3,511 reputation
637
bio website
location Germany
age 48
visits member for 3 years, 7 months
seen 6 hours ago

My interests:

  • abstract structures
    (e.g. graphs, groups, polytopes, spaces, ...)

    in the course of this

  • category theory

  • model theory

  • presentations and representations
    (e.g. of abstract structures by or inside other abstract structures)

    next to this

  • philosophy
    (esp. of mathematics, science, and mind)

    especially concerned with

  • atomism
    (i.e. reductionistic or other theories referring to some kind of "atoms")

  • their refutations


Mar
2
comment The deep structure of logical formulas
I considered the Sheffer stroke, too, but deliberately didn't mention it in my question. In any case, it must be proved that a Sheffer stroke presentation with minimal numbers of variables, occurrences of variables, and parantheses is unique. (Or is this by any means obvious?)
Feb
24
comment The deep structure of logical formulas
It's not only about perspicuousness (= unambiguousness), but also about conspicuousness (= salience).
Feb
24
revised The deep structure of logical formulas
added 4 characters in body
Feb
24
comment Is the singleton graph 2-connected?
Also in graphs? What then is the difference between a point with and without a loop? And even when I agree (what I do): Is it always 2-connected, too?
Feb
24
comment The deep structure of logical formulas
Your objection is legitimate: even in linguistics the deep structure of a sentence doesn't have the same "look and feel" as its surface structure. (And there is no reason, why it should.) On the other hand, truth tables are not quite what I am looking for. It will take me some time to explain why. (They are somehow "too far away" from the surface structure.)
Feb
24
asked Is the singleton graph 2-connected?
Feb
24
comment The deep structure of logical formulas
Thanks, but PNF doesn't deal with the matrix. (see math.stackexchange.com/questions/18743/…)
Feb
24
comment The deep structure of logical formulas
I would like to be able to define the notion of a "simple" graph property (given as a closed formula in the language of graphs). This would be a formula that genuinely is not of the form $\neg\phi$ or $\phi \vee \psi$ and so on. Example: $(\forall x,y)\ R(x,y)$ (= the graph is complete).
Feb
24
asked The deep structure of logical formulas
Feb
17
asked Natural definitions of families of subgraphs
Jan
15
comment Construction Types or Type Constructions?
The kind of "individuals" is something extra, it applies to types $t_1$ and $t_2$ but not to terms of types $t_1$ or $t_2$.
Jan
15
comment Construction Types or Type Constructions?
@Giorgio: Thank you for being interested in the question. By "kinds" I mean something like "sorts" (i.e. of types of individuals). Consider for example one type of indidivuals $t_1$, and another type of individuals $t_2$, both of kind "individuals".
Jan
14
asked Construction Types or Type Constructions?
Jan
10
revised Representation theorems for graphs
added 26 characters in body
Jan
10
asked Representation theorems for graphs
Jan
6
revised Generalization of simple and transfinite induction
added 88 characters in body
Jan
6
comment Generalization of simple and transfinite induction
I gave a hopefully more correct example 4.
Jan
6
answered Easy visualizations of small countable ordinals
Jan
6
comment Easy visualizations of small countable ordinals
But the $n$-th turn contains $|\omega|^{n-1}$ copies of $\omega$, so there would be $|\omega|^{|\omega|}$ copies of $\omega$ below $\omega^\omega$. Doesn't this imply that the picture is somehow misleading?
Jan
5
comment Easy visualizations of small countable ordinals
@Marc: How can one be sure that in the first picture only countably many copies of $\omega$ are present?