

I think this would end up giving precisely the same mathematical theorems, no? You just restate things in terms of connections and parts. Like: the me...

Can you apply the same level of doubt to what's making you doubt all this?

Go eat something and find out?

You do stuff. Like doubt you exist. You probably also eat things sometimes. Doubting's one thing you do. Try doing something else for a bit. If you ne...