[lit-ideas] Re: The Immanuel

 
 
In a message dated 9/28/2004 11:01:21 AM Eastern Standard Time,  
erin.holder@xxxxxxxxxxx writes:
I really  thought there were
1) Maxims
2) Hypothetical imperatives
3)  Categorical imperatives
Maxims, I thought, were practical precepts that  assume purposes or
particular ends.  Imperatives, I thought were  practical laws and that
practical laws do _not_ assume purposes or  particular ends, that they are
followed out of adherence to the law in and  of itself.  I thought that this
is how maxims and imperatives  differ.  Kant says it himself in the Remark on
Definition I (at 5:20  in my books) - "Thus maxims are indeed principles but
_not  imperatives_".  The difference I thought then between maxims  and
hypothetical imperatives was this:
A maxim is merely a subjective  desire dependent on sensibility - it can be
either physical or intellectual  (I want pizza or I want truth).  A
hypothetical imperative is _not_ a  maxim insofar as it is not just a
particular desire.  Yes, it is   a desire, and it is subjective, but, unlike
in a maxim, there is a  subjectively conditioned _necessity_ (you, as a
general rule, should work  in your youth so as not to want in old age),
albeit a necessity that cannot  be "presupposed in the same degree in all
subjects"  (5:21).


-----

 
Okay. If you get a chance, you could consult Grice's second book, _The  
Conception of Value_. In the chapter 2 he very much focuses on the logical form 
 of 
a maxim _qua_ imperative. Examples discussed by Grice:
 
If let the cat be taken to the vet, then let it be put in a cage.
If let the cat be taken to the vet and there is no cage available, then let  
Martha put it on her lap.
If the cat is sick, let it be taken to the vet.
Let the cat go to the vet, so let it be put in a cage.
Let the cat go to the vet; there isn't a cage, so let Martha put the cat on  
her lap. 
You should give up popcorn.
To get slim, you should give up popcorn.
If you want to get slim, you should give up popcorn.
 
---- Grice gets more formal in his _third_ book, where he proposes a  
derivation of Kant's ideas: Ceteris paribus, for any creature x (for any A, B), 
 if x 
wills A and judges that if A, then A as a result of B, then x wills b. x  
wills that (for any A, B) if x wills A and judges that if A, A as a result of 
B,  
then x is to will that A. Etc., etc. I provide some further quotes below.

Cheers,
 
JL
 
-----
 
Grice writes: "Today's Special (2. Cats and Hypes) calls  (even clamours) for
interpretation" (Aspects of Value p. 49). 
 
 
In _The Conception of Value_ (2nd lecture) Grice  explores at some length 
_four_ alternative interpretations of the hypohtetical  imperative. 
 
The first is a Formal Interpreation: 
 
"A blind logical nose might lead us (or be led) to the  assumption of a link
between hypothetical imperatives and hypothetical  statements
(propositions). Such a link no doubt exists, but the most obvious  version
of it is plainly inadequate. At least one other philosopher besides  myself
hs noticed that"

(1) If she molests the children, have her  arrested!

"is unlike to express a hypothetical imperative; and that even  if one
restricts oneself to caes in which the antecedent clause specifies a  _will_
we find pairs of examples like":

(2) If you will to go to  Chicago, travel by AA via Cleveland!
(3) If you will to go to Philadelphia,  see a psychiatrist!

"where it is plain that one is, and the other is not,  the expression of a
hypothetical imperative (I won't tell you which). A less  easily eliminable
suggestion, yet one which would still interpret the notion  of a
'hypothetical imperative' in terms of that particular logical form to  which
the names 'hypothetical' and 'conditional' attach, would be the  following.
Let us assume that it is established, or conceded, as legitimate  to
formulate conditionals in which not only the consequents (_apodoses_)  are
couched in some mode other than the indiative, as in conditional  commands:

(4) If you see the whites of their eyes, shoot  (fire)!

but also the antecedents (_protases_) or some part (clause) of  them; in
which case all of the following might be admissible  conditionals:

Judicatival Antecedent:

(5) If the cat is sick, take it to the  vet.

Mixed (Judicatival-cum-Volitival  Antecedent)

(6) If you are to take the cat to the vet & there's  no cage available,
put it on Martha's  lap!

Volitival Antecedent:

(7) If you are to take the cat to the vet, put it in a  cage!

"If this suggestion seems rebarbative, think of these quaint  conditionals
(when they are quaint) as conditionalised versions of  _arguments_, such as:

Volitival-cum-Judicatival Premises:
(8) i. Take  the cat to the vet!
ii. There isn't a  cage.
________________________________
iii. Put the cat on Martha's  lap!
Volitival Premise:
(23) i. Take the cat to the  vet!
_________________________________
ii. Put it in a cage!

"and  then maybe the discomfort will be reduced".

Grice considers a second  Formal Interpretation: "Among conditionals with an
imperatival or volitival  consequent some will have, then, 'mixed'
antecedents (partly judicative,  partly volitival) and some will have purely
_judicatival_ antecedents (like  'If the cat is sick, take him to the vet!).
I might now give a provisional  definition of the terms categorical and
hypothetical imperative. A  hypothetical imperative is _either_ a
conditional the consequent of which is  imperatival and the antecedent of
which is volitival or mixed (partly  judicatival, partly volitival) _or_ it
is an _elliptical_ version of such an  imperative. A categorical imperative
is an imperative which is either _not_  conditional in form or else, if it
is conditional, has a purely judicatival  antecedent." Grice makes three
'quick comments' on this second  interpretation:
(i) REAL IMPERATIVES: The structures which are being offered  as a way
of interpreting hypothetical and categorical imperatives do not, as  they
stand, offer any room for the appearance of practical modalities  like
'ought' and 'should' which are so prominently visible in the  standard
examples of those kinds of imperatives. Grice writes: "the  imperatives
suggested by me are _really_ imperatives": they conclude "Do  such-&-such!"
not 'You/one ought to do such and such'. "But maybe my  suggestion could be
modified to meet the demand for the appearance or  occurrence of 'ought'
(etc) if such occurrence is needed.
(ii) "It would  remain to be decided how close the preferred reading of
my 'deviant'  conditional imperatives would be to the accepted
interpretation of standard  hypothetical imperatives. But even if there were
some divergence, that might  be acceptable if the 'new' interpretation
turned out to embody a more preicse  notion than the standard conception.
(iii) NEUSTICAL vs TROPICAL ANTECEDENTS.  "There are, I think, serious
doubts of the admissibility of conditionals with  _non-judicatival_
antecedents, which will be to my mind connected with the  very difficult
question whether the Judicative and the Volitival Mode are  co-ordinate or
whether the Judicatival Mode is in some crucial sense _prior_  to the
Volitival. I do not know the answer to this question."

A third  formal interpretation "links the categorical-hypothetical
distinction to the  absolute-relative value distinction. Hypothetical
imperatives would be  _end-relative_ and might be analogous to
evidence-relative probabilities.  Categorical imperatives would not be
end-relative.

Finally, a fourth  Interpretation is not formal, but _material_: "This is
close to part of what  Kant says on the topic." It is a distinction between
an imperative being  _escapable_ (hypothetical), through the absence of a
particular _will_ and  its not being escapable (categorical). If we
understand the idea of  escabability sufficiently widely, the following
imperatives are all  escapable, even though their logical form is not in
every case the  same".

(24) Give up popcorn!
(25) To get slim, give up  popcorn!
(26) If you will to get slim, give up popcorn!

"Suppose I  have no will to get slim. One might say that the first
imperative is  'escaped', provided giving up popcorn has nothing else to
recommend it, by  _falsifying_ 'You should give up popcorn'. The second and
the third  imperatives would not, perhaps, involve _falsification_ but they
would, in  the circumstances, be _inapplicable_ to me -- and
inapplicability, too,  counts, as escape. Categorical imperatives however,
are in no way  escapable".

The Dynamics of Imperatives in Discourse.
Grice then gives  three examples which I've discussed in the thread on
_Aspects of Reason_,  which concern _arguments_: This we may see as an
elucidation to grasp the  logical form of an hypothetical imperative in its
dynamics in argumentation.  Grice writes: "We should, I suggest, consider
not merely imperatives of each  sort, together with the range of possible
characterisations, but also the  possible forms of _argument_ into which
_particular_ hypothetical imperatives  might enter". His examples being:

(27) i. Defend the Philosophy  Department!
ii. If you are to defend the philosophy department,
learn to  use bows and  arrows!
______________________________________________________
iii. Learn  to use bows and arrows!

Comments: Grice says he's "using the dichotomy of  original-derived value.
Re i, it is not specified whether the will is  original or derived. ii
specifies 'conducive to' (means), iii. would involve  a 'derived' will,
provided ii. is _true_.

(28) i. Fight for your  country!
ii. If you're to fight for your country, join up (one of the  services)!
________________________________________
iii. Join  up!

Comments: i and iii do not specify the _protasis_. If iii did, it  would
repeat premise ii.

(29) i. Increase your holdings in oil  shares!
ii. If you visit your father, he'll give you some oil  shares.
______________________________________________________________
iii.  Visit your father!

Comments: "this argument (purportedly) transmits  value".

Let us explore these characterisations by Grice with the aid of  Hare's
distinctions. Holdroft has Hare saying that, in a hypothetical  imperative,
"the protasis contains a neustic/tropic" (_Language of Morals_,  p.37).
Holdcroft makes a distinction between 'hypothetical imperative' and a  term
used by Grice in his first interpretation of the hypothetical  imperative,
that of 'conditional command' ('If you see the whites of their  eyes,
shoot!)): Holdcroft writes: "A hypothetical imperative can be  distinguished
from a _conditional_ imperative:

(30) If you want to  make bread, use yeast!
(31) If you see anything suspicious, telephone the  police!

"by the fact that _modus ponens_ is not valid for it." Holdcroft  writes
(p.93). "I use 'conditional imperative' for an imperative which  is
_grammatically_ conditional, and reserve 'conditional command' for  a
command which is conditional on the satisfaction of the antecedent".  Thus,
on Holdcroft's view, treating the major premiss of the following  argument
as a hypothetical imperative, turns the argument  invalid':

Major Premise as Hypothetical Imperative
(32) i. Major  Premise:
If you will to make someone mad, give him drug D!
ii. Minor  Premise:
You will to make Peter  mad.
__________________________________________________
Give Peter drug  D!

Holdcroft comments: "The hypothetical imperative tells one only  what
_means_ to adopt to achieve a given _end_ in a way which does  not
necessarily _endorse_ the adoption of that end, and hence of the means  to
it. Thus someone might say,

(33) If you will to make someone mad,  give him drug D!
But, of course, even if you will to do that,
you must  _not_ try to do so.

On the other hand, Holdcroft says the following is  "arguably valid" because
the major premise is a 'conditional' imperative and  not a mere hypothetical
one:

(34) Major Premise as Conditional  Imperative:
i. Major Premise:
I you will to make someone mad, give him  drug D!
ii. Minor Premise:
Make Peter  mad!
__________________________
iii. Give Peter drug D!

Holdcroft  explains this in terms of the presence of the neustic in the
antecedent of  the imperative working as the major premise: "The supposition
that the  antecedent of a hypothetical imperative contains a neustic, as
Hare proposes,  neatly explains why the argument with the major premise as a
hypothetical  imperative is not valid, but the argument with the major
premise as a  conditional imperative is, as well as helping to differentiate
a hypothetical  imperative from a _conditional_ one. For, if the
_antecedent_ of the major  premise in the hypothetical imperative is
volitival, the mere fact that you  will to make Peter mad does not license
the inference of the imperative to  give him the drug; but this _can_ be
inferred from the major premise of the  hypothetical imperative _together
with an imperative -- the minor premise in  the conditional imperative -- to
make Peter mad." In other words, whether  "the subordinate clause contains a
neustic" thus does have have a consequence  as to "the validity of
inferences" into which the complex sentence  enters".

The Principle of Mode Constancy in Imperative and Indicative  Inference
(Clarke). Holdcroft then tries to elucidate Hare's ideas on the  logical
form of the hypothetical imperative proper.
Holdcroft writes:  "Hare's suggestion is, admittedly, rather tentative. But
it might be argued,  in the spirit of it, that a hypothetical imperative is
of the  form

(35) i. !p -> !q
ii. |-p
______________
iii.  !q

But this violates a principle of MODE CONSTANCY (see Clarke): a  phrastic
must remain _in the same mode_ (within the scope of the same  _tropic_)
throughout an argument. A conditional imperative does not violate  the
principle of Modal Constancy, since it is of the form

(36) i. p  -> !q
ii. !p
_______________
iii. !q

Holdcroft has a caveat  here: "The question of the logical form of the
hypothetical imperative is too  obscure to base much on arguments concerning
it". Holdcroft mentions an  alternative to Hare's account of the validity of
an argument featuring a  conditional imperative. This is to treat the major
premise of a conditional  imperative, "as some have urged it should be" as
an _indicative_ tantamount  to "In order to make someone mad, you have to
give him drug D". Then someone  who _asserts_ the major premise of a
conditional imperative and _commands_  the second premise is in consistency
committed to commanding the conclusion".  Holdcroft concludes that "if"
"does not always connect phrastic with phrastic  but sometimes connects two
expressions consisting of a phrastic and a tropic"  (p.87). Holdcroft
further considers:

(37) If you walk past the post  office, post the letter!

Holdcroft writes: The antecedent of this  imperative states, it seems, the
_CONDITION_ under which the imperative  expressed becomes operative, and so
can _not_ be construed imperatively,  since an imperative cannot itself
state a condition. Hence, the antecedent  ought not be within the scope of
the imperative modal operator "!", and  whatever we take to represent the
form of the utterance above we must not  take "!(p -> q)"
to do so." One way out: "On certain interpretation of the  Isomorphism
Thesis between Indicative and Imperative Inference the utterance  has to be
construed as an imperative (in the generic sense) to make the  indicative
conditional "If you will walk past the post office, you will post  the
letter" _true_.

Leaving aside issues of the implicature of "if",  Holdcroft writes: "That
the utterance can _not_ be so construed seems to be  shown by the fact that
the imperative to make the associated indicative  conditional true is
conformed with by one who does not walk past the post  office. But it seems
strange at best to say that the utterance is conformed  with in the same
circumstances." (I think this 'strangeness' is aptly  explained away by Hare
in terms of Gricean implicature). Interestingly,  Holdcroft quotes Dummett
(1958) as endorsing this idea that a conditional  imperative be construed as
an imperative to make an indicative material  conditional true (also Dummett
1973:339) (Dummett urges to divide conditional  imperatives into those whose
antecedent is "within the power of the  addressee" --- like the utterance in
question -- and those in which it is  not). Consider:

(38) If you go out, wear your coat!

Holdcroft is  not so much concerned with how to _escape_ this, as Grice was,
but how to  _conform_ it. He writes: "A child may choose not to go out in
order to comply  with the imperative". For an imperative whose antecedent is
_not_ "within the  power of the addressee", e.g.

(39) If anyone tries to escape, shoot  him!

it is, Holdcroft thinks, "indifferent whether we treat it as a  conditional
imperative or not", so why bother. There's a small caveat by  Holdcroft
here: If no one tries to escape, the imperative is _not violated_.  He asks:
"might there not be an important practical difference bewteen saying  that
an imperative has not been violated and that it has been complied  with?"
(Holdcroft thinks Dummett ignores this distinction). Honestly, I  don't
think there is much of a practical difference there (Am I an  intuitionist?).
Holdcroft writes: "Suppose that you are a frontier guard and  the antecedent
of (65) has remained unfulfilled. Then, whether we say that  you complied
with it, or simply did not _violate_ it will make a great deal  of
difference if you appear before a war crimes tribunal". But then I  don't
see why I would be in the war crimes tribunal in the first  place...
Holdcroft here quotes from Dummett.

Holdcroft quotes Dummett:  "The fact that in the case of an imperative
expressed by a conditional  imperative in which the antecedent is not within
the agent's power, we should  not say that the agent had obeyed just on the
ground that the antecedent is  false, is no ground for construing an
imperative as expressing a conditional  command: for there is no question of
fixing what shall constitute obedience  independently of the determination
of what shall constitute disobedience"  (Dummett 1973:343). Personally, I
think this complicates the  issues.

Holdcroft cites Geach, who with Grice and Hare, defends  imperative
inference against Kenny and B. A. O. Williams. Holdcroft writes:  "What is
questioned by the sceptics about imperative inference is whether if  each
one of a set of imperatives is used with the force of a command, one  can
infer a _further_ imperative with that force from them". Cfr. Aristotle  on
the practical syllogism. In some respects, Holdcroft is more  conservative
than Hare. Holdcroft considers:

(40) i. If you stand by  Jane, don't look at her!
ii. You stand by  Jane
__________________________________________
iii. Don't look at  her!

