The Grice Club


The Grice Club

The club for all those whose members have no (other) club.

Is Grice the greatest philosopher that ever lived?

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Wednesday, November 8, 2017

Norm for Implicature


Timothy Williamson and others have made a strong case for the claim that knowledge is the norm of assertion. 

Reasons to think that assertion has an epistemic norm also, interestingly, provide a reason to think that conversational implicature has a norm as well. 

This norm, it is argued, cannot be knowledge. 

In addition to highlighting an under-explored topic at the intersection of epistemology and linguistics, the discussion of conversational implicature puts dialectical pressure on the knowledge norm of assertion account. 

The fact that knowledge is not the norm of conversational implicature forces one either to claim that there is one epistemic norm for the conveying of information and that it is not knowledge, or else to embrace a heterogeneous picture of communicative norms generally that undercuts some of the grounds for thinking that the norm of assertion should be presumed to be a simple norm as Williamson argues.

Grice: principles and desiderata for implicature


Grice: norm for implicature


Grice on norms for implicature


Timothy Williamson and others have made a strong case for the claim that knowledge is the norm of assertion. Reasons to think that assertion has an epistemic norm also, interestingly, provide a reason to think that conversational implicature has a norm as well. This norm, it is argued, cannot be knowledge. In addition to highlighting an under-explored topic at the intersection of epistemology and linguistics, the discussion of conversational implicature puts dialectical pressure on the knowledge norm of assertion account. The fact that knowledge is not the norm of conversational implicature forces one either to claim that there is one epistemic norm for the conveying of information and that it is not knowledge, or else to embrace a heterogeneous picture of communicative norms generally that undercuts some of the grounds for thinking that the norm of assertion should be presumed to be a simple norm as Williamson argues.

Conative and Doxastic Norms for Implicature


Norm for Implicature


A psychological-attitude norm for implicature


An epistemic norm for implicature?


Wednesday, November 1, 2017

Grice's Friend, Kantotle


Judith Baker, as cited by Grice, provides a conceptual analysis of ‘friend’ from an Aristotelian (or Kantotelian) point of view. 

Is 'friend' a value-oriented concept? It obviously seems so!

Although Grice gives “He is a fine friend,” as said of a scoundrel, as his first example of ‘irony,’ it might be argued that ‘fine’ is not ‘good’. 

“Good” is more basic. 

Thus, to use another example, ‘sentence,’ is a value-oriented concept, so that ‘good sentence’ is well-formed sentence, making ‘good’ otiose.

But why did Aristotle think that one’s friend is one’s alter ego? 

Grice mentions Baker’s analysis, “Another Self: Aristotle on Friendship,” in Grice’s WoW – Way of Words.

As Grice notes, rather than ‘another self’ we should have ‘another me’, or ‘another I,’ strictly.

“At his point,” Grice notes, “I turn to [this] essay by Judith Baker, entitled, "Another Self": Aristotle on friendship. On the present occasion, my concern is focused on METHODOLOGICAL,” rather than substantive “questions; so I propose first to consider the ideas about METHODOLOGY, in particular Aristotle's methodology,” with a view to an analysis as to “whether these ideas by Aristotle suggest any additions to the subject matter of philosophical eschatology.” “Baker
suggests that Aristotle's philosophical method treats the existence of a common consensus of opinions with respect to a proposition as conferring at least provisional validity (validity ceteris paribus) upon the proposition in question. In general, no external justification of the acceptance of the objects of universal agreement is called for. This idea has not always been accepted by philosophers." "If my perception of Moore is correct, he would in Aristotle's view have been looking for an EXTERNAL justification for the acceptance of the deliverances of common sense where none is required. Though no EXTERNAL justification is
required for accepting the validity of propositions which are generally or
universally believed, the validity in question is only provisional. For a common consensus may be undermined in either of two ways. First, there may be a common consensus that proposition “p” is true, but there may be two mutually inconsistent propositions, (q1 and q2), where while there is a common consensus that q1 or q2, there is no common consensus concerning the truth of q1 or the truth of q2; there are, so to speak, two schools of thought, one favouring q1 and one favouring q2. Furthermore (we may suppose) the combination of q1 with p will yield r1, whereas the combination of q2 with p will yield r2; and r1 and r2 are mutually inconsistent. In such a situation, it becomes a question whether the acceptability of p is LEFT INTACT. If it is, a method will have to be devided for deciding between q1 and q2. Second, to cope with problems created by the appearance on the scene of conflicts or other stumbling blocks the theorist may be expected to systematise
the data which are vouched for by common consensus by himself devising general
propositions which are embedded in his theory. Such generalities will NOT be directly attested by the consensus, but their ACCEPTABILITY will depend on the ADEQUACY of the theory in which they appear to yield propositions which are directly matters of general agreement. When an impasse ("aporia") arises, the aim of the theorist will be to ELIMINATE the impasse with minimal disturbance to the material regarded as acceptable BEFORE the impasse, including the theoretical generalities of the theorist."

It is here that Grice makes use of Aristotle:

amicus = alter ego.

Or in Grice’s translation:

friend = another I.

Since Aristotle’s equivalence (“friend = another I”) HAS BEEN MET with criticism (Baker mentions David Sachs), Grice concludes that the reflections in which I have just been engaged, suggest to me TWO FURTHER items which might be added to a prospective subject matter of philosophical eschatology. One would be a classification of the various kinds of impasse or “aporia” by theorists who engaged in the Aristotelian undertaking of attempting to systematise mterial with which they are presented as LAY inquirers, together with a classification of the variety of responses which might be effective against such impasses. The other would be a thorough-going analysis of the boundary between legitimate and ILLEGITIMATE imputations to a theorist of the sin of 'having changed the subject.’ Beyond these additions I have at the moment only one further suggestion. Sometimes, the activities of the eschatologist might involve the suggestion of certain PRINCIPLES and some of the material embodied in those principles might contain the potentialty of independent life, a potentiality which it would be theoretically advantageous to explore. This further exploration might be regarded as being itself A PROPER OCCUPATION for the eschatologist. One example might be a further examination of the theoretical notion of an “alter ego.””

In fact, it is Cicero who translates Aristotle here (“állos egṓ,” “héteros egṓ,
 “heteros autos,” Nich. Eth. 9. 9.10
), as “alter ego” (Ad Atticum 3.15.4, Ad familiaris, 7.5.1). Grice’s “another I.” Cicero prefers to translate Aristotle’s “heteros autos” as “alter idem,” in the nominative (“De Amicitia.”). For the record, Zeno uses “allos ego” (as cited by Diogenes Laertius).

Aristotle does not strictly argue that one ought to have only ONE friend, but, as Richard Kraut notes, he does not argue, either, that “one is always too few.” Kraut continues to note that Aristotle notes that “the friendships commemorated in verse are those that exist between just two people” (Eth. Nich. 1171a15).

Aristotle: “[T]he famous examples [of friendships] of poetry [such as Achilles and Patroclus, Orestes and Pylades, Theseus and Pirithous] are pairs of friends.”

The passage is slightly tricky: “Friendships between comrades only include a few people, and the famous examples of poetry are pairs of friends.”

Therefore, it is not quite or exactly clear whether pairs like Achilles/Patroclus, Orestes/Pylades and Theseus/Pirithous] are quoted as examples of comradeship or friendship in general.

And stuff! 

Monday, October 23, 2017

Groupe de Recherche sur l’Inference et la Compréhension Élémentaire


The Split Implicature


Is there a way to provide a Griceian theory of the implicatures generated by a so-called ‘split infinitive’. We hope so.
We should start by conceptual analysis.
A split infinitive, so-called, also known as a “cleft” infinitive, is a syntactical construction in which an expression, or expressions, comes between the “to” and the bare infinitive.
A well-known example occurs in the opening sequence of “The Star Trek” (incidentally, Grice was a “Trekkie.”)
i.                   To boldy go where no man has gone before.
“Boldly” clearly splits the infinitive “to go”.
Sometimes more than one expression splits the infinitive, as in:
ii.                 The population is expected to more than double in the next years.
In the 19th century, some syntactical authorities around Oxford sought to introduce a prescriptive “rule” AGAINST the split infinitive. They disliked its implicatures.
The split infinitive is still today, and in Oxford, too, the subject of disagreement, though some usage guides have dropped any Griceian objection to it.
In the old language, which was almost like Latin, being Indo-European, the infinitive is a single expression ending in “-an” or “-n” (Compare the cognate forms in Dutch and German, ending in “-en” and “-n”.)
Now, in the old language, a gerund is formed using “to” followed by a verbal noun in the dative case, which ends in “-anne” or “-enne” (e.g. tō cumenne = "coming, to come").
At a later stage of the language, the bare infinitive and the gerund coalesced into the same form ending in “-(e)n” (e.g. comen "come"; to comen "to come").
The “to” infinitive was NEVER split in the old language.
The first “known” (to use a Popperian verb) example of a split infinitive in which a pronoun splits the infinitive, is in Layamon's novella “Brut”:
iii.              and he cleopede him to alle his wise cnihtes for to him reade.
iv.               And he called to him all his wise knights to him advise.
v.                 And he called to him all his wise knights for to him read.
This, Grice allows, may be a poetic inversion for the sake of the metre, and therefore says little about whether Layamon (or his mother, for that matter) would have felt the construction to be syntactically natural – or ‘ordinary language,’ as Grice would prefer.
However, no such reservation applies to the following prose example from Wycliffe, who splits infinitives like the plague:
vi.              For this was great unkindeness, to this manner treat their brother.
After its rise, the construction became, luckily, rare in the 15th and 16th centuries.
Shakespeare, for all that he wrote, split an infinitive only once (or perhaps twice – if you count the encore – the thing was set to music). But the uncontroversial example appears to be, even for Grice, again a syntactical inversion (or liberty) for the sake of, if not metre, rhyme:
vii.            root pity in thy heart that when it grows
thy pity may deserve to pitied be.
SpenserDrydenPope, and the King James Version of the Bible never split an infinitive, and split infinitives are very rare in the writing of Dr. Johnson
Donne uses them, granted, several times, and Pepys at least once.
No good reason for the disappearance of the split infinitive is known (by Popper or Grice). In particular, no prohibition (alla “Thou shalt not kill” = “Thou shalt try to not split an infinitive”) is recorded.  
Split infinitives, however, re-appeared in the 18th century and became more common in the 19th.
DefoeFranklinWordsworthLincolnEliotJames, and Cather are among the famous writers (to use Noel Coward’s phrase in “Let’s do it”) who use the split infinitive.
Examples in Burns’s poems attest its presence also in 18th-century Scots:
viii.         Who dared to nobly stem tyrannic pride. 
In colloquial speech, the split infinitive actually comes to enjoy widespread use. Today, according to the Heritage Book of Usage, “people split infinitives all the time without giving it a thought.”
The reference is obviously to Frege, “The Thought.”
In corpora of contemporary spoken language, actually, some expressions, notably “always” and “completely” appear more often in the split position than the unsplit.
Although it is difficult to say why the split infinitive developed, or why it revived so powerfully in modern times, a number of Popperian theories have been postulated – but they are pretty complex.
Let us revise some of what Grice might call Popperian theories for the explanation of the ‘split infinitive’ and the implicatures it may invite briefly.
Syntacticians suggest that the split infinitive appears because people frequently place expressions before finite verbs. 
Thus, Curme states:
“If an expression should immediately precede the finite verb, we feel that it should immediately precede also the infinitive.”
Thus, if one says:
ix.              She gradually will get rid of her stutter. 
x.                 She will gradually get rid of her stutter.
--both correct--one may, by analogy, wish to say:
xi.              She wants to gradually get rid of her stutter.
This is supported by the fact that a split infinitive is often used as what Grice calls an “echo”, as in the following exchange, in which the riposte parodies the slightly odd collocation in the original sentence:
xii.            A: I accidentally forgot to feed the tortoises!
B: Well, you shall have to try next time harder not to accidentally forget.
B’s utterance is an example of an expression being transferred into a split infinitive position from a parallel position in a correct, if odd, different construction.
Transformational grammarians attribute the split infinitive to a (wrong, Grice thinks) re-analysis of the role of “to.”
In the modern language, splitting involves an expression coming between the verb and the ‘to’.
Very frequently, this is an EMPHATIC expression, as in:
xiii.         I need you all to really pull your weight.
xiv.         I am going to totally pulverise him.
However, in modern colloquial lingo, almost any expression may be found in this syntactic position, especially when the expression and the verb form a close syntactic unit (really-pull, not-split).
Compound split infinitives, i.e., infinitives split by more than one expression, usually involve a pair of expressions:
xv.            I am determined to completely and utterly eradicate the disease.
xvi.         Grice is thought to almost never have made such a gesture before.
xvii.       This is a great opportunity to once again communicate our basic message.
Examples of non-adverbial elements participating in the split-infinitive construction luckily seem rarer in modern times than in the Dark Ages.
 “All” commonly appears in this position:
xviii.    It was their nature to all hurt one another.
and may even be combined with an adverb:
xix.         I need you all to really pull your weight.
However, an object pronoun, as in the Layamon example, would be unusual in the modern language, perhaps because this might cause the Griceian addressee to mis-understand the “to” as a preposition:
xx.            *And he called to him all his wise knights for to him read.
While, structurally, acceptable as poetic formulation, the utterance would result in what Grice calls a garden-path sentence  particularly evident if the indirect object is omitted:
xxi.         *And he called all his wise knights for to him read.
xxii.       And he called all his knights for to come to him (and read him)
xxiii.    And he called all his knights, so that they might read him.
Other parts of speech would be pretty unusual in this position (unless Grice is trying to build what he called a ‘big implicature.’)
However, in verse, poetic inversion for the sake of metre or of bringing a rhyme word to the end of a line often results in what Grice calls “abnormal syntax,” as with Shakespeare’s cited split infinitive (“to pitied be”), in fact an inverted passive construction in which the infinitive is split by a past participle.
Presumably, this would not have occurred in a love letter by the same author to Anne Hattaway.
It was not until the very end of the 19th-century Oxford that a ‘term of art’, “split infinitive” emerged as a matter of history to describe the construction.
The earliest use of the term of art, “split infinitive” dates from 1897, with te cognate “infinitive-splitting” and “infinitive-splitter” following in 1926 and 1927, respectively.
The now rare “cleft infinitive,” is, as it should, slightly older (Grice’s father used it thrice), attested from 1893.
The term “compound split infinitive” appears to be pretty recent (especially in The Telegraph).
This terminology implies conceptually analysing the full infinitive as a two-expression infinitive, which not all syntacticians accept (Quine doesn’t).
As one who used "infinitive" to mean the single-word verb, Otto Jesperson (his surname was Jespersen, but Grice prefers “Jesperson” – and I agree since “sen” means “son” in Jesperson’s native language) challenged the epithet:
"'To,’ Jesperson writes, “is no more an essential part of an infinitive than the definite article is an essential part of a nominative, and no one would think of calling 'the Oxonian philosopher' a split nominative."
However, (a) Otto Jesperson is no Oxonian philosopher, and (b) no alternative terminology has been proposed.
No other grammatical issue has so divided Oxford ordinary language philosophers since the split infinitive was declared to be a solecism in the 19th century: raise the subject of ordinary language in any Oxonian conversation today at any common room and it is sure to be mentioned. — Henry Watson FowlerPocket Fowler's Modern English Usage.
Although it is sometimes reported that a prohibition on split infinitives goes back to Italian Renaissance times (which Popper refuted by noting that they speak Italian in Italy) and frequently Robert Lowth is cited as the originator of the prescriptive rule, such a rule is not to be found in Lowth's publications, and is not known to appear in any text before the 19th century.
Possibly the earliest comment against split infinitives was by an anonymous American in 1834:
“The practice,” this anonymous American writes, “of separating the prefix of the infinitive mode from the verb, by the intervention of an adverb, is not unfrequent.”
“I am not conscious, that any rule has been heretofore given in relation to this point.”
“The practice, however, of not separating the particle from its verb, is so general and uniform and the [Popperian] falsifiers are so rare, that the rule which I am about to propose will, I believe, prove to be as accurate as most rules, and may be found beneficial.”
“It is this.”
“The particle, “TO,” which comes before the verb in the infinitive mode, must not be separated from it by the intervention of any expression; but the expression should immediately precede the particle, or immediately follow the verb.”
Richard Taylor also condemns split infinitives as an implicature-inviting “affectation", and in 1859, Solomon Barrett, Jr., (of all people) plainly calls the split infinitive “a common fault.”
However, the issue seems not to have attracted wider public attention until Alford addressed it in his Plea for the Queen’s English:
“A correspondent states as his own usage, and defends, the insertion of an expression between the sign of the infinitive mood and the verb.”
“He gives as an instance,
xxiv.    to scientifically illustrate.
But surely this is a practice entirely unknown to me – or my friend Grice.”
“It seems to me, that we ever regard the “to” of the infinitive as inseparable from its verb.”
“And, when we already have a choice between two forms of expression:
xxv.       scientifically to illustrate.
xxvi.    to illustrate scientifically.
there seems no good reason for flying in the face of Oxonian usage.”
Others followed, among them Bache:
“The “to” of the infinitive mood is inseparable from the verb.”
William B. Hodgson, and Raub:
“The sign to must not be separated from the remaining part of the infinitive by an intervening expression”
Even as these authorities are condemning the split infinitive, others were endorsing it, which Popper found amusing.
Brown, says that some grammarians have criticized the split infinitive and grants it may be less elegant than other adverb placements even if, oops, CLEARER – is Brown being Griceian? – cfr. Grice’s desideratum of conversational clarity); Hall, Onions, Jespersen, and Fowler and Fowler, followed suit.

Despite the defence by some syntacticians, by the beginning of the 20th century the prohibition was firmly established.
In his “The King's English,” the Fowler brothers wrote:
“The ‘split’ infinitive has taken such hold upon the consciences of some Oxford dons that, instead of warning the tutee against splitting his infinitives, we must warn him against the curious superstition that the splitting or not splitting makes the difference between a good and a bad ordinary language philosopher.”
In large parts of the Oxonian tutorial system, the construction was opposed with ruthless vigour.
A member of Austin’s Saturday mornings’ Play Group notes:
 “One reason why we, Oxford dons of Grice’s generation, feel so strongly about syntax is that we were severely punished back in our respective public schools, if we did NOT obey our master’s rules, desiderata, or maxims! One split infinitive, one whack; two split infinitives, two whacks; and so on.”
As a result, the debate took on a degree of passion which the bare facts of the matter never, to Popper, warrant.
There is frequent skirmishing between the splitters and anti-splitters.
 Shaw wrote letters to newspapers supporting authors who used the split infinitive, and Raymond Chandler complains to the editor of The Atlantic about a proof-reader who changed Chandler's split infinitives:
“By the way, would you convey my compliments to the purist who reads your proofs and tell him that I write in a sort of broken-down patois which is something like the way a Swiss-waiter talks, and that, when I split an infinitive, God damn it, I split it so it will remain split, and when I interrupt the velvety smoothness of my more or less literate syntax with a few sudden words of bar-room vernacular, this is done with the eyes wide open and the mind relaxed and attentive. The method may not be perfect, but it is all I have. And no implicatures are intended!”
Still, authorities show a strong tendency to accept the split infinitive.
Follett, in Modern Usage writes:
“The split infinitive has its place in good composition.”
“It should be used when it is EXPRESSIVE [implicatural?] and well led up to."
Fowler (Gower's revised second edition) offers the following example of the consequences of a refusal to split an infinitive:
xxvii.  The greatest difficulty about assessing the economic achievements of the Soviet Union is that its spokesmen try absurdly to exaggerate them.
xxviii.           In consequence the visitor may tend badly to underrate them.
This question becomes: "Has dread of the split infinitive led the utterers to attach the expressions ['absurdly' and 'badly'] to the wrong verbs, and would he not have done better to boldly split both infinitives, since he cannot put the adverbs after them without spoiling his rhythm?” 
Bernstein argues that, although infinitives should not ALWAYS be split, they should be split where doing so improves the utterance, in a form that abides with Grice’s conversational maxims:
"The natural position for a modifier is before the expression it modifies.”
“Thus, the natural position for an expression modifying an infinitive should be just after the “to”.”
Bernstein continues:
"Curme's contention that the split infinitive is often an improvement cannot be disputed."
Heffernan and Lincoln, in their composition textbook, agree with Bernstein.
Some sentences, Heffernan and Lincoln write, "are weakened by cumbersome splitting", but in other utterances "an infinitive may be split by a one-expression modifier that would be awkward in any other position".
Objections to the split infinitive fall into three categories, of which only the first is accorded any credence by Grice.
An early proposed rule proscribing the split infinitive, expressed by an anonymous author in the New-England Magazine is based on the purported observation that it is a feature of a form commonly used.
Alford, in his Plea for the Queen's language goes further, stating that use of the "split infinitive" is "a practice entirely unknown to utterers.”
A second argument is summed up by Alford's statement:
"It seems to me that we ever regard the “to” of the infinitive as inseparable from its verb."
The “to” in the infinitive construction, which is found throughout the Germanic languages, is originally a preposition before the dative of a verbal noun.
But in the modern languages it is widely regarded as a particle which serves as a marker of the infinitive.
In German, this marker, “zu,” sometimes precedes the infinitive, but is not regarded (by Germans at least) as part of it.
In Oxonian, on the other hand, it is traditional to speak of the "bare infinitive" without “to” and the "FULL infinitive" with it, and to conceive of “to” as part of the full infinitive.
In the sentence "I had my daughter clean her room", clean is a bare infinitive; in "I told my daughter to clean her room", “to clean” is a full infinitive.
Possibly this is because the absence of an inflected infinitive form makes it useful to include the particle in the citation form of the verb, and in some nominal constructions in which other Germanic languages would omit it (e.g. to know her is to love her).
The concept of a two-expression infinitive can re-inforce an intuitive sense that the two expressions belong together.
For instance, the rhetorician Quackenbos says:
"“To have” is as much one thing, and as inseparable by modifiers, as the original form “habban,” or the Latin “habere.”"
Opdycke bases a similar argument on the closest French, German, and Latin translations.
That there are two parts to the infinitive is disputed, and some philosophers say that the infinitive is a single-expression verb form, which may or may not be preceded by the particle “to.”
Some modern generative analysts classify to as a "peculiar" auxiliary verb.
Other analysts, classify the infinitive as the infinitival subordinator.
Moreover, even when the concept of the “full infinitive” is accepted, it does not necessarily follow that any two expressions that belong together grammatically need be adjacent to each other.
They usually are, but Popperian counter-examples are easily found, such as an adverb splitting a two-word finite verb ("will not do", "has not done").
A frequently discussed argument states that the split-infinitive prohibition is based on Greek and Latin, that were like second and third nature to Grice at Clifton (and later Corpus Christi).
An infinitive in Latin is never used with a marker equivalent to “to,” and thus there is no parallel in Latin for the construction.
The claim that those who dislike split infinitives are applying rules of Latin grammar to the Oxonian vernacular is asserted in many references that, however, accept the split infinitive.
One example is in the Heritage Book of Usage:
"The only rationale for condemning the construction is based on a false analogy with Latin."
In more detail, Marilyn Moriarty states:
“The rule forbidding a split infinitive comes from the time when Latin was the universal language of the world.”
“All scholarly writing was done in Latin. Scientists and scholars even took Latin names to show that they were learned. In Latin, infinitives appear as a single word. The rule which prohibits splitting an infinitive shows deference to Latin and to the time when the rules which governed Latin syntax were applied to other languages.”
The assertion is also made in the Oxford Guide to Plain Lingo, Compact Oxford Dictionary, and, of all essays, Steven Pinker's Language Instinct, among other sources.
The argument implies an adherence to the humanist idea of the greater purity of the classics, which particularly in Renaissance times led people to regard aspects of language that differed from Latin as inferior.
However, by the 19th century such views are no longer widespread.
Moriarty is in error, too, about the age of the prohibition.
It has also been stated that an argument from Latin would be fallacious because "there is no precedent in these languages for condemning the split infinitive because in Greek and Latin (and all the other romance languages) the infinitive is a single word that is impossible to sever".
However, this form of reasoning is something of a straw man argument as very few proponents of the rule argue from Latin in any case.
Certainly, it is clear that dislike of the split infinitive does not originate from Latin.
None of the prescriptivists who started the split-infinitive controversy mentioned Latin in connection with it.
Occasionally philosophers can be found who do oppose the split infinitive with such an argument, but it is not found in any statements of the position from the 19th or early 20th century, when the prohibition first develops.
Of the writers who ascribe the split-infinitive prohibition to Latinism, none cite an authority who condemns the construction on that basis.
According to Bailey, the prohibition does not come from a comparison with Latin, and the belief that it does is "part of the folklore of Oxonian ordinary language philosophers".
Present style and usage manuals deem simple split infinitives unobjectionable.
For example, Curme's Grammar says that not only is the split infinitive correct, but it "should be furthered rather than censured, for it makes for [Griceian] clearer expression" – i.e. devoid of a potential clumsy implicature.
The Columbia Guide to Standard Lingo notes that the split infinitive "eliminates all possibility of ambiguity" (cfr. Grice’s maxim, ‘avoid ambiguity’) in contrast to the "potential for confusion" in an unsplit construction.
Merriam–Webster's Dictionary of Usage says: "the objection to the split infinitive has never had a rational basis,” but then neither has economy according to the Nobel Prize.
According to Mignon Fogarty, "today almost everyone agrees that it is o-kay to split infinitives".
Nevertheless, many philosophers still admonish their tuttees against using split infinitives because of this or that ‘unwanted implicature.’
Because the prohibition has become so widely known, the Columbia Guide recommends that writers "follow the conservative path of avoiding split infinitives when they are not necessary, especially when the utterer is uncertain of his addressee’s expectations and sensitivities on this matter".
Likewise, the dictionaries do not regard the split infinitive as ill-formed or unsyntactical, but on balance consider it likely to produce a implicature-laden style and advise against its use.
Burchfield's revision of Fowler's Modern Usage goes farther (quoting Burchfield's own “The Spoken Word”):
"Avoid splitting infinitives whenever possible, but do not suffer undue remorse if a split infinitive is unavoidable for the completion of a sentence already begun."
Still more strongly, the style guide of “The Economist” says:
"Happy the man who has never been told that it is wrong to split an infinitive.”
“The ban is pointless.”
“Unfortunately, to see it _flouted_ can be so annoying to so many people that you should observe it."
As well as register, tolerance of split infinitives varies according to type.
While most authorities accept split infinitives in general, it is not hard to construct an example which any utterer would reject.
Interestingly, Wycliff's compound split would, if transferred to the modern vernacular, be regarded by most philosopher as not a wff (well-formed formula), but ill-formed and un-syntactical (“It was most unkind to in this manner treat their brother.”) and thus non-evaluable in terms of truth-conditions.
Attempts to define the boundaries of normality are, granted, controversial.
The usage panel of The Heritage Book is evenly divided for and against such sentences as:
xxix.    I expect Popper to completely and utterly fail.
but more than three-quarters of the panel rejected the following:
xxx.       Grice is seeking a plan to gradually, systematically, and economically relieve the burden that implicature may cause.
Here the problem appears to be the breaking up of the verbal phrase to be seeking a plan to relieve: a segment of the head verbal phrase is so far removed from the remainder that the addressee must expend greater effort to understand the utterance (never mind work out the implicature).
By contrast, 87% of the panel deems acceptable the multi-word adverbial in
xxxi.    Grice expect his output to more than double in a year.
not surprisingly perhaps, because here there is no other place to put the words more than without substantially recasting the sentence.
Although the usage of 'not' in splitting infinitives is an issue that has not attracted much attention from the utterers, contemporary syntax puts the phrase into the same category.
This appears to be because the traditional idiom, placing “not” before the marker, as in:
xxxii.   I soon learned not to provoke her.
or with verbs of desire, negating the finite verb, as in
xxxiii.           I do not want to see you anymore.
remains easy and natural, and is still overwhelmingly the more common construction.
On the other hand, in other cases, a search on the corpus of contemporary displays a different aspect.
Its usage is more commonly found in these context, where we can find at least 2,200 cases of the usage of 'not' in splitting infinitives.
Some argue that the two forms have different meanings or implicatures, while others see a syntactic (‘formation’) difference, but most utterers (even Griceian ones) do not make such a distinction.
Utterers who avoid splitting infinitives either place the splitting element elsewhere in the utterance or reformulate the utterance, perhaps rephrasing it without an infinitive and thus avoiding the issue.
However, an utterance, such as
xxxiv.           to more than double.
must be completely rewritten to avoid the split infinitive.
It is ungrammatical to put the words "more than" anywhere else in the utterance.
While split infinitives may be avoided, an utterer must be careful not to produce an awkward or ambiguous sentence, Grice forbid!
Fowler stresses that, if a sentence is to be rewritten to remove a split infinitive, this must be done without compromising the language:
“It is of no avail merely to fling oneself desperately out of temptation; one must so do it that no traces of the struggle remain; that is, sentences must be thoroughly remodeled instead of having a word lifted from its original place and dumped elsewhere.”
In some cases, moving the adverbial creates an ill-formed un-syntactical utterance or invites the wrong implicature. 
R. L. Trask uses this example:
xxxv.  She decided to gradually get rid of the teddy bears she had collected.
"Gradually" splits the infinitive "to get".
However, if the adverb were moved, where could it go? Cfr.
xxxvi.           She decided gradually to get rid of the teddy bears she had collected.
This might implicate (to use Grice’s and Sidonius’s term of art) that the decision was gradual.
Or cfr.:
xxxvii.         She decided to get rid of the teddy bears she had collected gradually.
This implicates, worse, that it was the collecting process that was gradual.
xxxviii.      She decided to get gradually rid of the teddy bears she had collected.
This sounds rather awkward to Grice’s ears, as it plainly splits the well-known phrase "get rid of".
xxxix.            She decided to get rid gradually of the teddy bears she had collected.
Grice considers this almost as unwieldy as its immediate predecessor.
xl.              Gradually, she decided to get rid of the teddy bears she had collected.
This might implicate that her decision or the fact that she will get rid of her teddy bears is gradual – but what implicature would THAT invite?
The utterance can be rewritten to maintain its meaning, however, by using a noun or a different grammatical aspect of the verb, or by eschewing the informal "get rid":
xli.            She decided to get rid of her teddy bear collection gradually.
xlii.          She decided she would gradually get rid of the teddy bears she had collected.
xliii.       She decided to rid herself gradually of the teddy bears she had collected.

Grice notes that the option of rewriting is always available but this questions whether it is always worth the trouble, “if all that we may risk is this or that subtle implicature.”