Recourse to arithmetic

Write a one page paper (double spaced) describing and discussing the following ethical concepts found in chapter 1; logical, factual and normative. You may use definitions or scenarios in your writing. The goal of this paper is to gain a level of understanding of all three (logical, factual and normative).

Textbook:

1.
Logical,  or  formal,  statements
are  definitions  or  statements  derivable  from
definitions, including the entirety of mathematical discourse (e.g., “2
+
2
=
4,”
or “A square has four equal sides”). Such statements can be
verified by a for
–
mal  procedure
(“recourse  to  arithmetic”)  derived  from  the  same  definitions
that control the rest of the terms of the field in question (i.e., the same axioms
define “2,” “4,” and the procedure of “addition”; the four equal sides and right
angles define the “square”). True formal statements are
analytic
:
they are true
logically,  necessarily,  or  by  the  definitions  of  the  terms
.  False  statements  in
this category are
self–contradictory
. (If you say, “2
+
2
=
5,” or start talking
about  “round  squares,”  you  contradict  yourself,  for  you  assert  that  which  can-
not  possibly  be  so—you  conjoin  ideas  that  are  incompatible).  A  logically  true
or  logically  valid  statement  can  never  be  false,  or  disproved  by  any  discovery
of facts; it will never be the case that some particular pairs of 2 do not add up
to 4, or some particular squares turn out to be circular—and if you think you’ve
found  such  a  case,  you’re  wrong!  “2
+
2
=
4”  is  true,  and  squares  are  equi-
lateral  rectangles,  as  philosophers  like  to  say,
in  all  possible  worlds
.  For  this
reason we say that these statements are “
true a priori
”: we can know them to
be correct prior to any examination of the facts of the world, without having to
count up lots of pairs of pairs, just to make sure that 2
+
2 really equals 4.
2.
Factual, or empirical, statements
are assertions about the world out there, the
physical  environment  of  our  existence,  including  the  entirety  of  scientific  dis-
course, from theoretical physics to sociology. Such statements are
verifiable by
controlled  observation
(“recourse  to  measurement,”  “recourse  to  weighing”)
of  that  world,  by  experiment  or  just  by  careful  looking,  listening,  touching,
smelling, or tasting. This is the world of our senses, the world of space, objects,
time  and  causation.  These  empirical  statements  are  called
synthetic,
for  they
“put  together”  in  a  new  combination  two  ideas  that  do  not  initially  include  or
entail  each  other.  As  a  result  they  cannot  be  known  a  priori,  but  can  be  deter
–
mined only
a posteriori, that is, after investigation of the world
. When they
are true, they are
true only contingently, or dependently, as opposed to nec-
essarily;
their  truth  is  contingent  upon,  or  depends  on,  the  situation  in  which
they  are  uttered.  (As  I  write  this,  the  statement  “it  is  raining  out”  is  true,  and
has been all day. The weatherman tells me that tomorrow that statement will be
false.  The  statement  “2  + 2  =4,”  like  the  rectangularity  of  squares,  does  not flick in and out of truth like that).
3.
Normative  statements  are  assertions  about  what  is  right,  what  is  good,  or
what  should  be  done.We  know  these  statements  as  value  judgments,  pre-
scriptions  and  proscriptions,  commands  and  exhortations  to  do  or  forbear.
There is no easy way of assigning truth value to these statements. The cri-
teria  of  “truth”  that  apply  to  formal  and  factual  statements  do  not  apply

5 to  normative  statements. This  is  why,  when  we  disagree  about  them,  we
become “hostile,” and “lose our temper” at each other; there is no easy way to
resolve the dispute. We can certainly say of such judgments (formally) that they
conform  or  fail  to  conform  with  other  moral  judgments,  or  with  more  general
and  widely  accepted  moral  principles.  We  can  also  say  (empirically)  that  they
receive  or  fail  to  receive  our  assent  as  a  society,  as  compatible  or  incompat-
ible  with  our  basic  intuitions  of  what  is  just  or  right  (as  determined  by  a  poll
or survey). We may also say that a judgment succeeds or fails as a policy rec-
ommendation on some accepted pattern of moral reasoning, like adducing con-
sequences  of  that  judgment  and  estimating  how  human  wants  will  be  affected
should it become law (see the section on Moral Reasoning, below). But the cer
–
tainties of math and science are forever beyond the grasp of any normative sys-
tem, which is, possibly, as it should be.