## 1. Introduction



Arthur has the measles and stays in a closed environment with his
sister Mafalda. If Mafalda ends up contracting the measles herself
because of her staying in close contact with Arthur, there must be
something--the measles virus--which is transmitted from
Arthur to Mafalda in virtue of a relation--the relation of
staying in close contact with one another--instantiated by the
two siblings. Epistemologists have been devoting their attention to
the fact that *epistemic* properties--like being justified
or known--are often transmitted in a similar way. An example (not
discussed in this entry) is the transmission of knowledge via
testimony. A different but equally important phenomenon (which
occupies center stage in this entry) is the transmission of epistemic
justification across an inference or argument from one proposition to
another.



Consider proposition \(q\) constituting the conclusion of an argument
having proposition \(p\) as premise (where \(p\) can be a set or
conjunction of propositions). If \(p\) is justified for a subject
\(s\) by evidence \(e\), this justification may transmit to \(q\) if
\(s\) is aware of the entailment between \(p\) and \(q\). When this
happens, \(q\) is justified for \(s\) *in virtue of* her
justification for \(p\) based on \(e\) and her knowledge of the
inferential relation from \(p\) to \(q\). Consider this example from
Wright (2002):



*Toadstool*

\(\rE\_1\).
 Three hours ago, Jones inadvertently consumed a large risotto of
Boletus Satana.
\(\rP\_1\).
 Jones has absorbed a lethal quantity of the toxins that toadstool
contains.


Therefore:



\(\rQ\_1\).
 Jones will shortly die.



Here \(s\) can deductively infer
 \(\rQ\_1\)
 from
 \(\rP\_1\)
 given background information.[1]
 Suppose \(s\) acquires justification for \(\rP\_1\) by learning
 \(\rE\_1\).
 \( s\) will also acquire justification for \(\rQ\_1\) in virtue of her
knowledge of the inferential relation from \(\rP\_1\) to \(\rQ\_1\) and
her justification for
 \(\rP\_1\).[2]
 Thus, \(s\)'s justification for \(\rP\_1\) will transmit to
\(\rQ\_1\).



It is widely recognized that epistemic justification sometimes
*fails* to transmit across an inference or argument. In
interesting cases of transmission failure, \(s\) has justification for
believing \(p\) and knows the inferential link between \(p\) and
\(q\), but \(s\) has no justification for believing \(q\) *in
virtue of* her justification for \(p\) and her knowledge of the
inferential link. Here is an example from Wright (2003). Suppose
\(s\)'s background information entails that Jessica and Jocelyn
are indistinguishable twins. Consider this possible reasoning:



*Twins*

\(\rE\_2\). 
This girl looks just like Jessica.
\(\rP\_2\).
 This girl is actually Jessica.


Therefore:



\(\rQ\_2\).
 This girl is not Jocelyn.



In *Twins*
\(\rE\_2\)
 can give \(s\) justification for believing
 \(\rP\_2\)
 only if \(s\) has *independent* justification for believing
 \(\rQ\_2\)
 in the first instance. Suppose that \(s\) does have independent
justification for believing \(\rQ\_2\), and imagine that \(s\) learns
\(\rE\_2\). In this case \(s\) will acquire justification for believing
\(\rP\_2\) from \(\rE\_2\). But it is intuitive that \(s\) will acquire
no justification for \(\rQ\_2\) *in virtue of* her justification
for believing \(\rP\_2\) based on \(\rE\_2\) and her knowledge of the
inferential link between \(\rP\_2\) and \(\rQ\_2\). So, *Twins*
instantiates transmission failure when \(\rQ\_2\) is independently
justified.



An argument incapable of transmitting to its conclusion a
*specific* justification for its premise(s)--e.g., a
justification based on evidence \(e\)--may be able to transmit to
the same conclusion a different justification for its
premise(s)--e.g., one based on different evidence \(e^\*\).
Replace for instance
 \(\rE\_2\)
 with 



\(\rE\_2^\*.\)
 This girl's passport certifies she is Jessica.


in *Twins*,
 \(\rE\_2^\*\)
 can provide \(s\) with justification for believing
 \(\rP\_2\)
 even if \(s\) has no independent justification for
 \(\rQ\_2\).
 Suppose then that \(s\) has no independent justification for
\(\rQ\_2\), and that she acquires \(\rE\_2^\*\). It is intuitive that
\(s\) will acquire justification from \(\rE\_2^\*\) for \(\rP\_2\) that
does transmit to \(\rQ\_2\). Now the inference from \(\rP\_2\) to
\(\rQ\_2\) instantiates epistemic transmission.



Although many of the epistemologists participating in the debate on
epistemic transmission and transmission failure speak of transmission
of *warrant*, rather than *justification*, almost all of
them use the term 'warrant' to refer to some kind of
epistemic justification (in
 Sect. 3.3
 we will however consider an account of warrant transmission failure
in which 'warrant' is interpreted differently.) Most
epistemologists investigating epistemic transmission and transmission
failure--e.g., Wright (2011, 2007, 2004, 2003, 2002 and 1985),
Davies (2003, 2000 and 1998), Dretske (2005), Pryor (2004), Moretti
(2012) and Moretti & Piazza (2013)--broadly identify the
epistemic property capable of being transmitted with
*propositional*
 justification.[3]
 Only a few authors explicitly focus on transmission of
*doxastic* justification--e.g., Silins (2005), Davies
(2009) and Tucker (2010a and 2010b
 [OIR]).
 In this entry we follow the majority in discussing transmission and
transmission failure of justification as phenomena primarily
pertaining to propositional justification. (See however the supplement
on
 Transmission of Propositional Justification *versus* Transmission of Doxastic Justification.)



Epistemologists typically concentrate on transmission of
(propositional or doxastic) justification across *deductively
valid* (given background information) arguments. The fact that
justification can transmit across deduction is crucial for our
cognitive processes because it makes the advancement of
knowledge--or justified belief--through deductive reasoning
possible. Suppose evidence \(e\) gives you justification for believing
hypothesis \(p\), and you know that \(p\) entails another proposition
\(q\) that you haven't directly checked. If the justification
you have for believing \(p\) transmits to its unchecked prediction
\(q\) through the entailment, you acquire justification for believing
\(q\) too.



Epistemologists may analyze epistemic transmission across
*inductive* (or *ampliative*) inferences too. Yet this
topic has received much less attention in the literature on epistemic
transmission. (See however interesting remarks in Tucker 2010a.) 



In the remaining part of this entry we will focus on transmission and
transmission failure of propositional justification across deductive
inference. Unless differently specified, by 'epistemic
justification' or 'justification' we always mean
'propositional justification'.


## 2. Epistemic Transmission



As said, \(s\)'s justification for \(p\) based on evidence \(e\)
transmits across entailment from \(p\) to \(p\)'s consequence
\(q\) whenever \(q\) is justified for \(s\) in virtue of \(s\)'s
justification for \(p\) based on \(e\) and her knowledge of
\(q\)'s deducibility from \(p\). This initial characterization
can be distilled into three conditions individually necessary and
jointly sufficient for epistemic transmission:



> 
> 
> \(s\)'s justification for \(p\) based on \(e\) transmits to
> \(p\)'s logical consequence \(q\) if and only if:
> 
> 
> 
> (C1)
> \(s\) has justification for believing \(p\) based on \(e\),
> (C2)
> \(s\) knows that \(q\) is deducible from \(p\),
> (C3)
> \(s\) has justification for believing \(q\) *in virtue of*
> the satisfaction of
>  (C1)
>  and
>  (C2).
> 
> 



Condition
 (C3)
 is crucial for distinguishing *transmission* of justification
across (known) entailment from *closure* of justification
across (known) entailment. Saying that \(s\)'s justification for
believing \(p\) is closed under \(p\)'s (known) entailment to
\(q\) is saying that:



> 
> 
> If 
> 
> 
> 
> (C1)
>  \(s\) has justification for believing \(p\) and 
> (C2)
>  \(s\) knows that \(p\) entails \(q\), then 
> (C3\(^{\textrm{c}}\))
>  \(s\) has justification for believing \(q\).
> 
> 



One can coherently accept the above principle--known as the
 *principle of epistemic closure*--but
 deny a corresponding *principle of epistemic transmission*,
cashed out in terms of the conditions outlined above:



> 
> 
> If 
> 
> 
> 
> (C1)
>  \(s\) has justification for believing \(p\) and 
> (C2)
>  \(s\) knows that \(p\) entails \(q\), then 
> (C3)
>  \(s\) has justification for believing \(q\) *in virtue of*
> the satisfaction of (C1) and (C2).
> 
> 



The *principle of epistemic closure* just requires that when
\(s\) has justification for believing \(p\) and knows that \(q\) is
deducible from \(p, s\) have justification for believing \(q\). In
addition, the *principle of epistemic transmission* requires
this justification to be had in virtue of her having justification for
\(p\) and knowing that \(p\) entails \(q\) (for further discussion see
Tucker 2010b
 [OIR]).



Another important distinction is the one between the *principle of
epistemic transmission* and a different principle of transmission
discussed by Pritchard (2012a) under the label of *evidential
transmission principle*. According to it,



> 
> 
> If \(s\) perceptually knows that \(p\) in virtue of evidence set
> \(e\), and \(s\) competently deduces \(q\) from \(p\) (thereby coming
> to believe that \(q\) while retaining her knowledge that \(p)\), then
> \(s\) knows that \(q\), where that knowledge is sufficiently supported
> by \(e\). (Pritchard 2012a: 75)
> 
> 
> 



Pritchard's principle, to begin with, concerns (perceptual)
knowledge and not propositional justification. Moreover, it deserves
emphasis that there are inferences that apparently satisfy
Pritchard's principle but fail to satisfy the *principle of
epistemic transmission*. Consider for instance the following
triad:



*Zebra*

\(\rE\_3\).
 The animals in the pen look like zebras.
\(\rP\_3\).
 The animals in the pen are zebras.


Therefore:



\(\rQ\_3\).
 The animals in the pen are not mules cleverly disguised to look
like zebras.



According to Pritchard, the evidence set of a normal zoo-goer standing
before the zebra enclosure typically includes, above and beyond
 \(\rE\_3\),
 the background proposition that 



\((\rE\_B)\)
 to disguise mules like zebras would be very costly and
time-consuming, would bring no comparable benefit and would be
relatively easy to unmask.


Suppose \(s\) knows
 \(\rP\_3\)
 on the basis of her evidence set, and competently deduces
 \(\rQ\_3\)
 from \(\rP\_3\) thereby coming to believe \(\rQ\_3\). Pritchard's
*evidential transmission principle* apparently accommodates the
fact that \(s\) thereby comes to know \(\rQ\_3\). For her evidence
set--because of its inclusion of
 \(\rE\_B\)--sufficiently
 supports \(\rQ\_3\). But the *principle of epistemic
transmission* is not satisfied. Although 



(C1\(\_{\textit{Zebra}}\))
 \(s\) has justification for \(\rP\_3\) and 
(C2\(\_{\textit{Zebra}}\))
she knows that \(\rP\_3\) entails \(\rQ\_3\), 


she has justification for believing \(\rQ\_3\) in virtue of, not
(C1\(\_{\textit{Zebra}}\)) and (C2\(\_{\textit{Zebra}}\)),
but the independent
support lent to it by \(\rE\_B\).



Condition
 (C3)
 suffices to distinguish the notion of epistemic transmission from
different notions in the neighborhood. However, as it stands, it is
still unsuitable for the purpose to completely characterize epistemic
transmission. The problem is that there are cases in which it is
intuitive that the justification for \(p\) based on \(e\) transmits to
\(q\) even if (C3), strictly speaking, is *not* satisfied.
These cases can be described as situations in which *only part*
of the justification that \(s\) has for \(q\) is based on her
justification for \(p\) and her knowledge of the entailment from \(p\)
to \(q\). Consider this example. Suppose you are traveling on a train
heading to Edinburgh. At 16:00, as you enter Newcastle upon Tyne, you
spot the train station sign. Then, at 16:05, the ticket controller
tells you that you are not yet in Scotland. Now consider the following
reasoning:



*Journey*

\(\rE\_4\).
 At 16:05 the ticket controller tells you that you are not yet in
Scotland.
\(\rP\_4\).
 You are not yet in Scotland.


Therefore:



\(\rQ\_4\).
 You are not yet in Edinburgh.



As you learn
 \(\rE\_4\),
 given suitable background information, you get justification for
 \(\rP\_4\);
 moreover, to the extent to which you know that not being in Scotland
is sufficient for not being in Edinburgh, you also acquire via
transmission justification for
 \(\rQ\_4\).
 This additional justification is transmitted irrespective of the fact
that you *already* have justification for \(\rQ\_4\), acquired
by spotting the train station sign 'Newcastle upon Tyne'.
If
 (C3)
 were read as requiring that the *whole* of the justification
available for a proposition \(q\) were had in virtue of the
satisfaction of
 (C1)
 and
 (C2),
 cases like these would become invisible.




A way to deal with this complication is to amend the tripartite
analysis of epistemic transmission by turning
 (C3)
 into (C3\(^{+}\)), saying that *at least part* of the
justification that \(s\) has for \(q\) has been achieved by her in
virtue of the satisfaction of
 (C1)
 and
 (C2).
 Let us say that a justification for \(q\) is an *additional*
justification for \(q\) whenever it is not a *first-time*
justification for it. Condition (C3\(^{+}\)) can be reformulated as
this disjunction:



(C3\(^{+}\))
 \(s\) has *first-time* justification for \(q\) in virtue
of the satisfaction of
 (C1)
 and
 (C2),
  

or
  

\(s\) has an *additional* justification for \(q\) in virtue
of the satisfaction of
 (C1)
 and
 (C2).



Much of the extant literature on epistemic transmission concentrates
on examples of transmission of first-time justification. These
examples include
 *Toadstool*.
 We have seen, however, that what intuitively transmits in other cases
is simply additional justification. Epistemologists have identified at
least two--possibly overlapping--kinds of additional
justification (cf. Moretti & Piazza 2013).



One is what can be called *independent* justification because
it appears--intuitively--independent of the original
justification for \(q\). This notion of justification can probably be
sharpened by appealing to counterfactual analysis. Suppose
\(s\)'s justification for \(p\) based on \(e\) transmits to
\(p\)'s logical consequence \(q\). This justification
transmitted to \(q\) is an additional *independent*
justification just in case these three conditions are met: 



(IN1)
\(s\) was already justified in believing \(q\) before acquiring
\(e\), 
(IN2)
as \(s\) acquires \(e, s\) is still justified in believing \(q\),
and 
(IN3)
if \(s\) had not been antecedently justified in believing \(q\),
upon learning \(e, s\) would have acquired via transmission a
first-time justification for believing \(q\). 


*Journey*
 instantiates transmission of justification by meeting
 (IN1),
 (IN2), and
 (IN3).
 Thus, *Journey* exemplifies a case of transmission of
additional independent justification.



Consider now that justification for a proposition or belief normally
comes in degrees of strength. The second kind of additional
justification can be characterized as *quantitatively
strengthening* justification. Suppose again that \(s\)'s
justification for \(p\) based on \(e\) transmits to \(p\)'s
consequence \(q\). This justification transmitted to \(q\) is an
additional *quantitatively strengthening* justification just in
case these two conditions are satisfied:



(STR1)
 \(s\) was already justified in believing \(q\) before acquiring
\(e\), and 
(STR2)
 as \(s\) acquires \(e\), the strength of \(s\)'s
justification for believing \(q\) increases. 


Here is an example from Moretti (2012). Your background information
says that only one ticket out of 5,000 of a fair lottery has been
bought by a person born in 1970, and that all other tickets have been
bought by older or younger people. Consider now this reasoning:



*Lottery*

\(\rE\_5\).
 The lottery winner's passport certifies she was born in
1980.
\(\rP\_5\).
 The lottery's winner was born in 1980.


Therefore:



\(\rQ\_5\).
 The lottery's winner was not born in 1970.



Given its high chance,
 \(\rQ\_5\)
 is already justified on your background information only. It is
intuitive that as you learn
 \(\rE\_5\),
 you acquire an additional quantitatively strengthening justification
for \(\rQ\_5\) via transmission. For your justification for
 \(\rP\_5\)
 transmitted to \(\rQ\_5\) is intuitively quantitatively stronger than
your initial justification for \(\rQ\_5\).



In many cases when \(q\) receives via transmission from \(p\) an
additional independent justification, \(q\) also receives a
quantitatively strengthening justification. This is not always true
though. For there seem to be cases in which an additional independent
justification transmitted from \(p\) to \(q\) intuitively
*lessens* an antecedent justification for \(q\) (cf. Wright
2011).



An interesting question is whether it is true that as \(q\) gets via
transmission from \(p\) an additional quantitatively strengthening
justification, \(q\) also gets an independent justification. This
seems true in some cases--for instance in
 *Lottery*.
 It is controversial, however, if it is the case that
*whenever* \(q\) gets via transmission a quantitatively
strengthening justification, \(q\) also gets an independent
justification. Wright (2011) and Moretti & Piazza (2013) describe
two examples in which a subject allegedly receives via transmission a
quantitatively strengthening but not independent additional
justification.



To summarize, *additional* justification comes in two species
at least: *independent* justification and *quantitatively
strengthening* justification. This enables us to lay down three
specifications of the general condition
 (C3\(^{+}\))
 necessary for justification transmission, each of which represents a
condition necessary for the transmission of one particular type of
justification. Let's call these specifications
 (C3\(^{\textrm{ft}}\)),
 (C3\(^{\textrm{ai}}\)), and
 (C3\(^{\textrm{aqs}}\)).



(C3\(^{\textrm{ft}}\))
 \(s\) has *first time* justification for \(q\) in virtue
of the satisfaction of
 (C1)
 and
 (C2).


(C3\(^{\textrm{ai}}\))
 \(s\) has *additional independent* justification for \(q\)
in virtue of the satisfaction of
 (C1)
 and
 (C2).
 


(C3\(^{\textrm{aqs}}\))
 \(s\) has *additional quantitatively strengthening*
justification for \(q\) in virtue of the satisfaction of
 (C1)
 and
 (C2).
 


Transmission of first-time justification makes the advancement of
justified belief through deductive reasoning possible. Yet the
acquisition of first-time justification for \(q\) isn't the sole
possible improvement of one's epistemic position relative to
\(q\) that one could expect from transmission of justification.
Moretti & Piazza (2013), for instance, describe a variety of
different ways in which s's epistemic standing toward a
proposition can be improved upon acquiring an additional justification
for it via transmission.



We conclude this section with a note about *transmissivity as
resolving doubts*. Let us say that \(s\) *doubts* \(q\)
just in case \(s\) either *disbelieves* or *withholds*
belief about \(q\), namely, refrains from both believing and
disbelieving \(q\) *after deciding about* \(q\). \(s\)'s
doubting \(q\) should be distinguished from \(s\)'s being
*open minded* about \(q\) and from \(s\)'s having
*no* doxastic attitude whatsoever towards \(q\) (cf. Tucker
2010a). Let us say that a deductively valid argument from \(p\) to
\(q\) is able to resolve doubt about its conclusion just in case it is
possible for \(s\) to be rationally moved from doubting \(q\) to
believing \(q\) solely in virtue of grasping the argument from \(p\)
to \(q\) and the evidence offered for \(p\).



Some authors (e.g., Davies 1998, 2003, 2004, 2009; McLaughlin 2000;
Wright 2002, 2003, 2007) have proposed that we should conceive of an
argument's epistemic transmissivity in a way that is very
closely related or even identical to the argument's ability to
resolve doubt about its conclusion. Whereas some of these authors have
eventually conceded that epistemic transmissivity cannot be defined as
ability to resolve doubt (e.g., Wright 2011), others have attempted to
articulate this view in full (see mainly Davies 2003, 2004, 2009).



However, there is nowadays wide agreement in the literature that the
property of being a transmissive argument *doesn't*
coincide with the one of being an argument able to resolve doubt about
its conclusion (see for example, Beebee 2001; Coliva 2010; Markie
2005; Pryor 2004; Bergmann 2004, 2006; White 2006; Silins 2005; Tucker
2010a). A good reason to think so is that whereas the property of
being transmissive appears to be a genuinely *epistemic*
property of an argument, the one of resolving doubt seems to be only a
*dialectical* feature of it, which varies with the audience
whose doubt the argument is used to address.


## 3. Failure of Epistemic Transmission


### 3.1 Trivial Transmission Failure *versus* Non-Transmissivity



It is acknowledged that justification sometimes fails to transmit
across known entailment (the acknowledgment dates back at least to
Wright 1985). Moreover, it is no overstatement to say that the
literature has investigated transmission failure more extensively than
transmission of justification. As we have seen, justification based on
\(e\) transmits from \(p\) to \(q\) across the entailment if and only
if 



(C1)
 \(s\) has justification for \(p\) based on \(e\), 
(C2)
\(s\) knows that \(q\) is deducible from \(p\), and 
(C3\(^{+}\))
 at least part of \(s\)'s justification for \(q\) is based
on the satisfaction of (C1) and (C2).


It follows from this characterization that *no* justification
based on *e transmits* from \(p\) to \(q\) across the
entailment if
 (C1),
 (C2), or
 (C3\(^{+}\))
 are not satisfied. These are cases of transmission failure.



Some philosophers have argued that knowledge and justification are not
always *closed* under competent (single-premise or
multiple-premise) deduction. In the recent literature, the explanation
of closure failure has often been essayed in terms of
*agglomeration of epistemic risk*. This type of explanation is
less controversial when applied to multi-premise deduction. An example
of it concerning justification is the deduction from a high number
\(n\) of premises, each of which specifies that a different ticket in
a fair lottery won't win, which are individually justified even
though each premise is *somewhat* risky, to the conclusion that
none of these \(n\) tickets will win, which is *too risky* to
be justified. (For more controversial cases in which knowledge or
justification closure would fail across single-premise deduction
because of risk accumulation, see for example Lasonen-Aarnio 2008 and
Schechter 2013; for responses, see for instance Smith 2013 and 2016.)
These cases of failure of epistemic closure can be taken to also
involve failure of justification *transmission*. For instance,
it can be argued that even if 



(C1\(^{\*}\))
 \(s\) has justification for each of the \(n\) premises stating
that a ticket won't win, and 
(C2\(^{\*}\))
 \(s\) knows that it follows from these premises that none of the
\(n\) tickets will win, 


\(s\) has no justification--and, therefore, no justification in
virtue of the satisfaction of
 (C1\(^{\*}\))
 and
 (C2\(^{\*}\))--for
 believing that none of the \(n\) tickets will win. In these cases,
transmission failure appears to be a consequence of closure failure,
and it is therefore natural to treat the former simply as a
symptomatic manifestation of the latter. For this reason, we will
follow the current literature on transmission failure in not
discussing these cases. (For an analysis of closure failure, see the
entry on
 epistemic closure,
 especially section 6.)



The current literature treats transmission failure as a self-standing
phenomenon, in the sense that it focuses on cases in which
transmission failure is not imputed--and thus not considered
reducible--to an underlying failure of closure. For the rest of
this entry, we shall follow suit and investigate transmission failure
in this pure or genuine form.



The most trivial cases of transmission failure are such that
 (C3\(^{+}\))
 is unsatisfied because
 (C1)
 or
 (C2)
 are unsatisfied, but it is also true that (C3\(^{+}\))
would have been satisfied if both
 (C1)
 and
 (C2)
 have been satisfied (cf. Tucker 2010b
 [OIR]).
 It deserves emphasis that these cases involve arguments that
aren't unsuitable for the purpose to transmit justification
depending on evidence \(e\): had the epistemic circumstances been
congenial to the satisfaction of
 (C1)
 and
 (C2),
 these arguments would have transmitted the justification based on
\(e\) from \(p\) to \(q\). As we could put the point, these arguments
are *transmissive* of the justification depending on
 \(e\).[4]



Cases of transmission failure of a more interesting variety are those
in which, regardless of the validity of closure of justification,
 (C3\(^{+}\))
 isn't satisfied because it could not have been satisfied, no
matter whether or not
 (C1)
 and
 (C2)
 have been satisfied. These cases concern arguments
*non-transmissive* of justification depending on a given
evidence, i.e., arguments incapable of transmitting justification
depending on that evidence under any epistemic circumstance. An
example in point is
 *Twins*.
 Suppose first that \(s\) has independent justification for
 \(\rQ\_2\).
 In those circumstances 



(C1\(\_{\textit{Twins}}\))
 \(s\) has justification from
 \(\rE\_2\)
 for
 \(\rP\_2\).


Furthermore 



(C2\(\_{\textit{Twins}}\))
 \(s\) does know that
 \(\rP\_2\)
 entails
 \(\rQ\_2\).


However, \(s\) hasn't justification for \(\rQ\_2\) in virtue of
the satisfaction of
 (C1\(\_{\textit{Twins}}\))
 and
 (C2\(\_{\textit{Twins}}\)).
 So
 (C3\(^{+}\))
 is not met. Suppose now that \(s\) has no independent justification
for \(\rQ\_2\). Then, it isn't the case that 



(C1\(\_{\textit{Twins}}\))
 \(s\) has justification from
 \(\rE\_2\)
 for
 \(\rP\_2\).
 


So,
 (C3\(^{+}\))
 is not met either. Since there is no other possibility--either
\(s\) has independent justification for
 \(\rQ\_2\)
 or she doesn't--it cannot be the case that \(s\)'s
belief that \(\rQ\_2\) is justified *in virtue of* her
justification for
 \(\rP\_2\)
 from
 \(\rE\_2\)
 and her knowledge that \(\rP\_2\) entails \(\rQ\_2\).



Note that none of the cases of transmission failure of justification
considered above entails failure of epistemic closure. For in none of
these cases \(s\) has justification for believing \(p, s\) knows that
\(p\) entails \(q\), and \(s\) fails to have justification for
believing \(q\).



Unsurprisingly, the epistemologists contributing to the literature on
transmission failure have principally devoted their attention to cases
involving non-transmissive arguments. Epistemologists have endeavored
to identify conditions whose satisfaction suffices to make an argument
*non-transmissive* of justification based on a given evidence.
The next section reviews the most influential of these proposals.


### 3.2 Varieties of Non-Transmissive Arguments



Some non-transmissive arguments *explicitly* feature their
conclusion among their premises. Suppose \(p\) is justified for \(s\)
by \(e\), and consider the premise-circular argument that deduces
\(p\) from itself. This argument cannot satisfy
 (C3\(^{+}\))
 even if
 (C1)
 and
 (C2)
 are satisfied. The reason is that no part of \(s\)'s
justification for \(p\) can be acquired *in virtue of*, among
other things, the satisfaction of
 (C2).
 For if
 (C1)
 is satisfied, \(p\) is justified for \(s\) by \(e\)
*independently* of \(s\)'s knowledge of \(p\)'s
self-entailment, thus not in virtue of
 (C2).



Non-transmissive arguments are not necessarily premise-circular. A
different source of non-transmissivity instantiating a subtler form of
circularity is the dependence of evidential relations on background or
collateral information. This type of dependence is a rather familiar
phenomenon: the boiling of a kettle gives one justification for
believing that the temperature of the liquid inside is approximately
100degC *only if* one knows that the liquid is water and that
atmospheric pressure is the one of the sea-level. It doesn't if
one knows that the kettle is on the top of a high mountain, or the
liquid is, say, sulfuric acid.



Wright argues, for instance, that the following epistemic set-up,
which he calls the *information-dependence template*, suffices
for an argument's inability to transmit justification.



> 
> 
> A body of evidence, \(e\), is an information-dependent justification
> for a particular proposition \(p\) if whether \(e\) justifies \(p\)
> depends on what one has by way of collateral information, \(i\).
> [...] Such a relationship is always liable to generate examples
> of transmission failure: it will do so just when the particular \(e,
> p\), and \(i\) have the feature that needed elements of the relevant
> \(i\) are themselves entailed by \(p\) (together perhaps with other
> warranted premises). In that case, any warrant supplied by \(e\) for
> \(p\) will not be transmissible to those elements of \(i\). (Wright
> 2003: 59, edited.)
> 
> 
> 



The claim that \(s\)'s justification from \(e\) for \(p\)
requires \(s\) to have background information \(i\) is customarily
understood as equivalent (in this context) to the claim that
\(s\)'s justification from \(e\) for \(p\) depends on some type
of independent justification for believing or accepting
 \(i\).[5]



Instantiating the *information-dependence template* appears
sufficient for an argument's inability to transmit
*first-time* justification. Consider again this triad:



*Twins*

\(\rE\_2\). 
This girl looks just like Jessica.
\(\rP\_2\).
 This girl is actually Jessica.


Therefore:



\(\rQ\_2\).
 This girl is not Jocelyn.



Suppose \(s\)'s background information entails that Jessica and
Jocelyn are indistinguishable twins. Imagine that \(s\) acquires
 \(\rE\_2\).
 It is intuitive that \(\rE\_2\) could justify
 \(\rP\_2\)
 for \(s\) only if \(s\) had *independent* justification for
believing
 \(\rQ\_2\)
 in the first instance. Thus, *Twins* instantiates the
*information-dependence template*. Note that \(s\) acquires
first-time justification for \(\rQ\_2\) in *Twins* only if 



(C1\(\_{\textit{Twins}}\))

\(\rE\_2\)
 gives her justification for
 \(\rP\_2\),
 


(C2\(\_{\textit{Twins}}\))
 \(s\) knows that
 \(\rP\_2\)
 entails
 \(\rQ\_2\)
 and


 (C3\(^{\textrm{ft}}\_{\textit{Twins}}\))
 \(s\) acquires first-time justification for believing
 \(\rQ\_2\)
*in virtue of*
(C1\(\_{\textit{Twins}}\))
 and
 (C2\(\_{\textit{Twins}}\)).
 


The satisfaction of
 (C3\(^{\textrm{ft}}\_{\textit{Twins}}\))
 requires \(s\)'s justification for believing
 \(\rQ\_2\)
*not* to be independent of \(s\)'s justification from
 \(\rE\_2\)
 for
 \(\rP\_2\).
 However, if
 (C1\(\_{\textit{Twins}}\))
 is true, the *informational-dependence template* requires
\(s\) to have justification for believing \(\rQ\_2\)
*independently* of \(s\)'s justification from \(\rE\_2\)
for \(\rP\_2\). Thus, when the *information-dependence template*
is instantiated,
 (C1\(\_{\textit{Twins}}\))
 and (C3\(^{\textrm{ft}}\_{\textit{Twins}}\)) cannot be satisfied at
once. In general, no argument satisfying this template together with a
given evidence will be transmissive of first-time justification based
on that evidence.



One may wonder whether a deductive argument from \(p\) to \(q\)
instantiating the *information-dependence template* is unable
to transmit *additional* justification for \(q\). The answer
seems affirmative when the additional justification is
*independent* justification. Suppose the
*information-dependence template* is instantiated such that
\(s\)'s justification for \(p\) from \(e\) depends on
\(s\)'s independent justification for \(q\). Note that \(s\)
acquires additional independent justification for \(q\) only if 



(C1)
 \(e\) gives her justification for \(p\), 
(C2)
 \(s\) knows that \(p\) entails \(q\), and 
(C3\(^{\textrm{ai}}\))
 \(s\) acquires an additional independent justification in virtue
of (C1) and (C2).


