I just had a weird thought
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From: taffer on 11 May 2010 07:17 I just had a weird thought. It actually left me confused about what is mathematical, and what is physical. The statement was: "Every finite set can be generated by adding one element at a time, starting from nothing". This seems to be true. But then (and this is what confused me) I wondered, is that a mathematical statement? If so, would there not be a formal mathematical theorem expressing the statement? Or if it's a definition, a formal mathematical definition? Or maybe it's not a mathematical statement after all?
From: Aatu Koskensilta on 11 May 2010 09:07 taffer <djrt20(a)bath.ac.uk> writes: > I just had a weird thought. It actually left me confused about what is > mathematical, and what is physical. The statement was: > > "Every finite set can be generated by adding one element at a time, > starting from nothing". > > This seems to be true. Sure. But why should you think it a physical matter? It's a mathematical triviality. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Charlie-Boo on 11 May 2010 09:29 On May 11, 7:17 am, taffer <djr...(a)bath.ac.uk> wrote: > I just had a weird thought. It actually left me confused about what is > mathematical, and what is physical. The statement was: > > "Every finite set can be generated by adding one element at a time, > starting from nothing". > > This seems to be true. But then (and this is what confused me) I > wondered, is that a mathematical statement? If so, would there not be > a formal mathematical theorem expressing the statement? Or if it's a > definition, a formal mathematical definition? Or maybe it's not a > mathematical statement after all? Sure it is. And formalizing it is an excellent idea. (I have maintained for a while that the fundamental problem of theoretical computer science is its formalization. And look all around you - music, movies, televisions - everything is being digitized. Digitize = Formalize.) So how do we formalize this statement? I would first break it down into its primitive concepts. They would still be expressed informally, but breaking it down (divide and conquer) would be a first step in introducing formality. What are its informal primitive parts? C-B
From: Charlie-Boo on 11 May 2010 09:34 On May 11, 9:07 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > taffer <djr...(a)bath.ac.uk> writes: > > I just had a weird thought. It actually left me confused about what is > > mathematical, and what is physical. The statement was: > > > "Every finite set can be generated by adding one element at a time, > > starting from nothing". > > > This seems to be true. > > Sure. But why should you think it a physical matter? The obvious close relationship with the movement of physical objects from one location in space (relative!) to another. > It's a mathematical > triviality. So? Do you forget that the most trivial of matters (FOM - FLT - Arithmetic) have been debated for centuries and that problems trivial to state can be massively difficult to solve? Or are you just trying to be arrogant? (You used to be one of the rebels - now you sound like the rest of the lying abusive nutcakes.) C-B > -- > Aatu Koskensilta (aatu.koskensi...(a)uta.fi) > > "Wovon man nicht sprechan kann, darüber muss man schweigen" > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Marshall on 11 May 2010 09:42
On May 11, 6:34 am, Charlie-Boo <shymath...(a)gmail.com> wrote: > On May 11, 9:07 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > > taffer <djr...(a)bath.ac.uk> writes: > > > I just had a weird thought. It actually left me confused about what is > > > mathematical, and what is physical. The statement was: > > > > "Every finite set can be generated by adding one element at a time, > > > starting from nothing". > > > > This seems to be true. > > > Sure. But why should you think it a physical matter? > > > It's a mathematical triviality. > > (You used to be one of the rebels ... ) Remember that haircut he had back when he was younger? Now THAT was rebellion. Marshall |