This is valid. However, the following, obtained by anti-logism, is  _not_:

(41) i. If you stand by Jane, don't look at her!
ii. Look at  her!
_____________________________________________
iii. You don't stand by  Jane.

"Honestly, it seems more reasonable", Holdcroft says, to deny  Hare's thesis
and maintain that Anti-logism is valid in imperative inference  than it is
to hold onto Hare's thesis and deny that antilogism is valid in  the case in
question."

The ordering of tropics and  neustics.
Consider Holdcroft's example:

(42) i. Varnish every piece of  furniture you make!
ii. You are going to make a  table.
_______________________________________________
iii. Varnish  it!

This is, Holdcroft writes, "_prima facie_ valid". The following,  however,
switching the order of the neustics in the premisses is  not:

(43) i. You are going to varnish every piece
of furniture that  you make.
ii. Make a  table!
___________________________________________
iii. Varnish  it!

Conversational Implicature at the Rescue.
Problems with "or":  Holdcroft then considers A. Ross's famous example

(44) i. Post the  letter!
_______________________________
ii. Post the letter or burn  it!

as 'invalid' (Ross 1944:38 -- endorsed by B. Williams). Holdcroft  starts by
quoting H. Kamp: "To permit to do p or q is to permit to do p and  to permit
to do q". (Similarly, to give permission to do something is to lift  a
prohibition against doing it). "Admittedly, Williams does not need this  so
I'm stating his claim more strongly than he does". Holdcrot reviews  Hare's
way out (defense of the validity of the utterance above in terms of  Gricean
implicature. Hare claims that whilst the premise's  "permissive
presupposition" (to use the term introduced by Williams) is  entailed by it,
the conclusion's is only _conversationally implicated_.  Typically for an
Isomorphist, Hare says this is something shared by  indicative inferences.
Holdcroft quotes Hare's passage in 'Some alleged  differences between
imperatives and indicatives:

"If, being  absent-minded, I ask my wife, 'what have I done with the
letter?' and she  replies that I have
posted it or burnt it, she conversationally implicates  that she is not in a
position to say which I have done [...] She also  conversationally
implicates that I may not have post it, so long as I have  burnt it."

Similarly, he maintains the future tense indicative, "You are  going to post
the letter" has the conversational implicature "You may be not  going to
post the letter so long as you are going to burn it". But this  surely does
not validate "p, ergo p or q"". As Holdcroft notes, one _can_,  similarly,
say: "Eclipse will win. He may not, of course, if it rains. And I  _know_ it
will not rain".

Problems with "and": Holdcroft considers  Hare's example in 'Imperative
Sentences':

(45) i. Put on your  parachute & jump out!
____________________________________
ii. Jump  out!

Holdcroft comments: "Someone who _only_ jumps out of an aeroplane  does not
fulfil 'Put on your parachute & jump out!' He has done only what  is
necessary, but not sufficient to fulfil it. Imperatives do not differ  from
indicatives in this respect, except, Hare notes "that fulfilment takes  the
place of belief (which is the form of acceptance apprpriate to  statements"
(cfr. _Language of Morals_, p. 20). "Someone who is  told
"Jones put on his parachute & jumped out" is entitled to believe  that Jones
jumped out. But if he believes that this is _all_ Jones did he is  in error"
(Holdcroft here refers to R. Edgley's treatment of this).  Holdcroft
discussses Hare's test of cancellability in the case of the  transport
officer who says:

(46) Go via Coldstream or  Berwick!

-- analysed in first post of this thread. Holdcroft comments:  "It seems the
transport officer's way of expressing himself is extremely  _eccentric_. If
he's not sure if a storm may block one of the routes, what he  should say is

(47) _Prepare_ to go via Coldstream or Berwick!

As  for Hare's application of Grice's cancellability thesis here, to yield,
in  the circumstances:

(48) Go either via Coldstream or Berwick! But you may  not go via Coldstream
if you do not go via Berwick, & you may not go via  Berwick if you do not go
via Coldstream.

Such qualifications seem to  empty the imperative of all content and is thus
"reminiscent of Henry Ford's  utterance that people can choose what colour
car they like provided it is  black". But then I don't think Ford was being
illogical, was  he.




Grice writes considers Kant's example in GRUNDLEGUNG  (the only fully 
explicitly 'stated' technical imperative, Grice writes, to be  found in Kant's 
writings):

(1) It is _necessary_, given that one is to  bisect a line on an unerring 
principle that I'm to draw from its extremities 2  intersecting arcs.

