THIS is where the "scientism" myth comes from. closed-minded idiots project their own stupid way of thinking onto us, even though their way of thinking directly contradicts the entire point of Science.

lolol aigh completely ignore concepts like buddhism n monoconsciousness to justify your simple ass view of reality. yo jus because a philosophy's implications are massively detrimental to your lifestyle n worldview don mean they don xist.

word of advice man, you wanna avoid philosophical/moral dead ends? drop tha scientism/material reductionist/positivist bullshit, theyre dinosaur acts, leave philosophy to the philosophers and get over tha very biased, very subjective scientific establishment's narcissistic appropriation of tha apparent objectivity n conceptual freedom from bias possessed by tha scientific method

I'm sure your fame in the mathematical community will be assured if you manage to refute one of Tarski's proofs :-)

Thank you, Andrew, I am going to have to give that more thought.

Yes, you're allowed a unit length (the theory of real closed fields contains all the field axioms, including the existence of a multiplicative identity). You're not allowed induction unless you define it yourself, though.

But that doesn't help you, because we're talking about a first-order theory here, so you have no way to specify "the smallest set containing 0 and closed under the operation of +1". If you could specify that set, then it would be a model of PA, but it's a general issue with first-order logic that although you can define "the set containing ...", you can't define "the set containing only ..." for an arbitrarily large or infinite set. Therefore there is no way to pin down first-order PA as a substructure of first-order RCF or elementary Euclidean geometry.

Andrew, I am not sure that is true. I think it should be possible to construct Peano arithmetic out of Euclidean geometry. However, I might need a unit length to do it (I think that is allowed). A point has zero length, and if you have a unit length you have 1, and adding length gives you all the natural numbers. Length additions are transitive and lengths of successors (unit length plus) are equal. Also if any line 'l' is in set k, and the successor of any line in k is in k, then all lines of natural number length >= to l are in k (induction).

Alternately, I think Russel and Whitehead showed that Peano arithmetic could be constructed out of first order logic, if you have true, false, not, or and a test of equality. If those can be encoded by geometric operations, then you have arithmetic, if you have arithmetic you can encode analytic geometry, and theorems about that geometry. Now, no way am I going to spend the time to figure out the Gödel numbering in that representation (a huge mess), but think it is conceptually possible.

Thanks. Your CoB vignette clarifies the issue. I mistakenly thought you had proposed a conflict between the geocentric and heliocentric depictions. In a vignette I prefer to use motion picture cameras as observers rather than humans and fleas. Also I prefer a bicyclist to a runner. That way a camera can be mounted on a rotating wheel of the bike with a view perpendicular to its plane of motion. In the vignette each of the several records of the motion is true because the others are true and mathematically equivalent. We agree. No reference frame has any special standing except simplicity.

You are correct, GCBill, it is hard to support the idea that there ever was a sudden change (in just a few generations) of any human characteristic across the population of our ancestors, intelligence or moral impulses included. I like to ask those who think that souls were, somehow, phased in during the process, "Which came first, souls or language?"

‘Why do we measure time geo-specifically?’

Probably for the same reason that if someone comes up to us and asks for direction to the nearest coffee shop, we start with the assumption that the person asking wants to know the direction, from where he/she is located at the moment, and not from some other place where he/she is not...

In other words, it's extremely convenient...

Glen