An upside-down iota logic symbol
Errol Martin
Whitehead and Russell. It is, effectively, an upside-down
iota, just as the exists and forall operators are upside-
down E and A. Examples are in Whitehead and Russell's Principia
Mathematica, e.g. there are several uses at the bottom of
p.66 of Vol. I of Principia Mathematica (same pagination as
the paperback "to *56").
What do I have to do to get this symbol? If it is part of a
regular font set then I will be embarassed at having asked the
net, but pleased to get an answer. If I need to use Metafont
to create such a symbol, has anyone already done this?
Thank you,
Errol Martin
e...@shubshub.canberra.edu.au
Faculty of Information Sciences and Engineeering
PO Box 1 Belconnen ACT 2602 Australia
Ph: +61 6 201 2153 Fax: +61 6 201 5041
Dag Asheim
>Whitehead and Russell. It is, effectively, an upside-down
>iota, just as the exists and forall operators are upside-
>down E and A.
>What do I have to do to get this symbol? If it is part of a
>regular font set then I will be embarassed at having asked the
>net, but pleased to get an answer.
I have tried to look for one, but with no luck. Please inform me
if it is.
>If I need to use Metafont
>to create such a symbol, has anyone already done this?
Yes, my father needed it to his Ph.d. theses, so I lent him the
Metafont book, and after a while he came up with these:
mode_setup;
font_size 10pt#;
hor#:=5/2pt#; ver#:=9/2pt#; u#:=1/2pt#;
diam#:=1/2pt#;
define_pixels(hor,ver,u);
define_blacker_pixels(diam);
beginchar("I",hor#,ver#,0);
pickup pencircle scaled diam;
lft x1=0; rt x3=w-2u;rt x4=x3; x2=2u;
y1=y3=h-2u; top y2=h; bot y4=0;
draw z1..z2..z3---z4;
labels(1,2,3,4);
endchar;
mode_setup;
font_size 12pt#;
hor#:=30/9pt#; ver#:=5pt#; u#:=5/9pt#;
diam#:=5/9pt#;
define_pixels(hor,ver,u);
define_blacker_pixels(diam);
beginchar("I",hor#,ver#,0);
pickup pencircle scaled diam;
lft x1=0; rt x3=w-2u; rt x4=x3; x2=2u;
y1=y3=h-2u; top y2=h; bot y4=0;
draw z1..z2..z3---z4;
labels(1,2,3,4);
endchar;
It is two versions because the 12 point one didn't look too good when
just downscaled to 10 point.
Good luck!
Dag Asheim da...@ifi.uio.no
Department of Informatics
University of Oslo, Norway
Bob Riemenschneider
> >I would like to use the 'definite description' operator of
> >Whitehead and Russell. It is, effectively, an upside-down
> >iota, just as the exists and forall operators are upside-
> >down E and A.
> > ...
>
> my father needed it to his Ph.d. theses, so I lent him the
> Metafont book, and after a while he came up with these: ...
I've been meaning to take a shot at this myself for awhile, and this
posting inspired me to do it. While Mr. Asheim Sr.'s definitions have
some undeniable virtues (e.g., use of a round pen results in greater
consistency with the rest of the logic symbols), they also have some
problems (e.g., the slant looks too small to me).
Here's an alternative which is precisely the result of inverting the
standard iota in cmmi. Enjoy!
-- rar
======================================8x--------------------------------------
%% Filename: iiota10.mf
%% Author: R. A. Riemenschneider (r...@csl.sri.com)
%% Version: 1.0b (7 August 1992)
%% This is a METAFONT file that can be used to generate a font consisting
%% solely of an inverted iota.
%% It was constructed by combining Knuth's cmmi10.mf with the relevant
%% parts of mathit.mf and greekl.mf, then changing the definition of iota
%% to include a rotation. (I am a complete METAFONT novice, and have no idea
%% whether this is the "right" way to do it or not, but it seems to work okay.)
%% "%%" means the comment is mine, "%" means it's Knuth's.
%% For other sizes, just replace the line cribbed from cmmi10.mf by the
%% corresponding lines from the appropriate cmmi*.mf. For bold,
%% do the same using cmmib*.mf.
