Philos. Technol. DOI 10.1007/s13347-014-0155-x C O M M E N TA RY
The Information Liar Paradox: A Problem for Floridi’s RSDI Definition Björn Lundgren
Received: 17 January 2014 / Accepted: 2 February 2014 # Springer Science+Business Media Dordrecht 2014
Abstract In this commentary, I discuss the effects of the liar paradox on Floridi’s definition on semantic information. In particular, I show that there is at least one sentence that creates a contradictory result for Floridi’s definition of semantic information that does not affect the standard definition. Keywords Floridi . Semantic information . Liar paradox
1 Introduction In this commentary, I discuss the effects of the liar paradox on Floridi’s definition of DOS information (declarative, objective, and semantic information) that he presented in Floridi 2005. 1 I compare the effects of the liar paradox on the standard definition of DOS information with Floridi’s definition, and I argue that Floridi’s definitions have serious problems that the standard definition is not afflicted with. The standard definition of information says that: SDI) σ is an instance of DOS information if and only if: SDI.1) σ consists of n data (d), for n≥1; SDI.2) the data are well-formed (wfd); SDI.3) the wfd are meaningful (mwfd=δ) (Floridi 2005:353). 1
The author is aware that the idea presented by Floridi is not a novel one. Floridi himself refers to it as the”Dretske-Grice approach” (Floridi 2005:366). B. Lundgren (*) Department of Philosophy and History of Technology, Division of Philosophy, KTH—The Royal Institute of Technology, 100 44 Stockholm, Sweden e-mail:
[email protected]
B. Lundgren
The SDI definition allows for DOS information that is false. Floridi presents both negative arguments against the idea that DOS information could be false and positive arguments for why it need be true. Since I will not discuss these arguments, but some consequences of Floridi’s proposal, it is sufficient to present it: RSDI) σ is an instance of DOS information if and only if: 1. σ consists of n data (d), for n≥1; 2. the data are well-formed (wfd); 3. the wfd are meaningful (mwfd=δ); 4. the δ are truthful. (Floridi 2005:366). Floridi continues to explain the meaning, and usages, of truthful instead of true: “Truthful” is used here as synonymous for “true”, to mean representing or conveying true contents about the referred situation or topic”. It is preferable to speak of “truthful data” rather than “true data” because the data in question may not be linguistic (a map, for example, is truthful rather than true) and because we have seen that “true data” may give rise to a confusion, as if one were stressing the genuine nature of the data in question, not their positive alethic value (Floridi 2005:366f). What will be under consideration in this article is semantic information in the form of ordinary sentences. Given this we can use the synonym ‘true’ for ‘truthful’ and, in this context, we may consider the RSDI definition to be equivalent to: x is semantic information iff x is true meaningful well-formed data. The fourth requirement of RSDI can thus be stated as: if x is information then x is true, ∀x (Ix⊃Tx). I will speak of the RSDI definition and its fourth requirement in this sense to simplify. As a result of the RSDI definition we may note that there is no ‘false information’. Thus, those σ that are meaningful, well-formed data, but are not true are simply referred to as ‘pseudo-information’ (cf. Floridi 2005:366).
2 Semantic Information and the Liar Paradox So what are the effects of the liar paradox on these competing definitions of semantic information? Let us first consider a simple liar. It is often presented by a sentence of the following form:
The Information Liar Paradox
(0) This sentence is false. On an SDI analysis, (0) would be information even though it might be contested what, if any, truth-value (0) might have. On an RSDI analysis, determining if (0) is information is something that can only be determined if a truth-value is first assigned to it. This is not necessarily something that the RSDI definition can be criticized for, given that it is a more general problem. But we may note that SDI may determine if (0) is information without any further ado. The normal liar paradox obviously did not cause any extra sensations in relation to the different definitions. Thus, what I will do now is to look at modified versions of both a simple liar and strengthened liar and compare the effects of the two different definitions of information. The idea here is to look at what happens if we start to involve information into the liar structure. We may refer to these variations as ‘information liars’. First out is: (1) This information is false. Given SDI the question of whether (1) is information is independent of its truth-value, thus given SDI (1) functions pretty much as a simple liar does in a normal context, i.e., ‘information’ in (1) might be replaced with, e.g. ‘sentence’. However, given RSDI requirement four, it follows that (1) cannot be true since it would then be true that some information is false. On the other hand, if it is false it cannot be information, thus (1) is unproblematically false and an instance of pseudoinformation. The interesting thing to note here is that RSDI enables us to solve a simple information liar. But what about a strengthened information liar: (2) This is information and it is false. For SDI, the answer to (2) is pretty much the same as for (1); ‘information’ may be replaced by, e.g. ