Information is a rich commodity. It is perhaps the richest of themall. It is by now almost post-truistic that interested parties, fromindividuals, to large-scale globalised private actors and nationstates, will go to extraordinary lengths to protect and to acquireinformation. If we allow ourselves to engage in a little armchairetymology, then something’s being information is justfor it to to be non-random. Indeed this armchair etymology getsstraight to the heart of how it is that we often speak of information,as a contrast to randomisation. Indeed “signal-to-noiseratio” may be restated as “information-to-noiseratio”, hence the ubiquity of the refrain “That is notinformation, it is just noise”.

Another way of putting this is to say that information is a non-randomdistinction with a difference. Information supervenes on patterneddeviations, and getting information from one’s environmentdepends on one being able to recognise and exploit these patterns.That one part of our environment may carry information about anotherpart of our environment depends on our environment behaving inreliable, non-randomised way. Our ability to use information at onepart of our environment to access information at another part of itdepends not only on our ability to recognise patterned regularities,but on our ability to recognise connections between suchregularities.

For example, for us to access the distal information that there isfire from the proximal information that there is smoke, we must beaware of the correlation between smoke and fire. That we do is markedby maxims such as ”smoke means fire”. Such correlations ofnatural meaning between events in the world is studied by theMathematical Theory of Communication (MTC) due to Shannon and Weaver(see the entry oninformation). This is the “industry standard” account of information,as analysed by communications engineers. What of the informationencoded by natural language however? What of information in this moreconcretely semantic sense? A semantic conception of information willnot investigate the mere surprise value of a signal given thelikelihood of the signal itself (as does MTC). Instead, it willinvestigate the nature of the information carried by, or encoded bythe messages transmitted themselves. Another way of approaching theissue is to understand such semantic conceptions of information to beconcerned with the investigation of theinformational contentof a piece of language of some sort. Such pieces of languagemight be propositions, singular terms, descriptions, and so on.

The first theory of such a semantic conception of information that wasarticulated in detail was Bar-Hillel and Carnap’stheory ofsemantic information. It is fitting then that we start here insection 1. Insection 1.1 we will see how the theory of semantic information has someconsequences for certain types of statements, namely logical truthsand contradictions, that many have found counterintuitive. Insection 1.2 we will see how Floridi responds to these problems, as well howothers have extended and responded to Floridi’s proposal that weaccept theveridicality thesis—that information befactive. A number of such responses are motivated by realist andnaturalist considerations with regard to the ontology of semanticinformation. Insection 2 we will look at semantic conceptions of information that takenaturalist metaphysics seriously. Here we will see how Fodor, Dretske,Evans, Lewis, Recanati, and Jackson propose and defend semanticconceptions of information that turn on modes of presentation, andthat are broadly naturalist insofar as they attempt to subsumeinformation within causal relations of various sorts. Any causaltheory of meaning or knowledge will face the problem of accounting forthe meaning of, and our epistemic access to, abstract objects.

Most of the theories of broadly semantic information outlined insection 2 appeal to information channels in one sense or another (with achannel being a relation allowing information the flow from one stateto another). Insection 3 we will look at theories of information channels directly. (For adetailed examination of the formal properties of the theory ofinformation channels, as well as how it is that the theory connectswith other issues in logic and information more generally, see theentry onlogic and information.) We will see how the original theory of information channels due toBarwise and Perry emerged from Austin’s theory of semanticcontent, as well as how it is that the theory of information channelshas been developed and extended in order to give a semantics forinformation flow itself, as well as informational semantics fornatural language fragments and epistemic phenomena.

• 1. Bar-Hillel and Carnap’s Theory of Semantic Information
  • 1.1 Problems for the theory of semantic information
  • 1.2 Floridi’s theory of strongly semantic information
• 2. Information, Modes of Presentation, and Meaning
• 3. The Theory of Information Channels
  • 3.1 The semantics of information flow
  • 3.2 Modelling epistemic phenomena informationally
• 4. Summary
• Bibliography
• Academic Tools
• Other Internet Resources
• Related Entries

1. Bar-Hillel and Carnap’s Theory of Semantic Information

The most natural starting point for any overview of semanticconceptions of information is Carnap and Bar-Hillel’s “AnOutline of a Theory of Semantic Information” (1952). Bar Hilleland Carnap’s theory of semantic information is a quantitativetheory that emerged from more general theories of information (see section 4.2 on Shannon in the entry oninformation). Their theory was designed with the goal of giving us a usableframework for calculating theamount of semantic informationencoded by a sentence in a particular language. In their case thelanguage in question is monadic predicate logic. The philosophicaldetails are grounded on an idea that has come to be known as theinverse range principle (IRP). Loosely, IRP states that theamount of information carried or encoded by a sentence is inverselyproportional to something else, where this something else is somethingto which one can attach a precise numerical value. Once this has beendone, one can use this numerical value to calculate the measure ofsemantic information as understood by the theory of semanticinformation.

For Bar-Hillel and Carnap,the amount of semantic informationencoded by a sentence is inversely proportional to the likelihood ofthe truth of that sentence. So for them, the likelihood of truthis the “something else” to which we can attach a precisenumerical value. To illustrate, we start with their method ofcalculating a qualitative individuation of semantic information,content or “Cont”.

Where \(s\) is a sentence and \(W\) isthe set of all possible worlds, content is defined as follows:

Given that theintension of a sentence \(s\)is the set of all worlds in which the sentence iftrue, andthat the content of a sentence is the set of all worlds in which \(s\)isfalse, the intension and the content of asentence \(s\) form a partition on the set of allworlds \(W\).