%% The following is from cmmi10.mf
if unknown cmbase: input cmbase fi
font_identifier:="IIOTA"; %% Was: "CMMI"
font_size 10pt#;
u#:=20/36pt#; % unit width
width_adj#:=0pt#; % width adjustment for certain characters
serif_fit#:=0pt#; % extra sidebar near lowercase serifs
cap_serif_fit#:=5/36pt#; % extra sidebar near uppercase serifs
letter_fit#:=0pt#; % extra space added to all sidebars
body_height#:=270/36pt#; % height of tallest characters
asc_height#:=250/36pt#; % height of lowercase ascenders
cap_height#:=246/36pt#; % height of caps
fig_height#:=232/36pt#; % height of numerals
x_height#:=155/36pt#; % height of lowercase without ascenders
math_axis#:=90/36pt#; % axis of symmetry for math symbols
bar_height#:=87/36pt#; % height of crossbar in lowercase e
comma_depth#:=70/36pt#; % depth of comma below baseline
desc_depth#:=70/36pt#; % depth of lowercase descenders
crisp#:=8/36pt#; % diameter of serif corners
tiny#:=8/36pt#; % diameter of rounded corners
fine#:=7/36pt#; % diameter of sharply rounded corners
thin_join#:=7/36pt#; % width of extrafine details
hair#:=9/36pt#; % lowercase hairline breadth
stem#:=24/36pt#; % lowercase stem breadth
curve#:=29/36pt#; % lowercase curve breadth
ess#:=27/36pt#; % breadth in middle of lowercase s
flare#:=32/36pt#; % diameter of bulbs or breadth of terminals
dot_size#:=38/36pt#; % diameter of dots
cap_hair#:=11/36pt#; % uppercase hairline breadth
cap_stem#:=30/36pt#; % uppercase stem breadth
cap_curve#:=35/36pt#; % uppercase curve breadth
cap_ess#:=33/36pt#; % breadth in middle of uppercase s
rule_thickness#:=.4pt#; % thickness of lines in math symbols
dish#:=1/36pt#; % amount erased at top or bottom of serifs
bracket#:=20/36pt#; % vertical distance from serif base to tangent
jut#:=30/36pt#; % protrusion of lowercase serifs
cap_jut#:=37/36pt#; % protrusion of uppercase serifs
beak_jut#:=10/36pt#; % horizontal protrusion of beak serifs
beak#:=70/36pt#; % vertical protrusion of beak serifs
vair#:=8/36pt#; % vertical diameter of hairlines
notch_cut#:=10pt#; % maximum breadth above or below notches
bar#:=11/36pt#; % lowercase bar thickness
slab#:=11/36pt#; % serif and arm thickness
cap_bar#:=11/36pt#; % uppercase bar thickness
cap_band#:=11/36pt#; % uppercase thickness above/below lobes
cap_notch_cut#:=10pt#; % max breadth above/below uppercase notches
serif_drop#:=4/36pt#; % vertical drop of sloped serifs
stem_corr#:=1/36pt#; % for small refinements of stem breadth
vair_corr#:=1/36pt#; % for small refinements of hairline height
apex_corr#:=0pt#; % extra width at diagonal junctions
o#:=8/36pt#; % amount of overshoot for curves
apex_o#:=8/36pt#; % amount of overshoot for diagonal junctions
slant:=.25; % tilt ratio $(\Delta x/\Delta y)$
fudge:=1; % factor applied to weights of heavy characters
math_spread:=0; % extra openness of math symbols
superness:=1/sqrt2; % parameter for superellipses
superpull:=1/6; % extra openness inside bowls
beak_darkness:=11/30; % fraction of triangle inside beak serifs
ligs:=2; % level of ligatures to be included
square_dots:=false; % should dots be square?
hefty:=false; % should we try hard not to be overweight?
serifs:=true; % should serifs and bulbs be attached?
monospace:=false; % should all characters have the same width?
variant_g:=true; % should an italic-style g be used?
low_asterisk:=false; % should the asterisk be centered at the axis?
math_fitting:=true; % should math-mode spacing be used?
%% The following is from mathit.mf
font_coding_scheme:="TeX math italic";
mode_setup; font_setup;
%% The following is from greekl.mf
cmchar "Lowercase Greek iota";
beginchar(oct"023",5u#,x_height#,0);
currenttransform:=currenttransform rotatedaround ((.5w, .5h), 180); %% Added for inversion
italcorr 1/3x_height#*slant+.5hair#+.5u#;
adjust_fit(if monospace: u#,u# else: 0,0 fi); pickup fine.nib;
pos1(stem,0); lft x1l=hround(1.5u-.5stem); y1+.5stem=h+oo;
x2=x1-.25u; x4=w; hook_out(2,3,4)(skewed); % closing hook
filldraw circ_stroke z1e{down}...{-u,-x_height}z2e; % stem
math_fit(0,ic#); penlabels(1,2,3,4); endchar;
%% The following is from mathit.mf
bye.