meaning of vdash symbol

[nukeymusic]

I started reading some texts concerning philosophy of mathematics and
they all use the following symbol:
|-
As I googled a bit I understood this symbol is called of vdash but
unfortunately the texts I have read so far don't explain the meaning
of this symbol, it is probably something used quite often. Can anyone
explain its meaning here in human understandable language

thanks
nukeymusic

[Joshua Cranmer]

Post by nukeymusic
I started reading some texts concerning philosophy of mathematics and
|-
As I googled a bit I understood this symbol is called of vdash but
unfortunately the texts I have read so far don't explain the meaning
of this symbol, it is probably something used quite often. Can anyone
explain its meaning here in human understandable language
thanks
nukeymusic

<http://en.wikipedia.org/wiki/Table_of_mathematical_symbols>.

Assuming you mean ⊢, it appears that it refers to derivability of steps,
i.e. "A implies B is derivable from not B implies not A.

[nukeymusic]

Post by Joshua Cranmer

Post by nukeymusic
I started reading some texts concerning philosophy of mathematics and
|-
As I googled a bit I understood this symbol is called of vdash but
unfortunately the texts I have read so far don't explain the meaning
of this symbol, it is probably something used quite often. Can anyone
explain its meaning here in human understandable language
thanks
nukeymusic

<http://en.wikipedia.org/wiki/Table_of_mathematical_symbols>.
Assuming you mean ⊢, it appears that it refers to derivability of steps,
i.e. "A implies B is derivable from not B implies not A.

...

Thanks for the link, I have to admit I didn't notice the symbol there
earlier, anyway they write x|-y means y is derived from x, however in
the texts I read the symbol is used a bit different e.g. |-
ss0+ss0=ssss0
As it is not explicitly mentioned from which data to derive
"ss0+ss0=ssss0", I guess -but I'm not sure at all- they mean by it:
_proof_that

can anyone confirm this?

[Frederick Williams]

Post by nukeymusic

Post by Joshua Cranmer

Post by nukeymusic
I started reading some texts concerning philosophy of mathematics and
|-
As I googled a bit I understood this symbol is called of vdash but
unfortunately the texts I have read so far don't explain the meaning
of this symbol, it is probably something used quite often. Can anyone
explain its meaning here in human understandable language
thanks
nukeymusic

<http://en.wikipedia.org/wiki/Table_of_mathematical_symbols>.
Assuming you mean ⊢, it appears that it refers to derivability of steps,
i.e. "A implies B is derivable from not B implies not A.

Thanks for the link, I have to admit I didn't notice the symbol there
earlier, anyway they write x|-y means y is derived from x, however in
the texts I read the symbol is used a bit different e.g. |-
ss0+ss0=ssss0
As it is not explicitly mentioned from which data to derive
_proof_that
can anyone confirm this?

...

|- phi means that phi is a theorem of some formal system. Which
formal system should be stated.

[...]

On Sat, 16 Aug 2008 08:39:53 -0700 (PDT), nukeymusic

Post by nukeymusic
I started reading some texts concerning philosophy of mathematics and
|-
As I googled a bit I understood this symbol is called of vdash but
unfortunately the texts I have read so far don't explain the meaning
of this symbol, it is probably something used quite often. Can anyone
explain its meaning here in human understandable language
thanks
nukeymusic

Assuming I've correctly identified the symbol, see:
<http://en.wikipedia.org/wiki/Turnstile_(symbol)>
<http://en.wikipedia.org/wiki/Table_of_logic_symbols>

[JEMebius]

Post by nukeymusic
I started reading some texts concerning philosophy of mathematics and
|-
As I googled a bit I understood this symbol is called of vdash but
unfortunately the texts I have read so far don't explain the meaning
of this symbol, it is probably something used quite often. Can anyone
explain its meaning here in human understandable language
thanks
nukeymusic

The symbols |- , -| , |= are used in formal/symbolic logic and in model theory.

In TeX/LaTeX one produces the symbol |- with the token \vdash , the symbol -| with \dashv
and the symbol |= with \models .

Presumably "vdash" means "vertical dash", shorthand for "vertical dash followed by dash".


Perform a Google >\vdash to obtain about 19700 hits.
In 3rd position I found the artistic one-page website http://vdash.org/ .

Google >\dashv shows a small overlap with Google >\vdash and leads besides that to lots of
completely different websites.

Google >\models yields of course countless hits in the fashion world.


BTW, even philosophers need in their own opinions formal systems to keep their trains of
thoughts at bay. The more complex the discourse, the more symbols are needed.


Cheers: Johan E. Mebius

[Aatu Koskensilta]

Post by JEMebius
BTW, even philosophers need in their own opinions formal systems to
keep their trains of thoughts at bay. The more complex the discourse,
the more symbols are needed.

Quite the opposite! When dealing with complex issues notational burden
is to be minimised. It is also worth noting that most uses of "formal
systems" and logical notation in philosophy amount to nothing but
mumbo-jumbo.

[j***@diegidio.name]

Post by Aatu Koskensilta

Post by JEMebius
BTW, even philosophers need in their own opinions formal systems to
keep their trains of thoughts at bay. The more complex the discourse,
the more symbols are needed.

Agreed.

Post by Aatu Koskensilta
Quite the opposite! When dealing with complex issues notational burden
is to be minimised.

Agreed.

Post by Aatu Koskensilta
It is also worth noting that most uses of "formal
systems" and logical notation in philosophy amount to nothing but
mumbo-jumbo.

For what it's worth, I disagree with both! ;)

I mean: the (serious) philosophical discourse is itself the apex of
the cathegorical. Formalization here is a matter of fact, despite the
mumbo-jumbo picasso notations.

(My 2c.)

-LV