Bar-Hillel and Carnap define two distinct methods forquantitative calculations of semantic information—acontent measure (cont), and aninformation measure(inf). They start with ana priori probability measure of asentence \(s\), \(p(s)\), which is gotten from anapriori distribution. Thea priori distribution onto \(W\)sums to 1, and we assume that all assignments areequiprobable, hence thea priori probability measure is thevalue of \(p(s)\) that results from this distribution. In this case,cont andinf can be defined as follows:

The two measures are required for technical reasons—in order tocapture additivity oncontent independence andinductiveindependence respectively. Two sentences \(s\) and\(s'\) are content independent when they do not have any worlds incommon. Two sentences \(s\) and \(s'\) are inductivelyindependent when the conditional probability of each sentence giventhe other is identical to their initial unconditional probability.Additivity on inductive independence fails for cont, since it might bethe case that \(\tcont(s\wedge s') \neq \tcont(s) + \tcont(s')\) onaccount of \(p(s)\) and \(p(s')\) having worlds in common—thatis, on account of them not being content independent in spite of theirbeing inductively independent. For additivity to hold on cont, it iscontent independence, as opposed to inductive independencethat is required. By contrast, additivity on inductive independencedoes not fail for inf. Bar-Hillel and Carnap’s proof isnon-trivial (found on their 1952: 244–5).

1.1 Problems for the theory of semantic information

Technical matters aside, some philosophical issues are immediate.Firstly, how do we know in practice how many possible words there are?If we are talking about the number of possible worlds with respect toall possible sentences in English, then there will be infinitely manyof them. Bar-Hillel and Carnap avoided this issue by talkingexclusively about the semantic information encoded by sentencesformulated in monadic predicate logic with a finite number ofpredicate letters. Where there are \(n\) predicateletters, there will be \(2^n\) possible objects, exhausting allpossible predicate combinations. There will then be \(2^{2^n}\)possible worlds (“state descriptions” in Bar-Hillel andCarnap’s parlance), corresponding to all possible combinationsof possible objects. Hintikka (1970, 1973), extended Bar-Hillel andCarnap’s theory of semantic information from monadic predicatelogic to fully general predicate logic.

Thirdly and more generally, Bar-Hillel and Carnap’s theory ofsemantic information has give rise to two problems of strongsignificance philosophically.

• The Bar-Hillel and Carnap Semantic Paradox (BCP)
• The Scandal of Deduction (SOD)

BCP refers to the fact that Bar-Hillel and Carnap’s theory ofsemantic information assigns maximal information to contradictorysentences. Where \(\perp\) is an arbitrary contradiction, given that\(\perp\) will be false in all possible worlds, we have the followingvia(1),(2), and(3) respectively:

Bar-Hillel and Carnap (1952: 229) responded to this situation asfollows:

It might perhaps, at first, seem strange that a self-contradictorysentence, hence one which no ideal receiver would accept, is regardedas carrying with it the most inclusive information. It should,however, be emphasised that semantic information is here not meant asimplying truth. A false sentence which happens to say much is therebyhighly informative in our sense. Whether the information it carries istrue or false, scientifically valuable or not, and so forth, does notconcern us. A self-contradictory sentence asserts too much; it is tooinformative to be true.

There are two dimensions to this response that have caused concern inphilosophical circles. The first is that their notion of semanticinformation isnon-factive—semantic information doesnot need to be true. The second is that they are taking their notionof semantic information to underpin informativeness in somenon-trivial sense.

SOD refers to the fact philosophical accounts of information are yetto give an account of the informativeness of logical truths anddeductive inferences. Bar-Hillel and Carnap’s theory of semanticinformation assigns minimal information to logical truths (and validdeductive inferences can be transformed into logical truths byconjoining the premises into an antecedent of a conditional that takesthe conclusion as its consequent). Where \(\top\) is an arbitrarytautology, given that \(\top\) will be false in all possible worlds,we have the following via(1),(2), and(3) respectively:

With respect to logically true sentences returning a minimalinformation value, Bar-Hillel and Carnap (1952: 223) respond asfollows:

This, however, is by no means to be understood as implying that thereis no good sense of ‘amount of information’ in which theamount of information of these sentences will not be zero at all, andfor some people, might even be rather high. To avoid ambiguities, weshall use the adjective ‘semantic’ to differentiate boththe presystematic sense of ‘information’ in which we areinterested at the moment and their systematic explicata from othersenses (such as “amount of psychological information for theperson P”) and their explicata.

We will return to SOD briefly insection 3.2 below. Note here however that Hintikka (1970, 1973) mounted atechnically heroic if ultimately unsuccessful attempt to solve it (seeSequoiah-Grayson (2008)), and for a properly detailed investigation,see the entry onlogic and information. For now we must recognise that the response of Bar-Hillel and Carnapabove brings with it some noteworthy philosophical claims of its own.Firstly, Bar-Hillel and Carnap are suggesting that the type ofinformation which is encoded by logical truths and for which theamount encoded is non-zero, is psychological in some sense or other.Furthermore, it may vary for one person from the other even withrespect to the same logical truth. Secondly, they are heeding thefollowing advice of Claude Shannon, the originator of the mathematicaltheory of communication, given just two years earlier.

The word ‘information’ has been given different meaningsby various writers in the general field of information theory. It islikely that at least a number of these will prove to be useful incertain applications to deserve further study and permanentrecognition. It is hardly to be expected that a single concept ofinformation would satisfactorily account for the numerous possibleapplications of the general field. (1950 [1993: 180]).

Shannon is advocating a richinformational pluralism, for adetailed development of which see Allo (2007). Shannon’s adviceon this point was, as we are about to see, nothing if notprescient.

1.2 Floridi’s theory of strongly semantic information

Luciano Floridi’s theory ofstrongly semanticinformation (2004, 2005), is a response to BCP motivated by thebelief that something has gone essentially amiss with Bar-Hillel andCarnap’s theory. The suspicion is that their theory is based ona semantic principle that is too weak,namely that truth-valuesare independent of semantic information. Floridi’s proposalis that an approach according to which semantic information is factivecan avoid the paradox, and that the resulting theory is more in linewith our ordinary conception of what generally counts as information.The line of argument is that a theory of strongly semanticinformation, based on alethic and discrepancy values rather thanprobabilities, can successfully avoid BCP. Relatedly, see Bremer andCohnitz (2004: chap. 2) for an overview of Floridi’s theory tobe described below, and Sequoiah-Grayson (2007) for a defence of thetheory of strongly semantic information against independent objectionsfrom Fetzer (2004) and Dodig-Crnkovic (2005).

Before we expound Floridi’s approach, note that some haveproposed a different alethic approach, one that uses truthlikeness, orverisimilitude, to explicate the notion of semanticinformation—Frické (1997), Cevolani (2011, 2014), andD’Alfonso (2011). Typically these seek to identify factualinformation with likeness to the complete truth about all empiricalmatters or about some restricted relevant domain of factual interest.These also avoid the BCP, and also do not use probabilities. However,truthlikeness is different from truth itself in as much as a truthbearer can be truth-like without actually being true, i.e., whilebeing false, so that verisimilitude accounts of information can permitthat false claims may possess information. Indeed false statements cansometimes carry more information than their true negations on thisaccount, see Frické (1997).

By contrast, Floridi’s strongly semantic factive information isdefined as well-formed, meaningful, andtruthful data. Thislatter factivity constraint on semantic information has come to beknown commonly as theveridicality thesis (VT) (prefigured inMingers (1995, 1996a, 1996b)). Importantly, versions of VT arise indebates about the ontological status of information in general, notmerely with regard to semantic information in particular—seeDretske (1981) for a classic example. Once the content is so defined,the quantity of strongly semantic information in a proposition \(p\)is calculated in terms of the distance of \(p\)from a situation \(z\) (wheresituations are partial or incomplete worlds) that \(p\)is supposed to model.

When \(p\) is true in all cases, but also when \(p\)is false in all cases, there is maximal distance (asopposed to maximal closeness) between \(p\) and thesituation \(z\) that \(p\) is supposedto model. By contrast,maximum closeness is equivalent to theprecise modelling of \(z\) at the agreed level ofabstraction or descriptive adequacy.Maximal distance in thedirection of truth will result in \(p\) being true inall cases in which case \(p = \mathord{\top}\) and is minimallyinformative. Similarly, maximal distance in the direction of falsityresults in \(p\) being false in all cases (all possiblesituations or probability 0) in which case \(p = \mathord{\perp}\) andis minimally informative also. The important difference here is thatany distance in this direction is distancebereft of stronglysemantic information entirely. This is on account of distance inthe direction of “the false” violating the factivitycondition on strongly semantic information.

Floridi distinguishesinformativeness from strongly semanticinformation itself. This is welcome, since strongly semanticinformation is factive, whereas false statements can still beinformative. Indeed a false statement \(s\) may bemore informative than a true statement \(s'\), in spite ofthe fact that \(s'\) carries strongly semantic information whereas \(s\)does not. By way of example, suppose that you arerunning a catering contract for an event, and that there will in factbe exactly 200 people in attendance. Suppose that \(s\)isthere will be 201 people in attendance, and \(s'\) isthere will be between 100 and 200 people in attendance.\(s'\) is true whilst \(s\) is false, but \(s\)is more informative than \(s'\) on any naturalunderstanding of the conceptinformative.

Where \(\sigma\) is a piece of strongly semantic (hence true)information, and \(z\) is the target situation that itdescribes with total accuracy, the more distant \(\sigma\) gets from\(z\), the larger the number of situations to which itapplies and the lower its degree of informativeness. Floridi uses‘\(\Theta\)’ to refer to the distance between a true\(\sigma\) and \(z\) (recall that Floridi is notinterested in non-factive information, and might well deny that thereis any sensible such commodity). \(\Theta\) indicates the degree ofsupport offered by \(z\) to \(\sigma\). Given aspecific \(\sigma\) and a corresponding target \(z\),Floridi maps the values of \(\Theta\) onto the x-axis of a Cartesiandiagram. We now need a formula to calculate the degree ofinformativeness \(\iota\) of\(\sigma\)—\(\iota(\sigma)\)—in relation to\(\Theta(\sigma)\). Floridi’s proposal is that we calculate thevalue of \(\iota(\sigma)\) via the complement of the distance of\(\Theta(\sigma)\) squared:

Values of \(\iota\) range from 0 to 1 and are mapped along the y-axisof the Cartesian diagram.Figure 1 shows the graph generated by(10) when we include negative values for false \(\sigma\). \(\Theta\)ranges from \(-1 = \mathord{\perp}\) to \(1 = \mathord{\top}\):

Figure 1

Responses and extensions

Floridi (2012) extends the theory of strongly semantic informationinto matters of traditional epistemology. Hisnetwork theory ofaccount involves an argument for the claim that should stronglysemantic information be embedded within a network of questions andanswers that account for it correctly, then this is necessary andsufficient for the strongly semantic information to count asknowledge. Floridi (2008) develops a theory ofrelevant semantic information in order to articulate a theoryofepistemic relevance. Here he argues that the nature ofrelevant semantic information is an additional vindication of theveridicality thesis. In Floridi (2011) he further explores just whatit might, or should mean for semantic information to be true. Ratherthan accept a correspondence, coherence, or pragmatic theory of truth,he develops what he calls acorrectness theory of truth forthe veridicality thesis, one which connects directly with his networktheory of account described above.

Floridi (2006) argues that the modal logic KTB is well placed to playthe role of a logic ofbeing informed (KTB is systemB described in the entry onmodal logic.) KTB itself licenses a version of the veridicality thesis within thecontext of being informed, \(I_\alpha p\to p\) (where \(I\)is a universal modal operator, on account of theaxiom \(\square p\to p\) being an axiom of KTB). “Beinginformed” is understood as a cognitive state distinct from bothknowledge and belief. Allo (2011) provides a formal semantics for thelogic of being informed, in both pure and applied versions. Primiero(2009) rejects the veridicality thesis for a logic ofbecoming informed. Primiero’s logic of becominginformed is a logic of epistemic constructive information, withinwhich the definition of information requires it to be kept distinctfrom truth. Epistemic constructive information understands informationfor propositional content in terms of proof-conditions as opposed totruth-conditions.

More broadly, Dinnen and Brauner (2015) search for a single definitionof information (be it semantic or not) and find the veridicalitythesis to be obstructive. By contrast, Mingers and Standing (2018)argue for a single definition of information that supports theveridicality thesis. Allo (2007) preempts such concerns with anargument for aninformational pluralism (analogous to alogical pluralism, see the entry) via arealist interpretation of semanticinformation itself. A realist interpretation of semantic informationleads naturally to the question of how it is that semantic informationcan emerge from and be a part of the natural world—a questionthat is addressed in detail in Vakarelov (2010). The question of howit might be that information could be accounted for naturalisticallyhas a rich history in philosophy, most notably ininformationalsemantics covered in the following section.

Although Floridi’s, and Bar-Hillel and Carnap’s stance onsemantic information is not uncontroversial (sans aninformational pluralism that is), Floridi’s motivating intuitionhas some philosophical precedent. Firstly, it is unlikely that manyare satisfied with Bar-Hillel and Carnap’s claim that “Aself-contradictory sentence asserts too much; it is too informative tobe true”. Secondly, with regard to logical truths having zerosemantic information on Floridi’s account, recall that asWittgenstein put it with typical bluntness—“All thepropositions of logic say the same thing, viz nothing. They aretautologies” (Tractatus, 4.46, 6.1). One way tounderstand Floridi’s theory of strongly semantic information isas a theory of the information we get from and about our particularobjective physical environment, as our physical environment is oneabout which contradictions and logical truths are typically maximallyuninformative. Semantic conceptions of information designed to tell anaturalistic story about the content of our putatively referring termshave a rich history of their own in philosophy, and this is the topicto which we now turn.

2. Information, Modes of Presentation, and Meaning

Theories of meaning that turn on modes of presentation have beencommon in philosophy in one way or another since Frege’sSense and Reference. The story is as follows. There must bemore to the meaning of a referring term than its referent, since termscan co-refer. For example,James Newell Osterberg Jr. andIggy Pop both refer to the same individual. In spite of thisthe intuition that they do not mean the same thing is strong.“Iggy Pop is Iggy Pop” and “Iggy Pop is James NewellOsterberg Jr.” do notseem to mean the same thing.Similarly, it seems to be the case that “Alice believes thatIggy Pop was the singer in The Stooges” might true, whilst“Alice believes that James Newell Osterberg Jr. was the singerin The Stooges” might be false, at least on one natural readingthat is in line with our intuitions with regard to meanings.

Frege’s well known response is that both the referent and thesense of a referring term play a role in specifying its semanticcontent. But what is the sense of a term? Frege’s own way ofcashing out the notion of sense is in terms of amode ofpresentation (MOP), an idea used by many later philosophers. TheMOP of a referring term is the way in which the putative referent ofthe term is presented to us by our phenomenology. MOPs are what wewould use in an attempt to identify or locate the referent of areferring term whose meaning we grasp. Many contemporary theories ofmeaning that turn on information, incorporate MOPs in one way oranother. The reason for this is that although reducing the meaning ofa term to the information carried or transmitted by it alone isattractive, it has proven to be fraught.

The temptation to take meaning and information to amount to prettymuch the same thing is a result of the following idea. The idea isthat the word ‘cat’ denotes the property of being a cat,and that it meanscat because it expresses the conceptcat,and the conceptcatmeanscat. The conceptcat meanscat because it carries the information\(\langle\)cat\(\rangle\), andcat carries theinformation \(\langle\)cat\(\rangle\) because its instances ortokenings are caused, by and large, by cats. This is a nice idea. Bytying meaning and information together and telling acausalstory about them, we have a naturalistic story to tell about theinformation that we get from our environment, and hence a naturalisticstory to tell about meaning. Such information-transmitting causalrelationships areinformation channels—causalconnections that facilitate the flow of information between the sourceof information and the receiver. We should take care to note thisstory is telling an informationally semantic story aboutsub-propositionally located pieces of information such as thepredicate ‘cat’ and paradigmatic uses of singular terms.As such it sits outside of the domain described by the theories ofsemantic and strongly semantic information described above. In spiteof this, we will see that a refinement of this story turns on trackingaccuracy, if not truth itself.

In a series of influential works on this area of informationalsemantics, Jerry Fodor (1990), and Fred Dretske (1981) proposed atheory of semantics very much like the one outlined above (see theentry oncausal theories of mental content). A noted problem for such an informational semantics has come to beknown commonly as thedisjunction problem. The disjunctionproblem is as follows.cat tokens are notalways caused by cats, they are sometimes caused by other things likesmall dogs for example (or by thoughts about balls of yarn orwhatever). Given this fact, if the story above is correct, then whydoescat meancat and notcat ordog? Fodor’s (1990) response is in two stages.

Firstly, Fodor’s initial proposal is that non cat-caused tokensofcat are asymmetrically dependent oncat-caused tokens ofcat. That is, there wouldnot be any non cat-caused tokens ofcat hadthere not been any cat-caused tokens ofcat.Secondly, on Fodor’s picture, meaning and informationcomeapart. Theinformation carried by a token of a conceptcovaries with its cause, whereas themeaning of a token iswhat all of the concept’s tokenings have in common—theinner vehicles of ourcat tokenings, or theirMOPs. Note that Fodor is not, strictly speaking, subsuming informationas part of meaning, but rather teasing them apart. Our failure toappreciate that meaning and information come apart is, according toFodor, a consequence of the fact that firstly, they are very oftencoextensive, and that secondly, ‘means’ is a homonym forboth semantic content (meaning) and information-carrying. Consider thefollowing two uses of “means”:

• Smoke means fire.
• ‘Smoke’ meanssmoke.

On Fodor’s view, the first use is in the sense ofinformation-carrying only. Smoke carries the information that there isfire, but that is not what it means semantically. What‘smoke’ means, in the semantic sense, issmoke,and this is captured by the latter use of “means” above.On Fodor’s story, just as with ‘cat’ above,‘smoke’ meanssmoke because it expressessmoke,and tokenings ofsmokeare caused paradigmatically (but not always!)by smoke itself. The “not always” qualification is coveredby the asymmetric dependence condition above. So far so good, but whatabout non-existent objects such as bunyips? Non bunyip-caused bunyiptokens ofbunyip cannot be asymmetricallydependent on bunyip-caused bunyip tokens ofbunyipbecause there are no bunyips around to causeanything at all.

In light of non-existent objects such as bunyips, and themeaningfulness ofbunyip tokens in spite ofthere being no bunyips, Fodor adjusts his proposal so that meaning nowrests onasymmetrical dependences among nomological relationsamong properties—the property of being a bunyip forexample—as opposed toactual causal relations betweenindividuals. Nomological relations are cashed out in terms ofcounterfactuals, so what we have now is an informational semanticsalong the lines of the following—bunyipmeansbunyip because if therewere bunyips, bunyipswould be the cause ofbunyip tokenson which all other causes would depend asymmetrically.

Recall again that Fodor is teasing meaning and information apart.Gareth Evans (1982) formulates a similar informational theory ofmeaning, but one where information and MOPs are both subsumed withinthe semantic story itself. For Evans, a full story about the meaningof thoughts about particular objects that are—putatively atleast—in the world, needs to take account of both the causalorigins of the thought, as well as the MOP engendered by it. Evanscalls such thoughtsinformation based particular thoughts,and such thoughts will bewell grounded if and only if theobject satisfying the MOP and the object at the source-end of thecausal route are one and the same thing.

What the Fodor/Dretske and Evans theories of informational semanticshave in common, is that they recognise that the meaning orcontent/object of a thought is robust across causal variation:

We want to be able to say that two informational states (states ofdifferent persons) embody the same information, provided that theyresult from the same initial informational event. (Evans 1982:128–129)

Informational theories…appeal to reliable covariances whilequantifying over the causal mechanisms by which these covariances aresustained. By doing so, they explain why information (indeed, why thevery same information ) can be transmitted over so many differentkinds of channels. (Fodor 1990: 100)

Moreover, although Evans did not put things in quite these terms,Fodor, Dretske, and Evans all recogniseinformation channelsas robust entities in their own right.

François Recanati (2012, 2016), has proposed a detailed versionof informational semantics, hismental files theory, withinwhich information channels play a central role. Recanati’smental files are cognitive counterparts to singular terms, and as suchare referring concepts. Recanati’s view looks very similar toEvan’s information based particular thoughts at first glance.However, on Recanati’s view, metal files contain informationin the form of MOPs of an object—be they given directlyand experientially, or indirectly via descriptions—theirreference is not fixed by the information that they contain/theirmodes of presentation. Rather, the reference of a metal file is fixedby the relationson which this file is based, and thereferent of a mental file will be the entity or object with which weare acquainted correctly in virtue of such relations obtaining. SoRecanati is allowing that MOPs contain information themselves, ratherthan restrict the role of information to the reference fixing relationitself (as do Evans and Fodor). The feature that identifies theserelations is that they areepistemically rewarding (ER)relations. For Recanati, a relation is an ER relation in virtue of thefact that it is the sort of relation that makes theflow ofinformation possible. In other words, ER relations areinformation channels.

Recanati’s ER relations draw heavily on Lewis’s (1983)relations of “epistemic rapport”—causal chains thatwould permit information flow, or information channels under anothername. Both Recanati and Lewis recognise the disjunction problem byallowing that both information and misinformation may be transmittedalong information channels. Recanati’s take is that thereference of a mental file is fixed by the object that sits at thedistal end of the information channel that contributes to theinformation that the mental file contains, irrespectively of the“fit”. Fit may of course be bad on account of noisychannels and/or misidentification on the agent’s behalf. AsRecanati puts it:

The role of a mental file based on a certain acquaintance relation isto store information acquired in virtue of that relation. Theinformation in question need not be veridical; we can think of it interms, simply, of a list of predicates which the subject takes thereferent to satisfy. The referent need not actually satisfy thepredicates in question, since the subject may be mistaken. Suchmistakes are possible because what determines the reference is not thecontent of the file but the relevant relation to the object. The filecorresponds to an information channel, and the reference is the objectfrom which the information derives, whether that information isgenuine information or misinformation. (2012: 37–38)

It reads here as though Recanati is conflating a mental file on theone hand, with the information channel that carries its informationalpayload. Indeed Recanati goes on to argue that there are two sensibleand “distinct notions of file” (p. 82). The first notionis simply a repository of evolving information that appears to be andmay be about a single distinct object. The second notion of file, whatRecanati calls the “proper notion”, involvesbotha specific relevant information channel,and the repositoryof information acquired via that channel.

Along with Fodor, Dretske, Evans, Recanati, and Lewis, Frank Jackson(2010) also articulates a semantic theory based upon informationchannels that supervene on causal relations, along with MOPs.Jackson’s MOPs are identified withdescriptions.Jackson’s description theory of reference for proper names turnson information channels, which are articulated in terms of causallinks that underpin information flow. Jackson’s motivating ideais that names are by and large sources of information about theentities that they name. The descriptive dimension is a function oftheir (the descriptions) being specified in terms ofinformation-carrying causal connections—informationchannels.

For Jackson, language is, in general, a representational system thattransmits information about the way that things are taken to be tothose who comprehend the language. When names are used in declarativesentences, speakers are representing things as being a certain way.The use of names in such contexts is to deliver putative informationabout the way things are to other speakers in the language community.According to Jackson, names do this as a function of their being partsof information channels that exist between users of the language, andthe world. In order for us to track the information channel itself forthe purposes of getting information from it, we must understand thestructured connection between linguistic items (words and sentences),and ways that the world might be. Names themselves facilitate thispractice in virtue of their being elements in the information channelsthat exist between us and the world. These channels are created byconventions of language use and established practices of baptism.

Given the ubiquity of information channels in the theories above, itis no surprise that information channels have become a topic of studyon their own terms. The theory of information channels has madecontributions to information-based analysis of natural language andformal semantics.

3. The Theory of Information Channels

The theory of information channels,channel theory, emergedfromsituation semantics (see the entry), with the latter being motivated by the observationthat meaning depends on systematic regularities in the world, and thatsuch regularities are a necessary condition on our grasping anymeanings at all (Barwise 1993). Jon Barwise and John Perry (1983)appealed to this observation in order to justify and motivate anaturalistic theory of meaning. Early work in situation theoryconcentrated on situations themselves, thought of best aspartialworlds in modal parlance. Importantly, situation theory itselfdealt with the formal side of things in terms of set theory as opposedto modally, although as we will see below, modal interpretations havecome to dominate.

Situation theory focused onconstraints early on, withconstraints thought of most usefully asconditionals.Situation theory builds its semantic theory on an Austinian theory oftruth—where an utterance \(u_s\) of a declarative sentence \(s\)is putting forward a claim that is about some type ofsituation \(x\), such that \(x\) is ofsome type \(\phi\) (Barwise 1993: 4). Austin (1950) calls the type\(\phi\) the descriptive content of \(s,\) with \(\phi\) specifyingthe type of situation (or event or thing etc.) in the world that isbeing described. He calls the situation \(x\) itselfthedemonstrative content of \(s\). In otherwords, \(\phi\) describes the content of \(s\), and \(x\)is the contentdemonstrated by \(s\)—whichis just to say that it is the part of theworld about which the utterer of \(u_s\) is speaking when they utter\(s\).

According to Barwise, for any conditional statementif \(s_1\)then \(s_2\), such that the descriptive content of \(s_1\) is oftype \(\phi\), and the descriptive content of \(s_2\) is of type\(\psi\), the descriptive content ofif \(s_1\) then \(s_2\)is the constraint \(\phi\to\psi\). Constraints are connections betweentypes. Thedemonstrative content ofif \(s_1\) then\(s_2\) will be a connection between the demonstrative contentsof \(s_1\) and \(s_2\). Supposing that \(x\) is thedemonstrative content of \(\phi\), and \(y\) is thedemonstrative content of \(\psi\), the demonstrative content ofif\(s_1\) then \(s_2\) will be a connection between \(x\)and \(y\), with this connection beinganinformation channel \(c\) between \(x\)and \(y\), written \(x\cmapsto y\). AsBarwise puts it succinctly:

By aninformation channel, let us mean one of these relationsbetween situations, since it is these relations which allowinformation about one situation to be gleaned from another situation.(1993: 5)

The proposal in sum is that when we express a constraint\(\phi\to\psi\) by way of utteringif \(s_1\) then \(s_2\),we are making a claim to the effect thatthere is an informationchannel supporting the constraint. For an information channel tosupport a constraint, Barwise’ proposal is the following:

(11) states that if information of type \(\phi\) is true at the situation\(x\), and there is an information channel \(c\)from the situation \(x\) to thesituation \(y\), and there is a constraint frominformation of type \(\phi\) to information of type \(\psi\), theninformation of type \(\psi\) is true at the situation \(y\).

Barwise refines the notion of a situation to that of“site”—a structured object that containsinformation. We now have sites \(x,\) \(y,\) \(z,\)… and types\(\phi,\) \(\psi,\)…, where \(x:\phi\) is read astheinformation site \(x\) is of type \(\phi\). Withthe qualification that the channels may or may not be among the sites,and that \(x\cmapsto y\) is a three-place (ternary) relation betweeninformation sites and channels. Barwise formulates theSoundnessAxiom for channel theory as follows:

At this stage, things are starting to look decidedlymodal inspirit, if not in practice.

Barwise and Perry’ssituations and Austin’sdemonstrative contents, are simply partial worlds under adifferent name. That is, they areincomplete possible worlds.Austin’s types, thedescriptive contents of statements,are looking very much like propositions—in particular theproposition that describes the claim being made by an utterance. Witha little bit of license, we might think of Austin’sdemonstrative content of a statement as that statement’struthmaker in a fine-grained sense. Barwise’ notationin (11) above with respect to \(x\vDash\phi\) betrays this reading. Moreover,given that \(x\cmapsto y\) is a ternary relation,(12) is starting to look very much like a semantic clause for theconditional that turns on a three-place accessibility relation insomething like a Kripke frame.