Obviously some notion of hypothesis is understood  here. Grice writes:

"Though Kant does not express himself very clearly  [for a similar claim:
i.e. an Oxonian complaining of Kant's obscurity -- see  Hare's remarks in
the interview with B. Magee] I am certain
that his claim  is that this imperative [(1) above] is validated in virtue
of the fact that  it is, ANALYTICALLY, a consequence of an INDICATIVE
statement which is TRUE,  and, viz. the statement vouched for by geometry,
that:

(2) If one  bisects a line on an unerring principle,
one does so _ONLY_ as a result of  having
drawn from its extremities two intersecting arcs.

Grice's own  example:

(3) To preserve a youthful complexion, one should
smear one's  face with peanut butter before
retiring at night.

Grice distinguishes  between "should" -- unqualified acceptability --,
"ought" -- ceteris paribus  acceptability -- and "must" -- unyielding
subscription, as R. M. Hare would  have it. 
 
Curiously, it's only "must" which has
an analogue  ("may") which allows a Deontic "Square of Opposition".

Grice smartly  notes that the person who will accept (3) should better 'buy'
it  provided it's based on something _true_ (not just 'nicey'):

"There is  some initial plausibility in the idea that the _practical_
acceptability  statement in (3) is satisfactory

iff the following ALETHIC [indicative.  JLS] acceptability statement is
acceptable:

(4) It should be, given  that

i. it is the case that one smears one's skin
with peanut butter  before retiring.

and

ii. it is the case that one has a  relatively
insensitive skin,

it is the case that one preserves a  youthful complexion.

(Cf. D. Potter's _Pennies from Heaven_.
Episode  between Gemma Craven and Nigel Havers. London: Faber).

Grice  reconstructs, on Kant's behalf, the argument to prove the
acceptability in  the geometry example as resting on the 'analyticity' of

(5) The agent who  wills the end wills the means.

Grice writes:

"It seems to be to be  very meritorious on Kant's part, _first_ that he saw
a need to justify  hypohtetical imperatives of this [problematic] sort [what
elsewhere, Grice  says, Kant refers to as 'technical imperatives' JLS] which
it is

ONLY  TO EASY TO TAKE FOR GRANTED

and _second_ that he invoked the principle  that (5)".

Grice proposes to remedy Kant's obscurity of style (and sloppy  thinking and
incomplete premisses) in the Stanford lectures.

Grice's  chain of reasoning is much better than Kant's (as anyone who is not
familiar  with Kant will agree) and involves nice seven steps: Here they go.
Comments  (easy ones) welcomed.

Step I:
It is a fundamental law of Human  Psychology that, ceteris paribus, for any
rational creature -- call it R -,  for any P and Q,
if R wills that P &
R judges that if P, P is a result  of Q,
R wills Q.

Step II. Placing this law within the scope of a  "willing" operator:
R wills for any P & Q,
if R wills that  P
&
R judges that if P, P is a result of Q,
R wills Q.

Step  III. Turning "will" to "should" [this is done via 'will' = 'shall'.
And  'shall'
= 'should']
If rational, R will have to block unsatisfactory  (literally)
attitudes:
R should (qua rational) judge
for any P &  Q,
if it's satisfactory to will that P
&
it's satisfactory to judge  that if P, P as a result of Q,
Ergo it's sastisfactory to will that  Q.

Step IV. Expliciting mode specifications:
A 'should' statement is  transformed into an utterance in the imperative
mode (symbolised !p).  Utterances in the indicative mode are symbolised by
Grice, a la Frege, as  "|-p".
R should (qua rational) judge for any P & Q,
if it's  satisfactory that !P
&
that if it |-P, |-P only as a result of  Q,
it's satisfactory that !Q.

Step V. Via (p & q -> r) -> (p  -> (q -> r)).
R should (qua rational) judge
for any P & Q,
if  it's satisfactory that if |-P, |-P only because Q,
it's satisfactory  that,
if let it be that P, let it be that Q.

Step VI.
R should (qua  rational) judge
for any P & Q,
if P, P only because p _yields_
if  let it be that P, let it be that Q.

Step VII.
For any P & Q if P,  P only because Q _yields_
if let it be that P, let it be that  Q.







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