This additional justification is independent of \(s\)'s
antecedent justification for \(q\) only if, in particular, condition
 (IN3)
 of the characterization of additional independent justification is
satisfied. (IN3) says that if \(s\) had not been antecedently
justified in believing \(q\), upon learning \(e, s\) would have
acquired via transmission a first-time justification for believing
\(q\). (IN3) entails that if \(q\) were not antecedently justified for
\(s, e\) would still justify \(p\) for \(s\). Hence, the satisfaction
of (IN3) is incompatible with the instantiation of the
*information-dependence template*, which entails that if \(s\)
had not antecedent justification for \(q, e\) would *not*
justify \(p\) for \(s\). The instantiation of the
*information-dependence template* then precludes transmission
of independent justification.



As suggested by Wright (2007), the instantiation of the
*information-dependence template* might also appear sufficient
for an argument's inability to transmit *additional
quantitatively strengthening* justification. This claim might
appear intuitively plausible: perhaps it is reasonable that if the
justification from \(e\) for \(p\) depends on independent
justification for another proposition \(q\), the strength of the
justification available for \(q\) sets an upper bound to the strength
of the justification possibly supplied by \(e\) for \(p\). However,
the examples by Wright (2011) and Moretti & Piazza (2013)
mentioned in
 Sect. 2
 appear to undermine this intuition. For they involve arguments that
instantiate the *information-dependent template* yet seem to
transmit quantitatively strengthening justification to their
conclusions. (Alspector-Kelly 2015 suggests that these arguments are a
symptom that Wright's explanation of non-transmissivity is
overall inadequate.) 



Some authors have attempted Bayesian formalizations of the
*information dependence template* (see the supplement on
 Bayesian Formalizations of the *Information-Dependence Template*.)
 Furthermore, Coliva (2012) has proposed a variant of the same
template. In accordance with the *information-dependence
template*, \(s\)'s justification from \(e\) for \(p\) fails
to transmit to \(p\)'s consequence \(q\) whenever \(s\)'s
possessing that justification for \(p\) requires \(s\)'s
independent justification for \(q\). According to Coliva's
variant, \(s\)'s justification from \(e\) for \(p\) fails to
transmit to \(q\) whenever \(s\)'s possessing the latter
justification for \(p\) requires \(s\)'s independent
*assumption* of \(q\), *whether this assumption is justified
or not*. Pryor (2012: SS VII) can be read as pressing
objections against Coliva's template, which are addressed in
Coliva (2012).



We have seen that non-transmissivity may depend on premise-circularity
or reliance on collateral information. There is at least a third
possibility: an argument can be non-transmissive of the justification
for its premise(s) based on given evidence because the evidence
justifies *directly* the conclusion--i.e.,
*independently* of the argument itself (cf. Davies 2009). In
this case the argument instantiates *indirectness*, for
\(s\)'s going through the argument would result in nothing but
an indirect (and unneeded) detour for justifying its conclusion. If
\(e\) directly justifies \(q\), no part of the justification for \(q\)
is based on, among other things, \(s\)'s knowledge of the
inferential relation between \(p\) and \(q\). So
 (C3\(^{+}\))
 is unfulfilled whether or not
 (C1)
 and
 (C2)
 are fulfilled. Here is an example from Wright (2002):



*Soccer*

\(\rE\_6\).
 Jones has just kicked the ball between the white posts.
\(\rP\_6\).
 Jones has just scored a goal.


Therefore:



\(\rQ\_6\).
 A game of soccer is taking place.



Suppose \(s\) learns evidence
 \(\rE\_6\).
 On ordinary background information, 



(C1\(\_{\textit{Socc}}\))

\(\rE\_6\)
 justifies
 \(\rP\_6\)
 for \(s\), 
(C2\(\_{\textit{Socc}}\))
 \(s\) knows that
 \(\rP\_6\)
 entails
 \(\rQ\_6\),
 and
 \(\rE\_6\)
 also justifies
 \(\rQ\_6\)
 for \(s\).


It seems false, however, that
 \(\rQ\_6\)
 is justified for \(s\) *in virtue of* the satisfaction of
 (C1\(\_{\textit{Socc}}\))
 and
 (C2\(\_{\textit{Socc}}\)).
 Quite the reverse, \(\rQ\_6\) seems justified for \(s\) by
 \(\rE\_6\)
 independently the satisfaction of (C1\(\_{\textit{Socc}}\)) and
(C2\(\_{\textit{Socc}}\)). This is so because in the (imagined) actual
scenario it seems true that \(s\) would still possess a justification
for \(\rQ\_6\) based on \(\rE\_6\) even if \(\rE\_6\) did *not*
justify
 \(\rP\_6\)
 for \(s\). In fact suppose \(s\) had noticed that the referee's
assistant raised her flag to signal Jones's off-side. Against
this altered background information, \(\rE\_6\) would no longer justify
\(\rP\_6\) for \(s\) but it would still justify \(\rQ\_6\) for \(s\).
Thus, *Soccer* is non-transmissive of the justification
depending on \(\rE\_6\). In general, no argument instantiating
*indirectness* in relation to some evidence is transmissive of
justification based on that evidence.



The *information-dependence template* and *indirectness*
are diagnostics for a deductive argument's inability to transmit
the justification for its premise(s) \(p\) based on evidence \(e\) to
its conclusion \(q\), where \(e\) is conceived of as a
*believed* proposition capable of supplying
*inferential* and (typically) *fallible* justification
for \(p\). (Note that even though \(e\) is conceived of as a belief,
the collateral information \(i\), which is part of the
*template*, doesn't need to be believed on some views.)
The justification for a proposition \(p\) might come in other forms.
For instance, it has been proposed that a proposition \(p\) about the
perceivable environment around the subject \(s\) can be justified by
the fact that \(s\) *sees* that \(p\) (where
'*sees*' is taken to be factive). In this case,
\(s\) is claimed to attain a kind of *non-inferential* and
*infallible* justification for believing \(p\). This view has
been explored by *epistemological disjunctivists* (see for
instance McDowell 1982, 1994 and 2008, and Pritchard 2007, 2008, 2009,
2011 and 2012a).



One might find it intuitively plausible that when \(s\) sees that \(p,
s\) attains non-inferential and infallible justification for believing
\(p\) that doesn't rely on \(s\)'s background information.
Since this justification for believing \(p\) would be *a
fortiori* unconstrained by \(s\)'s independent justification
for believing any consequence \(q\) of \(p\), in these cases the
information-dependence template could not possibly be instantiated.
Therefore, one might be tempted to conclude that when \(s\) sees that
\(p, s\) acquires a justification that typically transmits to the
propositions that \(s\) knows to be deducible from \(p\) (cf. Wright
2002). Pritchard (2009, 2012a) comes very close to endorsing this view
explicitly.



The latter contention has not stayed unchallenged. Suppose one accepts
a notion of epistemic justification with *internalist*
resonances saying that a factor \(J\) is relevant to \(s\)'s
justification only if \(s\) is able to determine, by reflection alone,
whether \(J\) is or is not realized. On this notion, \(s\)'s
seeing that \(p\) cannot provide \(s\) with justification for
believing \(p\) unless \(s\) can rationally claim that she is
*seeing* that \(p\) upon reflection alone. Seeing that \(p\),
however, is *subjectively* indistinguishable from hallucinating
that \(p\), or from being in some other delusional state in which it
merely *seems* to \(s\) that she is seeing that \(p\). Hence,
one may find it compelling that \(s\) can claim by reflection alone
that she's seeing that \(p\) only if \(s\) has an independent
reason for ruling out that it merely seems to her that she does (cf.
Wright 2011). If this is true, for many deductive arguments from \(p\)
to \(q, s\) won't be able to acquire non-inferential and
infallible justification for believing \(p\) of the type described by
the disjunctivist and transmit it to \(q\). This will happen whenever
\(q\) is the logical negation of a proposition ascribing to \(s\) some
delusionary mental state in which it merely seems to her that she
directly perceives that \(p\).



Wright's *disjunctive template* is meant to be a
diagnostic of transmission failure of non-inferential justification
when epistemic justification is conceived of in the internalist
fashion suggested
 above.[6]
 According to Wright (2000), for any propositions \(p, q\) and \(r\)
and subject \(s\), the *disjunctive template* is instantiated
whenever:

 

(D1)
 \(p\) entails \(q\);
(D2)
 \(s\)'s justification for \(p\) consists in \(s\)'s
being in a state subjectively indistinguishable from a state in which
\(r\) would be true;
(D3)
 \(r\) is incompatible with \(p\);
(D4)
 \(r\) would be true if \(q\) were false.


To see how this template works, consider again the following
triad:



*Zebra*

\(\rE\_3\).
 The animals in the pen look like zebras.
\(\rP\_3\).
 The animals in the pen are zebras.


Therefore:



\(\rQ\_3\).
 The animals in the pen are not mules cleverly disguised to look
like zebras.



The justification from
 \(\rE\_3\)
 for
 \(\rP\_3\)
 arguably fails to transmit across the inference from \(\rP\_3\) to
 \(\rQ\_3\)
 because of the satisfaction of the *information-dependence
template*. For it seems true that \(s\) could acquire a
justification for believing \(\rP\_3\) on the basis of \(\rE\_3\) only
if \(s\) had an independent justification for believing \(\rQ\_3\). Now
suppose that \(s\)'s justification for \(\rP\_3\) is based on,
not \(\rE\_3\) but \(s\)'s *seeing* that \(\rP\_3\).
Let's call *Zebra\** the corresponding variant of
*Zebra*. Given the *non-inferential* nature of the
justification considered for \(\rP\_3\), *Zebra\** could not
instantiate the *information-dependence template*. However, it
is easy to check that *Zebra\** instantiates the *disjunctive
template*. To begin with, 



(D1\(\_{\textit{Zebra}}\))

\(\rP\_3\)
 entails
 \(\rQ\_3\);
 
(D2\(\_{\textit{Zebra}}\))
 \(s\)'s justification for believing
 \(\rP\_3\)
 is constituted by \(s\)'s seeing that \(\rP\_3\), which is
subjectively indistinguishable from the state that \(s\) would be in
if it were true that


\(\rR\_{\textit{Zebra}}\).
 the animals in the pen are mules cleverly disguised to look like
zebras; 

(D3\(\_{\textit{Zebra}}\))
\(\rR\_{\textit{Zebra}}\)
 is incompatible with
 \(\rP\_3\);
 and, trivially, 
(D4\(\_{\textit{Zebra}}\))
 if
 \(\rQ\_3\)
 were false
 \(\rR\_{\textit{Zebra}}\)
 would be true.