The semantics from Routleyet al.’s (1982) relevance logicgives the evaluation conditions on a three-place accessibilityrelation, where the notion of an accessibility relation is familiarfrom their role in Kripke frames, used to specify the semantics ofmodal logic. Barwise notes the connection explicitly:

The work presented here work also suggests a way to think about thethree-place accessibility relation semantics for relevance logic ofRoutley and Meyer. (I have discussed this with both Gabbay and Dunnoff and on over the past year. More recently, Greg Restall hasobserved this connection, and has begun to work out the connection insome detail.) (1993: 26)

Restall (1996) along with Mares (1996) work out this connection asfollows. Restall assumes that channelsare amongst theinformation sites (Mares does not). Instead of informationsites, common terminology speaks of informationstates. Information states may be incomplete and/orinconsistent, indeed they may be sub-propositional entirely (as willbe the case below when we look at fine-grained information-basedsemantics for natural languages based on informationalised versions ofthe Lambek Calculi). In Kripke/frame semantics terms, we haveternary information frame \(\mathbf{F}:\langle S,\sqsubseteq, R\rangle\), where \(S\) is a set ofinformation states, \(\sqsubseteq\) is a partial order on \(S\),and \(R\) is a ternary accessibilityrelation on members of \(S\). Aninformationmodel is an information frame \(\mathbf{F}\) along with anevaluation/supports relation \(\Vdash\) between members of \(S\)and types/propositions \(\phi, \psi\ldots\). Howexactly we read \(x\Vdash\phi\) is going to depend on what sort ofinformation state \(x\) happens to be, and what type ofthing \(\phi\) is. The simplest case will be when \(x\)is a situation and \(\phi\) is a proposition. In this case we may read\(x\Vdash\phi\) as\(\phi\) is true at \(x\).Given this much,(12) is translated as follows:

In this context, the way that \(Rxyz\) is read is—if you takethe information that is true at \(x\), and you put ittogether with the information that is true at \(y\),then you get the information that is true at \(z\).However, \(Rxyz\) is not read so strictly in general. Although the\(\Vdash\) relationcan be read as a straightforward semanticrelation in line with \(\vDash\), it is considerably more flexible.Other readings \(x\Vdash\phi\) include\(x\)carries the information that \(\psi\),\(x\)carries the information of type \(\psi\),\(x\)supports the information that/of type \(\psi\),\(x\) is a record of the information that/of type\(\psi\), and so on. As a consequence of this, the way that\(Rxyz\) is read in practice will depend the applications to which theresulting information-based semantic models are being put—thatis, on the domain of the information channels in question.

The domain of information channels might be anything from channels forpropositionally structured environmental information along the linesFloridi is interested in (be it veridical or not), orsub-propositionally structured environmental information along thelines Fodor and Evans are interested in. Moreover, it might belinguistically focused sub-propositionally structured information fromnatural language semantics, or concern semantic informationalphenomena familiar from issues in the philosophy of language such asattitude reports and the semantic analysis of epistemic and otherattitudinal states. We will examine such approaches in some detail inthe section below.

For now, note that semantic models of different information channeltypes will be individuated in terms of how it is that the“putting together” of \(x\) and \(y\)in \(Rxyz\) is understoodprecisely. Forexample, putting \(x\) together with \(y\)might mean the same thing as putting \(y\)together with \(x\), or it might not,depending on whether or not one wants the ternary relation \(R\)to be acommutative relation. That is, onwhether or not one wants it to be the case the \(\forall x\;\forally\;\forall z(Rxyz\to Ryxz)\) Whether or not onedoes want \(R\)to be a commutative relation will depend onproperties of the information channels that one is trying to model(for which see the paragraph above).

By analogy, recall modal logic, where different properties of thetwo-place accessibility relation \(R^2xy\) will generate differentmodal logics (for example, to get the modal logic \(T\)one makes \(R^2xy\) reflexive, to get the modal logic \(S4\) one makes\(R^2xy\) reflexive and transitive and so on). Similar decisions canbe made with regard to the ternary relation \(Rxyz\). For example, onemight want \(Rxyz\) to have the properties ofcommutativity,associativity,contraction,monotonicity,and others, or none at all, or subtle combinations of these and more.These decisions will generatedifferent logics of informationchannels in the same way as do the choices on \(R^2\) with regardto different modal logics. These logics are known in general assubstructural logics on account of the way the properties of theternary accessibility relation (commutation etc.), correspond to thestructural rules that individuate the logics themselves. (One maythink of structural rules as the syntactic/proof-theoreticcounterparts to the semantic conditions being discussed presently.) Asa part of the growing field oflogic and information more generally, we will see in the following section that clusters ofsuch logics have found utility across a range ofinformational-semantic phenomena.

3.1 The semantics of information flow

A group of weak substructural logics known as theLambekcalculi rejectall structural rules, or else one or theother of either commutation or association, or possess both of theserules only. Designed by and named after Joachim Lambek, these logicswere designed originally to model the syntax, or formal grammar, ofnatural languages (see the entry ontypelogical grammar).

That they have found a home modelling—providing a semanticsfor—information flow across information channels is not assurprising as it might seem initially. Firstly, with some license wemay think of a natural language lexicon as a database, and a grammaras a specification of the processing constraints on that database suchthat the processing constraints guarantee well-formed outputs.Secondly, one of situation and channel theory’s targetsoriginally was natural language semantics itself, so the convergenceis far from totally surprising. For example, Massimo Poesio (1993)appeals to the formal nomenclature of situation theory in order tobuild a theory of definite descriptions. Ginzburg (1993) uses thenaturally fine-grained structures of situation theory to give asemantics for propositional attitudes. Hwang and Schubert (1993)implement natural Language Processing (NLP) controls via a situationtheoretic framework. Westerhåll, Haglund and Lager (1993) appealto situation theory to give a theory oftext meaning wheretexts are treated as abstract states coding readers’ cognitivestates.

Barwise, Gabbay, and Hartonas (1995, 1996), appeal to theassociative Lambek calculus in order to model, that is togive a semantics for,information flow itself. They define aninformation network \(\mathbf{N}\) as a quadruple such that\(\mathbf{N} := \langle S, C, \mapsto, \circ\rangle\), where \(S\)is a set of information states (called“sites” by the authors), \(C\) is a set ofinformation channels, \(\mapsto\) is a ternary accessibility relationon \(S \times C \times S\), and \(\circ\) is an associative binarycomposition operator on \(C\). For information to flow,there must be some way in which channels compose so that informationcan flow from one channel to another. The authors specify thefollowing constraint on serial channel composition. For all channels\(a\) and \(b\):

The author’s argue for channels associating, hence the binarycomposition operator on channels being associative, i.e., for allchannels \(a,\) \(b\), and \(c\), if\(a\circ(b\circ c)\), then \((a\circ b)\circ c\)). Those familiar withcategory theory will know the refrain “channelsassociate!”.

Care is needed so as to not conflate channelcomposition asspecified above in(14), with the channelapplication specified above in(12) and(13). The latter involves feeding a channel its input, whereas the formerinvolves the compositions of channels themselves. Tedder (2017) argueselegantly for the composition and application of information channelsto be treated separately, and that we should not expect the propertiesof both (specified via structural rules on the ternary relation\(\mapsto\) to be the same. For arguments with regard to just whatproperties it is that weshould expect channel compositionand application to possess, see Tedder (2021) and Sequoiah-Grayson(2021). Sequoiah-Grayson (2010) argues that a basic theory ofinformation flow with a semantics given by the Lambek calculi gives usan informational interpretation of thedynamic predicatelogic (DPL) of Groenendijk and Stokhof (1991).

Van Benthem (2010), by contrast, argues against the temptation tounderstand Lambek calculi in such foundational informational terms.This is not to suggest that van Benthem is opposed to extendedapplications of the Lambek calculi. For example, van Benthem (1996)argues for an application of the Lambek calculi for the purpose ofgiving a dynamic semantics forcognitive procedures. VanBenthem’s use of the Lambek calculi for a dynamic semantics ofcognitive procedures,in combination with the use ofsubstructurally interpreted Lambek calculi as a foundational model ofinformation flow, leads naturally to the idea that models fordynamic epistemic phenomena might be given in informationchannel-theoretic terms. We examine such information models in thefollowing section.

3.2 Modelling epistemic phenomena informationally

Sedlár and Punčochář (2019) extendpropositional dynamic logic (PDL) into the non-associativeLambek Calculus, which they callLambek PDL. They give LambekPDL three informal interpretations, one in terms of actions thatmodify linguistic resources, another in terms of actions that modifybodies of information, and another in terms of actions that modify theepistemic states of agents (see 2019: 358–539). In theirsemantics, specific readings of the ternary relation \(R\)from(13) above will depend on the interpretation of the information states intheir models. In particular, they are interested in threshold caseswhere commutation, \(x\circ y = y\circ x\), breaks down for channelapplication. Sedlár (2020) extends the non-associative andnon-commutative Lambek calculus withiterative channeloperations (both applicational and compositional) under aninformational interpretation.

Sedlár (2016) designs and explores substructural epistemiclogics under an informational interpretation with the explicit goal ofattending to theScandal of Deduction (SoD) fromsection 1.1 above. The motivating idea here is that there are channels from oneepistemic state of an agent to another epistemic state of that agent,and that certain epistemic actions (namely acts of reasoning) thatfacilitate information flow along such channels can be captured by theternary relation \(R\) that marks channel applicationin(13) above. Punčochář and Sedlár (2017) introducea substructural epistemic logic forpooling information in agroup of agents via structured communication (viz. structuredinformation flow) between them. In this context the binary combinationoperator \(\circ\) (‘\(\cdot\)’ in Sedlár andPunčochář’s notation) is a pooling operatorbetween the different epistemic states of agents in acommunicative group. The authors’ have several examples tosuggest that both association and commutation are misguided in thiscontext. Sedlár, Punčochář, and Tedder (2019)provide a semantics for universal and common knowledge operators viathe now-familiar informational reading of the non-associative LambekCalculus under an informational interpretation.

4. Summary

At this point it is clear that semantic conceptions of informationcover a large amount of territory, but not one without structure ofcohesion.

Carnap and Bar-Hillel’s (1952) theory of semantic informationfor formal languages has an intuitive starting point, one that takesintensions and semantic information to be very closely related.Whatever the shortcomings of their theory, it has motivated an entirefield of research into the nature of semantic information via thesystematic informational approach to semantic and related phenomena ofLuciano Floridi along with an increasingly large number of closelyrelated research programs.

The information-based semantics for natural languages and contentbearing mental states due largely to Dretske, Evans, Fodor, Lewis,Jackson, Recanati, and Zalta has led to refined theories of meaningand content in terms of informational relations. Suchrelations—information channels that allow information to flowfrom one part of a system to another—have proved to be soindispensable that they are in turn an object of research in their ownright.

The semantic theory of information channels due largely to Barwise hasbeen refined in such a way as to permit its adaptation for modelling arich range of philosophical phenomena. Logics designed originally tomodel linguistic artefacts on their own terms have been used tocapture the properties of information flow. This has lead quickly torigorously defined semantic models for such linguistic artefacts, aswell as to models for epistemic phenomena that are given in terms ofinformation flow itself.

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