Since *Zebra\** instantiates the *disjunctive template*,
it is non-transmissive of at least *first-time* justification.
In fact note that \(s\) acquires first-time justification for
 \(\rQ\_3\)
 in this case if and only if 



(C1\(\_{\textit{Zebra}}\))
 \(s\) has justification for
 \(\rP\_3\)
 based on seeing that \(\rP\_3\), 
(C2\(\_{\textit{Zebra}}\))
 \(s\) knows that
 \(\rP\_3\)
 entails
 \(\rQ\_3\),
 and 
(C3\(^{\textrm{ft}}\_{\textit{Zebra}}\))
 \(s\) acquires first-time justification for believing
 \(\rQ\_3\)
 in virtue of
 (C1\(\_{\textit{Zebra}}\))
 and
 (C2\(\_{\textit{Zebra}}\)).
 


Also note that
 (C3\(^{\textrm{ft}}\_{\textit{Zebra}}\))
 requires \(s\)'s justification for believing
 \(\rQ\_3\)
*not* to be independent of \(s\)'s justification for
 \(\rP\_3\)
 based on seeing that \(\rP\_3\). However, if
 (C1\(\_{\textit{Zebra}}\))
 is true, the *disjunctive template* requires \(s\) to have
justification for believing \(\rQ\_3\) *independent* of
\(s\)'s justification for \(\rP\_3\) based on her seeing that
\(\rP\_3\). (For if \(s\) could not independently exclude that
\(\rQ\_3\) is false, given (D4), (D3) and (D2), \(s\) could not exclude
that the incompatible alternative \(\rR\_{\textit{Zebra}}\) to
\(\rP\_3\), which \(s\) cannot subjectively distinguish from \(\rP\_3\)
on the ground of her seeing that \(\rP\_3\), is true.) Thus, when the
*disjunctive template* is instantiated,
 (C1\(\_{\textit{Zebra}}\))
 and (C3\(^{\textrm{ft}}\_{\textit{Zebra}}\)) cannot be satisfied at
once.



The disjunctive template has been criticized by McLaughlin (2003) on
the ground that the template is instantiated whenever the
justification for \(p\) is fallible, i.e. compatible with
\(p\)'s falsity. Here is an example from Brown (2004). Take this
deductive argument:



*Fox*

\(\rP\_7\).
 The animal in the garbage is a fox.


Therefore:



\(\rQ\_7\).
 The animal in the garbage is not a cat.



Suppose \(s\) has a fallible justification for believing
 \(\rP\_7\)
 based on \(s\)'s *experience* as if the animal in the
garbage is a fox. Take now \(\rR\_{\textit{fox}}\) to be
\(\rP\_7\)'s logical negation. Since the justification that \(s\)
has for \(\rP\_7\) is fallible, condition
 (D2)
 above is met *by default*. As one can easily check, conditions
 (D1),
 (D3), and
 (D4)
 are also met. So,
 *Fox*
 instantiates the *disjunctive template*. Yet it is intuitive
that *Fox* does transmit justification to its conclusion.



One could respond to McLaughlin that his objection is misplaced
because the *disjunctive template* is meant to apply to
*infallible*, and not fallible, justification. A more
interesting response to McLaughlin is to refine some condition listed
in the *disjunctive template* to block McLaughlin's
argument while letting this template account for transmission failure
of both fallible and infallible justification. Wright (2011) for
instance suggests replacing
 (D3)
 with the following
 condition:[7]



(D3\(^{\*}\))
 \(r\) is incompatible with some presupposition of the cognitive
project of obtaining justification for \(p\) in the relevant
fashion.


According to Wright's (2011) characterization, a presupposition
of a cognitive project is any condition such that doubting it before
carrying out the project would rationally commit one to doubting the
significance or competence of the project irrespective of its
 outcome.[8]
 For a wide class of cognitive projects, examples of these
presuppositions include: the normal and proper functioning of the
relevant cognitive faculties, the reliability of utilized instruments,
the obtaining of the circumstances congenial to the proposed method of
investigation, the soundness of relevant principles of inference
utilized in developing and collating one's results, and so
on.



With
 (D3\(^{\*}\))
 in the place of
 (D3),
 *Fox* no longer instantiates the *disjunctive
template*. For the truth of \(\rR\_{\textit{fox}}\), stating that
the animal in the garbage is not a fox, appears to jeopardize no
presupposition of the cognitive project of obtaining perceptual
justification for
 \(\rP\_7\).
 Thus (D3\(^{\*}\)) is not fulfilled. On the other hand, arguments that
intuitively don't transmit do satisfy (D3\(^{\*}\)). Take
*Zebra\**. In this case \(\rR\_{\textit{fox}}\) states that the
animals in the pen are mules cleverly disguised to look like zebras.
Since \(\rR\_{\textit{fox}}\) entails that conditions are unsuitable
for attaining perceptual justification for believing
 \(\rP\_3\),
 \(\rR\_{\textit{fox}}\) looks incompatible with a presupposition of
the cognitive project of obtaining perceptual justification for
\(\rP\_3\). Thus, \(\rR\_{\textit{fox}}\) does satisfy (D3\(^{\*}\)) in
this case.


### 3.3 Non-Standard Accounts



In this section we outline two interesting branches in the literature
on transmission failure of justification and warrant across valid
inference. We start with Smith's (2009) non-standard account of
non-transmissivity of justification. Then, we present
Alspector-Kelly's (2015) account of non-transmissivity of
Plantinga's warrant.



According to Smith (2009), epistemic justification requires
*reliability*. \(s\)'s belief that \(p\), held on the
basis of \(s\)'s belief that \(e\), is reliable in Smith's
sense just in case in all possible worlds including \(e\) as true and
that are as *normal* (from the perspective of the actual world)
as the truth of \(e\) permits, \(p\) is also true. Consider
 *Zebra*
 again.



*Zebra*

\(\rE\_3\).
 The animals in the pen look like zebras.
\(\rP\_3\).
 The animals in the pen are zebras.


Therefore:



\(\rQ\_3\).
 The animals in the pen are not mules cleverly disguised to look
like zebras.



\(s\)'s belief that
 \(\rP\_3\)
 is reliable in Smith's sense when it is based on \(s\)'s
belief that
 \(\rE\_3\).
 (Disguising mules to make them look like zebras is certainly an
*abnormal* practice.) Thus, all possible \(\rE\_3\)-worlds that
are as normal as the truth of \(\rE\_3\) permits aren't worlds in
which the animals in the pen are cleverly disguised mules. Rather,
they are \(\rP\_3\)-worlds--i.e., worlds in which the animals in
the pen *are* zebras.



Smith describes two ways in which a belief can possess this property
of being reliable. One is that a belief that \(p\) has it in virtue of
the modal relationship with its basis \(e\). In this case, \(e\) is a
contributing reliable basis. Another possibility is when it is the
content of the belief that \(p\), rather than the belief's modal
relationship with its basis \(e\), that guarantees by itself the
belief's reliability. In this case, \(e\) is a non-contributing
reliable basis. An example of the first kind is \(s\)'s belief
that
 \(\rP\_3\),
 which is reliable because of its modal relationship with
 \(\rE\_3\).
 There are obviously many sufficiently normal worlds in which
\(\rP\_3\) is false, but no sufficiently normal world in which
\(\rP\_3\) is false and \(\rE\_3\) true. An example of the second kind
is \(s\)'s belief that
 \(\rQ\_3\)
 as based on \(\rE\_3\). It is this belief's content, and not its
modal relationship with \(\rE\_3\), that guarantees its reliability. As
Smith puts it, there are no sufficiently normal worlds in which
\(\rE\_3\) is true and \(\rQ\_3\) is false, but this is simply because
there are no sufficiently normal worlds in which \(\rQ\_3\) is
false.



According to Smith, a deductive inference from \(p\) to \(q\) fails to
transmit to \(q\) justification relative to \(p\)'s basis \(e\),
if \(e\) is a contributing reliable basis for believing \(p\) but is a
non-contributing reliable basis for believing \(q\). In this case the
inference fails to *explain* \(q\)'s reliability: if
\(s\) deduced one proposition from another, she would reliably believe
\(q\), but not--not even in part--in virtue of having
inferred \(q\) from \(p\) (as held on the basis of \(e)\).
*Zebra* fails to transmit to
 \(\rQ\_3\)
 justification relative to
 \(\rP\_3\)'s
 basis
 \(\rE\_3\)
 in this
 sense.[9]



Let's turn to Alspector-Kelly (2015). As we have seen,
Wright's analysis of failure of warrant transmission interprets
the epistemic good whose transmission is in question as, roughly, the
same as epistemic
 justification.[10]
 By so doing, Wright departs from Plantinga's (1993a, 1993b)
influential understanding of warrant as the epistemic quality that
(whatever it is) suffices to turn true belief into knowledge. One
might wonder, however, if there are deductive arguments incapable of
transmitting warrant in Plantinga's sense. (Hereafter we use
'warrant' only to refer to Plantinga's warrant.)
Alspector-Kelly answers this question affirmatively contending that
certain arguments cannot transmit warrant because the cognitive
project of establishing their conclusion via inferring it from their
premise is *procedurally self-defeating.*



Alspector-Kelly follows Wright (2012) in characterizing a cognitive
project as a pair of a question and a procedure that one executes to
answer the question. An *enabling condition* of a cognitive
project is, for Alspector-Kelly, any proposition such that, unless it
is true, one cannot learn the answer to its defining question by
executing the procedure associated with it. That a given object \(o\)
is illuminated, for example, is an enabling condition of the cognitive
project of determining its color by looking at it. For one cannot
learn by sight that \(o\) is of a given color unless \(o\) is
illuminated.



Enabling conditions can be *opaque*. An enabling condition of a
cognitive project is opaque, relative to some actual or possible
result, if it is the case that whenever the execution of the
associated procedure yields this result, it would have produced the
same result had the condition been unfulfilled. The enabling condition
that \(o\) be illuminated of the cognitive project just considered is
not opaque, since looking at \(o\) never produces the same response
about \(o\)'s color when \(o\) is illuminated and when it
isn't. (In the second case, it produces *no*
response.)



Now consider the cognitive project of establishing by sight whether
 (\(\rP\_3)\)
 the animals enclosed in the pen are zebras. An enabling condition of
this project states that
 (\(\rQ\_3)\)
 the animals in the pen are not mules disguised to look like zebras.
For one couldn't learn whether \(\rP\_3\) is true by looking, if
\(\rQ\_3\)were true. \(\rQ\_3\) is opaque with respect to the possible
outcome that \(\rP\_3\). In fact, suppose \(\rQ\_3\) is satisfied
because the pen contains (undisguised) zebras. In this case, looking
at them will attest they are zebras, and the execution of the
procedure associated with this project will yield the outcome that
\(\rP\_3\). But this is exactly the outcome that would be generated by
the execution of the same procedure if \(\rQ\_3\) were *not*
satisfied. In this case too, looking at the animals would produce the
response that \(\rP\_3\).



We can now elucidate the notion of a *procedurally
self-defeating* cognitive project. The distinguishing feature of
any project of this type is that it seeks to answer the question
whether an *opaque* enabling condition--call it
'\(q\)'--of the project itself is fulfilled. A
project of this type has the defect that it necessarily produces the
response that \(q\) is fulfilled when \(q\) is unfulfilled. Given
this, it is intuitive that it cannot yield warrant to believe
\(q\).



As an example of a procedurally self-defeating project, consider
trying to answer the question whether your informant is sincere by
asking *her* this very question. Your informant's being
sincere is an enabling condition of the very project you are carrying
out. If your informant were not sincere, you couldn't learn
anything from her. This condition is also opaque with respect to the
possible response that she is sincere. For your informant would
respond that she is sincere both in case she is so and in case she
isn't. Since the execution of this project is guaranteed to
yield the result that your informant is sincere when she isn't,
it is intuitive that it cannot yield warrant to believe that the
informant is sincere.



Alspector-Kelly contends that arguments like *Zebra*
don't transmit warrant because the cognitive project of
determining inferentially whether their conclusion is true is
procedurally self-defeating in the sense advertised. Let's apply
the explanation to *Zebra*.



Imagine you carry out *Zebra*. This initially commits you to
executing the project of establishing whether
 \(\rP\_3\)
 by looking. Suppose you get
 \(\rE\_3\)
 and hence \(\rP\_3\) as an outcome. As we have seen,
 \(\rQ\_3\)
 is an opaque enabling condition relative to the outcome \(\rP\_3\) of
the cognitive project you have executed. Imagine that now, having
received \(\rP\_3\) as a response to your first question, you embark in
the second project which carrying out *Zebra* commits you to:
establishing whether \(\rQ\_3\) is true by inference from \(\rP\_3\).
This project appears doomed.



\(\rQ\_3\)
 is an enabling condition of the initial project of determining
whether
 \(\rP\_3\),
 which is opaque with respect to the very *premise* \(\rP\_3\).
It follows from this that \(\rQ\_3\) is also an enabling condition of
the second project. For if \(\rQ\_3\) were unfulfilled, you
couldn't learn \(\rP\_3\) and, *a fortiori,* you
couldn't learn anything else--\(\rQ\_3\) included--by
inference from \(\rP\_3\). Another consequence is that \(\rQ\_3\) is an
enabling condition of the second project that is *opaque*
relative to the very outcome that \(\rQ\_3\). Suppose first that
\(\rQ\_3\) is true and that, having visually inspected the pen, you
have verified \(\rP\_3\). You then execute the inferential procedure
associated with the second project and produce the outcome that
\(\rQ\_3\). Now consider the case in which \(\rQ\_3\) is false. Looking
into the pen still generates the outcome that \(\rP\_3\) is true. Thus,
when you execute the procedure associated with the second project, you
still infer that \(\rQ\_3\) is true. Since you would get the result
that \(\rQ\_3\) is true even if \(\rQ\_3\) were false, the second
project is procedurally self-defeating. In conclusion, carrying out
*Zebra* commits you to executing a project that cannot generate
warrant for believing its conclusion \(\rQ\_3\). This explanation of
non-transmissivity generalizes to all structurally similar
arguments.


## 4. Applications



The notions of transmissive and non-transmissive argument, above and
beyond being investigated for their own sake, have been put to work in
relation to specific philosophical problems and issues. An important
problem is whether Moore's infamous proof of an external world
is successful, and whether so are structurally similar Moorean
arguments directed against the perceptual skeptic and--more
recently--the non-believer. Another issue pertains to the
solution of McKinsey paradox. A third issue concerns
Boghossian's (2001, 2003) explanation of our logical knowledge
via implicit definitions, criticized as resting on a non-transmissive
argument schema (see for instance Ebert 2005 and Jenkins 2008). As the
debate focusing on the last topic is only at an early stage of its
development, it is preferable to concentrate on the first two, which
will be reviewed in respectively
 Sect. 4.1
 and
 Sect. 4.2
 below.


### 4.1 Moorean Proofs, Perceptual Justification and Religious Justification



Much of the contemporary debate on Moore's proof of an external
world (see Moore 1939) is interwoven with the topic of epistemic
transmission and its failure. Moore's proof can be reconstructed
as follows:



*Moore*

\(\rE\_8\).
 My experience is in all respects as of a hand held up in front of
my face.
\(\rP\_8\).
 Here is a hand.


Therefore:



\(\rQ\_8\).
 There is a material world (since any hand is a material object
existing in space).



Evidence
 \(\rE\_8\)
 in *Moore* is constituted by a proposition *believed*
by \(s\). One might suggest, however, that this is a misinterpretation
of Moore's proof (and variants of it that we shall consider
shortly). One might argue that what is meant to give \(s\)
justification for believing
 \(\rP\_8\)
 is \(s\)'s *experience* of a hand. Nevertheless, most of
the epistemologists participating in this debate implicitly or
explicitly assume that one's experience as if \(p\) and
one's belief that one has an experience as if \(p\) have the
same justifying power (cf. White 2006 and Silins 2007).



Many philosophers find Moore's proof unsuccessful. Philosophers
have proposed explanations of this impression according to which
*Moore* is non-transmissive in some of the senses described in
 Sect. 3
 (see mainly Wright 1985, 2002, 2007 and
 2011).[11] A different explanation is that Moore's proof does
transmit justification but is dialectically ineffective (see mainly
Pryor 2004).



According to Wright, there exist *cornerstone propositions* (or
simply *cornerstones*), where \(c\) is a cornerstone for an
area of discourse \(d\) just in case for any proposition \(p\)
belonging to \(d, p\) could not be justified for any subject \(s\) if
\(s\) had no independent justification for accepting \(c\) (see mainly
Wright
 2004).[12]
 Cornerstones for the area of discourse about perceivable things are
for instance the *logical negations of skeptical conjectures*,
such as the proposition that one's experiences are nothing but
one's hallucinations caused by a Cartesian demon or the Matrix.
Wright contends that the conclusion
 \(\rQ\_8\)
 of *Moore* is also a cornerstone for the area of discourse
about perceivable things. Adapting terminology introduced by Pryor
(2004), Wright's conception of the architecture of perceptual
justification thus treats \(\rQ\_8\) *conservatively* with
respect to any perceptual hypothesis \(p\): if \(s\) had no
independent justification for \(\rQ\_8\), no proposition \(e\)
describing an apparent perception could supply \(s\) with *prima
facie* justification for any perceptual hypothesis \(p\). It
follows from this that *Moore* instantiates the
*information-dependence template* considered in
 Sect. 3.2.
 For \(\rQ\_8\) is part of the collateral information which \(s\) needs
independent justification for if \(s\) is to receive some
justification for
 \(\rP\_8\)
 from
 \(\rE\_8\).
 Hence *Moore* is non-transmissive (see mainly Wright 2002).
Note that the thesis that Moore's proof is epistemologically
useless because non-transmissive in this sense is compatible with the
claim that by learning \(\rE\_8, s\) does acquire a justification for
believing \(\rP\_8\). For instance, Wright (2004) contends that we all
have a special kind of *non-evidential* justification, which he
calls *entitlement*, for accepting \(\rQ\_8\) as well as other
cornerstones in
 general.[13]
 So, by learning \(\rE\_8\) we do acquire justification for \(\rP\_8\).
Wright's analysis of Moore's proof and Wright's
conservatism have mostly been criticized in conjunction with his
theory of entitlement. A presentation of these objections is beyond
the scope of this entry. (See however Davies 2004; Pritchard 2005;
Jenkins 2007. For a defense of Wright's views see for instance
Neta 2007 and Wright 2014.)



As anticipated, other philosophers contend that Moore's proof
does transmit justification and that its ineffectiveness has a
different explanation. An important conception of the architecture of
perceptual justification, called *dogmatism* in Pryor (2000,
2004), embraces a generalized form of *liberalism* about
perceptual justification. This form of liberalism is opposed to
Wright's *conservatism*, and claims that to have
*prima facie* perceptual justification for believing \(p\) from
an apparent perception that \(p, s\) doesn't need independent
justification for believing the negation of skeptical conjectures or
non-perceiving hypotheses like \(\notQ\_8\). This is so, for the
dogmatist, because our experiences give us *immediate* and
*prima facie* justification for believing their contents.
Saying that perceptual justification is immediate is saying that it
doesn't presuppose--not even in part--justification
for anything else. Saying that justification is prima facie is saying
that it can be defeated by additional evidence. Our perceptual
justification would be defeated, for example, by evidence that a
relevant non-perceiving hypothesis is true or just as probable as its
negation. For instance, \(s\)'s perceptual justification for
\(\rP\_8\) would be defeated by evidence that \(\notQ\_8\) is true, or
that
 \(\rQ\_8\)
 and \(\notQ\_8\) are equally probable. On this point the dogmatist and
Wright do agree. They disagree on whether \(s\)'s perceptual
justification for
 \(\rP\_8\)
 requires independent justification for believing or accepting
\(\rQ\_8\). The dogmatist denies that \(s\) needs that independent
justification. Thus, according to the dogmatist, Moore's proof
*transmits* the perceptual justification available for its
premise to the
 conclusion.[14]



The dogmatist argues (or may argue), however, that Moore's proof
is *dialectically* flawed (cf. Pryor 2004). The contention is
that Moore's is unsuccessful because it is useless for the
purpose to convince the idealist or the external world skeptic that
there is an external (material) world. In short, neither the idealist
nor the global skeptic believes that there is an external world. Since
they don't believe
 \(\rQ\_8\),
 they are rationally required to distrust any *perceptual*
evidence offered in favor of
 \(\rP\_8\)
 in the first instance. For this reason they both will reject
Moore's proof as one based on an unjustified
 premise.[15]
 Moretti (2014) suggests that the dogmatist could alternatively
contend that Moore's proof is non-transmissive because
\(s\)'s experience of a hand gives \(s\) *immediate*
justification for believing both the premise \(\rP\_8\) and the
*conclusion* \(\rQ\_8\) of the proof at once. According to this
diagnosis, Moore's proof is *epistemically* flawed
because it instantiates a variant of *indirectness* (in which
the evidence is an *experience* of a hand). Pryor's
analysis of Moore's proof has principally been criticized in
conjunction with his liberalism in epistemology of perception. (See
Cohen 2002, 2005; Schiffer 2004; Wright 2007; White 2006; Siegel &
Silins 2015.)



Some authors (e.g., Wright 2003; Pryor 2004; White 2006; Silins 2007;
Neta 2010) have investigated whether certain *variants* of
Moore are transmissive of justification. These arguments start from a
premise like
 \(\rP\_8\),
 describing a (supposed) perceivable state of affairs of the external
world, and deduce from it the logical negation of a relevant
*skeptical conjecture*. Consider for example the variant of
*Moore* that starts from \(\rP\_8\) and replaces
 \(\rQ\_8\)
 with:



\(\rQ\_8^\*\).
 It is not the case that I am a handless brain in a vat fed with
the hallucination of a hand held up in front of my face.


Let's call *Moore\** this variant of
 *Moore*.
 While dogmatists *a la* Pryor argue that
*Moore\** is transmissive but dialectically flawed (cf. Pryor
2004), conservatives *a la* Wright contend that it is
non-transmissive (cf. Wright 2007). Although it remains very
controversial whether or not *Moore* is transmissive,
epistemologists have found some *prima facie* reason to think
that arguments like *Moore\** are non-transmissive.



An important difference between *Moore* and *Moore\** is
this: whereas the logical negation of
 \(\rQ\_8\)
 does *not* explain the evidential statement
 \(\rE\_8\)
 ("My experience is in all respects as of a hand held up in
front of my face") adduced in support of
 \(\rP\_8\),
 the logical negation of
 \(\rQ\_8^\*\)--\(\notQ\_8^\*\)--somewhat
 *explains* \(\rE\_8\). Since \(\notQ\_8^\*\) provides a potential
explanation of \(\rE\_8\), is it intuitive that \(\rE\_8\) is
*evidence* (perhaps very week) for believing \(\notQ\_8^\*\). It
is easy to conclude from this that \(s\) cannot acquire justification
for believing \(\rQ\_8^\*\) via transmission through *Moore\**
upon learning \(\rE\_8\). For it is intuitive that if this were the
case, \(\rE\_8\) should count as evidence for \(\rQ\_8^\*\). But this is
impossible: one and the same proposition cannot simultaneously be
evidence for a hypothesis and its logical negation. By formalizing
intuitions of this type, White (2006) has put forward a simple
Bayesian argument to the effect that *Moore\** and similar
variants of *Moore* are not transmissive of
 justification.[16]
 (See Silins 2007 for discussion. For responses to White, see
Weatherson 2007; Kung 2010; Moretti 2015.)



From the above analysis it is easy to conclude that the
*information-dependence template* is satisfied by
*Moore\** and akin proofs. In fact note that if
 \(\rE\_8\)
 is evidence for both
 \(\rP\_8\)
 and \(\notQ\_8^\*\), it seems correct to say that \(s\) can acquire a
justification for believing \(\rP\_8\) only if \(s\) has independent
justification for *disbelieving* \(\notQ\_8^\*\) and thus
*believing* \(\rQ\_8^\*\). Since \(\notQ\_8^\*\) counts as a
*non-perceiving* hypothesis for Pryor, this gives us a reason
to doubt dogmatism (cf. White
 2006).[17]



Coliva (2012, 2015) defends a view--baptized by her
*moderatism*--that aims to be a middle way between
Wright's conservatism and Pryor's dogmatism. The moderate
contends--against the conservative--that cornerstones cannot
be justified and that to possess perceptual justification \(s\) needs
no justification for accepting any cornerstones. On the other hand,
the moderate claims--against the dogmatist--that to possess
perceptual justification \(s\) needs to *assume* (without
justification) relevant
 cornerstones.[18]
 By relying on her variant of the *information-dependent
template* described in
 Sect. 3.2,
 Coliva concludes that neither *Moore* nor any proof like
*Moore\** is transmissive. (For a critical discussion of
moderatism see Avnur 2017; Baghramian 2017; Millar 2017; Volpe 2017;
Coliva 2017.)



Epistemological disjunctivists like McDowell and Pritchard have argued
that in paradigmatic cases of perceptual knowledge, what is meant to
give \(s\) justification for believing
 \(\rP\_8\)
 is, not
 \(\rE\_8\),
 but \(s\)'s factive state of seeing that \(\rP\_8\). This seems
to have consequences for the question whether *Moore\**
transmits propositional justification. Pritchard explicitly defends
the claim that when \(s\) sees that \(\rP\_8\), thereby learning that
\(\rP\_8, s\) can come to know by inference from \(\rP\_8\) the negation
of any skeptical hypothesis inconsistent with \(\rP\_8\), like
 \(\rQ\_8^\*\)
 (cf. Pritchard 2012a: 129-30). This may encourage the belief
that, for Pritchard, *Moore\** can transmit the justification
for \(\rP\_8\), based on *s'*s seeing that \(\rP\_8\), to
\(\rQ\_8^\*\) (see Lockhart 2018 for an explicit argument to this
effect). This claim must however be handled with some care.



As we have seen in
 Sect. 2,
 Pritchard contends that when one knows \(p\) on the basis of evidence
\(e\), one can know \(p\)'s consequence \(q\) by inference from
\(p\) only if \(e\) sufficiently supports \(q\). For Pritchard this
condition is met when \(s\)'s support for believing
 \(\rP\_8\)
 is constituted by \(s\)'s seeing that \(\rP\_8, s\)'s
epistemic situation is objectively good (i.e., \(s\)'s cognitive
faculties are working properly in a cooperative environment) and the
skeptical hypothesis ruled out by
 \(\rQ\_8^\*\)
 has not been epistemically motivated. For, in this case, \(s\) has a
reflectively accessible *factive* support for believing
\(\rP\_8\) that *entails*--and so sufficiently
supports--\(\rQ\_8^\*\). Thus, in this case, nothing stands in the
way of \(s\) competently deducing \(\rQ\_8^\*\) from \(\rP\_8\), thereby
coming to know \(\rQ\_8^\*\) on the basis of \(\rP\_8\).



If upon *deducing* one proposition from another, \(s\) comes to
justifiably believe
 \(\rQ\_8^\*\)
 for the first-time, the inference from
 \(\rP\_8\)
 to \(\rQ\_8^\*\) presumably transmits *doxastic* justification.
(See the supplement on
 Transmission of Propositional Justification *versus* Transmission of Doxastic Justification.)
 It is more dubious, however, that when \(s\)'s support for
\(\rP\_8\) is constituted by \(s\)'s seeing that \(\rP\_8\),
*Moore\** is also transmissive of *propositional*
justification. For instance, one might contend that *Moore\** is
non-transmissive because it instantiates the *disjunctive
template* described in
 Sect. 3.2
 (cf. Wright 2002). To start with, \(\rP\_8\) entails \(\rQ\_8^\*\), so
 (D1)
 is satisfied. Let \(\rR^{\*}\_{\textit{Moore}}\) be the proposition
that this is no hand but \(s\) is victim of a hallucination of a hand
held up before her face. Since \(\rR^{\*}\_{\textit{Moore}}\) would be
true if \(\rQ\_8^\*\) were false,
 (D4)
 is also satisfied. Furthermore, take the grounds of \(s\)'s
justification for \(\rP\_8\) to be \(s\)'s seeing that \(\rP\_8\).
Since this experience is a state for \(s\) indistinguishable from one
in which \(\rR^{\*}\_{\textit{Moore}}\) is true,
 (D2)
 is also satisfied. Finally, it might be argued that the proposition
that one is not hallucinating is a presupposition of the cognitive
project of learning about one's environment through perception.
It follows that \(\rR^{\*}\_{\textit{Moore}}\) is incompatible with a
presupposition of \(s\)'s cognitive project of learning about
one's environment through perception. Thus
 (D3\(^{\*}\))
 appears fulfilled too. So, *Moore\** won't transmit the
justification that \(s\) has for \(\rP\_8\) to \(\rQ\_8^\*\).



To resist this conclusion, a disjunctivist might insist that
*Moore\**, relative to \(s\)'s support for
 \(\rP\_8\)
 supplied by \(s\)'s seeing that \(\rP\_8\), doesn't always
instantiate the *disjunctive template* because
 (D2)
 isn't necessarily fulfilled (cf. Lockhart 2018.) By invoking a
distinction drawn by Pritchard (2012a), one might contend that (D2)
isn't necessarily fulfilled because \(s\), though unable to
introspectively discriminate seeing that \(\rP\_8\) from hallucinating
it, may have evidence that favors the hypothesis that she is in the
first state, which makes the state reflectively accessible. For
Pritchard, this happens--as we have seen--when \(s\) sees
that \(\rP\_8\) in good epistemic conditions and the skeptical
conjecture that \(s\) is having a hallucination of a hand hasn't
been epistemically motivated. In this case, \(s\) can come to know
 \(\rQ\_8^\*\)
 by inference from \(\rP\_8\) even if she is unable to introspectively
discriminate one situation from the other.



Pritchard's thesis that, in good epistemic conditions,
\(s\)'s factive support for believing
 \(\rP\_8\)
 coinciding with \(s\)'s seeing that \(\rP\_8\) is reflectively
accessible is controversial (cf. Piazza 2016 and Lockhart 2018). Since
this thesis is essential to the contention that *Moore\** may
not instantiate the *disjunctive template* and may thus be
transmissive of propositional justification, the latter contention is
also controversial.



So far we have focused on perceptual justification. Now let's
switch to *religious* justification. Shaw (2019) aims to
motivate a view in religious epistemology--he contends that the
'theist in the street', though unaware of the traditional
arguments for theism, can find independent rational support for
believing that God exists through proofs for His existence. These
proofs are based on religious experiences and parallel in structure
Moore's proof of an external world interpreted as having the
premise supported by an experience.



A Moorean proof for the existence of God is one that deduces a belief
that God exists from what Alston (1991) calls a 'manifestation
belief' (M-belief, for short). An M-belief is a belief based
non-inferentially on a corresponding mystical experience. Typical
M-beliefs are about God's acts toward a given subject at a given
time: for example, beliefs about God's bringing comfort to me,
reproving me for some wrongdoing, or demonstrating His love for me,
and so on. Here is Moorean proof for the existence of God:



*God*

\(\rP\_9\).
 God is comforting me just now.


Therefore:



\(\rQ\_9\).
 God exists.



Note that the 'good' case in which my experience that
 \(\rP\_9\)
 is veridical has a corresponding, subjectively indistinguishable,
'bad' case, in which it only seems to me that \(\rP\_9\)
because I'm suffering from a delusional religious experience. A
concern is, therefore, that *God* may instantiate the
*disjunctive template*. In this case, my experience as if
\(\rP\_9\) could actually justify \(\rP\_9\) only if I had independent
justification for
 \(\rQ\_9\)
 (cf. Pritchard 2012b). If so, *God* isn't
transmissive.



Shaw (2019) concedes that
 *God*
 is dialectically ineffective. To defend its transmissivity, he
appeals to religious epistemological disjunctivism, which says that an
M-belief that \(p\) can enjoy infallible rational support in virtue of
one's *pneuming* that \(p\), where this mental state is
both factive and accessible on reflection. Shaw intends
'pneuming that \(p\)' to stand as a kind of
religious-perceptual analogue to 'seeing that \(p\)' (cf.
Shaw 2016, 2019). When it comes to *God*, my belief that
\(\rP\_9\) is supposed to be justified by my pneuming that God is
comforting me just now. As we have seen in the case of
*Moore\**, a worry is that conceiving of the justification for
\(\rP\_9\) along epistemological disjunctivist lines may not suffice to
exempt *God* from the charge of instantiating the
*disjunctive template* and being thus non-transmissive.


### 4.2 McKinsey's Paradox



McKinsey (1991, 2002, 2003, 2007) has offered a reductio argument for
the incompatibility of first-person privileged access to mental
content and externalism about mental content. The privileged access
thesis roughly says that it is necessarily true that if \(s\) is
thinking that \(x\), then \(s\) can in principle know *a
priori* (or in a non-empirical way) that she is thinking that
\(x\). Externalism about mental content roughly says that predicates
of the form 'is thinking that \(x\)'--e.g., 'is
thinking that water is wet'--express properties that are
*wide*, in the sense that possession of these properties by
\(s\) logically or conceptually implies the existence of relevant
contingent objects external to \(s\)'s mind--e.g., water.
McKinsey argues that \(s\) may reason along these lines:



*Water*

\(\rP\_{10}\).
 I am thinking that water is wet.
\(\rP\_{11}\).
 If I am thinking that water is wet, then I have (or my linguistic
community has) been embedded in an environment that contains
water.


Therefore:



\(\rQ\_{10}\).
 I have (or my linguistic community has) been embedded in an
environment that contains water.



*Water* produces an absurdity. If the privileged access thesis
is true, \(s\) knows
 \(\rP\_{10}\)
*non-empirically*. If semantic externalism is true, \(s\)
knows
 \(\rP\_{11}\)
*a priori* by conceptual analysis. Since \(\rP\_{10}\) and
\(\rP\_{11}\) do entail
 \(\rQ\_{10}\)
 and knowledge is presumably closed under known entailment, \(s\)
knows \(\rQ\_{10}\)--which is an *empirical*
proposition--by simply competently deducing it from \(\rP\_{10}\)
and \(\rP\_{11}\) and without conducting any *empirical
investigation*. Since this is absurd, McKinsey concludes that the
privileged access thesis or semantic externalism must be false.



One way to resist McKinsey's *incompatibilist* conclusion
that the privileged access thesis and externalism about mental content
cannot be true together is to argue that
 *Water*
 is non-transmissive. Since knowledge is presumably closed under known
entailment, it remains true that \(s\) cannot know
 \(\rP\_{10}\)
 and
 \(\rP\_{11}\)
 while failing to know
 \(\rQ\_{10}\).
 However, McKinsey's paradox originates from the stronger
conclusion--motivated by the claim that *Water* is a
deductively valid argument featuring premises knowable
non-empirically--that \(s\), by running *Water*, could
know *non-empirically* the *empirical* proposition
\(\rQ\_{10}\) that she or members of her community have had contact
with water. This is precisely what could not happen if *Water*
is non-transmissive: in this case \(s\) couldn't learn
\(\rQ\_{10}\) on the basis of her non-empirical justification for
\(\rP\_{10}\) and \(\rP\_{11}\), and her knowledge of the entailment
between \(\rP\_{10}\), \(\rP\_{11}\), and \(\rQ\_{10}\) (see mainly
Wright 2000, 2003,
 2011).[19]



A first possibility to defend the thesis that *Water* is
non-transmissive is to argue that it instantiates the *disjunctive
template* (considered in
 Sect. 3.2)
 (cf. Wright 2000, 2003, 2011). If *Water* is non-transmissive,
\(s\) could acquire a justification for, or knowledge of,
 \(\rP\_{10}\)
 and
 \(\rP\_{11}\)
 only if \(s\) had an *independent* justification for, or
knowledge of,
 \(\rQ\_{10}\).
 (And to avoid the absurd result that McKinsey recoils from, this
independent justification should be empirical.) If this diagnosis is
correct, one need not deny \(\rP\_{10}\) or \(\rP\_{11}\) to reject the
intuitively false claim that \(s\) could know the empirical
proposition \(\rQ\_{10}\) in virtue of only non-empirical
knowledge.



To substantiate the thesis that *Water* instantiates the
*disjunctive template* one should first emphasize that the kind
of externalism about mental content underlying \(\rP\_{10}\) is
compatible with the possibility that \(s\) suffers from illusion of
content. Were this to happen with \(\rP\_{10}, s\) would seem to
introspect that she believes that water is wet whereas there is
nothing like that content to be believed by \(s\) in the first
instance. Consider:



\(\rR\_{\textit{water}}\).
 'water' refers to *no* natural kind so that
there is *no* content expressed by the sentence 'water is
wet'.


\(s\)'s state of having introspective justification for
believing
 \(\rP\_{10}\)
 is arguably subjectively indistinguishable from a situation in which
\(\rR\_{\textit{water}}\) is true. Thus condition
 (D2)
 of the *disjunctive template* is met. Moreover,
\(\rR\_{\textit{water}}\) appears incompatible with an obvious
presupposition of \(s\)'s cognitive project of attaining
introspective justification for believing \(\rP\_{10}\), at least if
the content that water is wet embedded in \(\rP\_{10}\) is constrained
by \(s\) or her linguistic community having being in contact with
water. Thus condition
 (D3\(^{\*}\))
 is also met. Furthermore, \(\rP\_{10}\) entails \(\rQ\_{10}\) (when
\(\rP\_{11}\) is in background information). Hence, condition
 (D1)
 is fulfilled. If one could also show that
 (D4)
 is satisfied in *Water*, in the sense that if \(\rQ\_{10}\)
were false \(\rR\_{\textit{water}}\) would be true, one would have
shown that the *disjunctive template* is satisfied by
*Water*. Wright (2000) takes (D4) to be fulfilled and concludes
that the *disjunctive template* is satisfied by
*Water*.



Unfortunately, the claim that
 (D4)
 is satisfied in *Water* cannot easily be vindicated (cf.
Wright 2003). Condition (D4) is satisfied in *Water* only if it
is true that if \(s\) (or \(s\)'s linguistic community) had not
been embedded in an environment that contains *water*, the term
'water' would have referred to no natural kind. This is
true only if the closest possible world \(w\) in which this
counterfactual's antecedent is true is like Boghossian's
(1997) *Dry Earth*--namely, a world where no one has ever
had any contact with any kind of watery stuff, and all apparent
contacts with it are always due to multi-sensory hallucination. If
\(w\) is not *Dry Earth*, but Putnam's *Twin
Earth*, however, the counterfactual turns out false, as in this
possible world people usually have contact with some other watery
stuff that they call 'water'. So, in this world
'water' refers to a natural kind, though not to
H2O. Since determining which of *Dry Earth* or
*Twin Earth* is modally closer to the actual world (supposing
\(s\) is in the actual world)--and so determining whether (D4) is
satisfied in *Water*--is a potentially elusive task, the
claim that *Water* instantiates the *disjunctive
template* appears less than fully
 warranted.[20]



An alternative dissolution of McKinsey paradox--also based on a
diagnosis of non-transmissivity--seems to be available if one
considers the proposition that 



\(\rQ\_{11}\).
 \(s\) (or \(s\)'s linguistic community) has been embedded
in an environment containing some *watery substance* (cf.
Wright 2003 and 2011).


This alternative strategy assumes that
 \(\rQ\_{11}\),
 rather than
 \(\rQ\_{10}\),
 is a presupposition of \(s\)'s cognitive project of attaining
introspective justification for
 \(\rP\_{10}\).



Even if *Water* doesn't instantiate the *disjunctive
template*, a new diagnosis of what's wrong with
McKinsey's paradox could rest on the claim that the different
argument yielded by expanding *Water* with
 \(\rQ\_{11}\)
 as conclusion--call it *Water\**--instantiates the
*disjunctive template*. If
 \(\rR\_{\textit{water}}\)
 is the same proposition as above, it is easy to see that
*Water\** satisfies conditions
 (D4),
 (D2), and
 (D3\(^{\*}\))
 of the *disjunctive template*. Furthermore
 (D1)
 is satisfied at least in the sense that it seems *a priori*
that
 \(\rP\_{10}\)
 via
 \(\rQ\_{10}\)
 entails
 \(\rQ\_{11}\)
 (if
 \(\rP\_{11}\)
 is in background information) (cf. Wright 2011). On this novel
diagnosis of non-transmissivity, what would be paradoxical is that
\(s\) could earn justification for \(\rQ\_{11}\) in virtue of her
non-empirical justification for \(\rP\_{10}\) and \(\rP\_{11}\) and her
knowledge of the *a priori* link from \(\rP\_{10}\),
\(\rP\_{11}\) via \(\rQ\_{10}\) to \(\rQ\_{11}\). If one follows
Wright's (2003)
 suggestion[21]
 that \(s\) is *entitled* to accept \(\rQ\_{11}\)--namely,
the presupposition that there is a watery substance that provides
'water' with its extension--*Water* becomes
*innocuously* transmissive, and the apparent paradox
surrounding *Water* vanishes. This is so at least if one grants
that it is *a priori* that water is the watery stuff of our
actual acquaintance, once it is presupposed that there is any watery
stuff of our actual acquaintance. For useful criticism of responses of
this type to McKinsey's paradox see Sainsbury (2000), Pritchard
(2002), Brown (2003, 2004), McLaughlin (2003), McKinsey (2003), and
Kallestrup (2011).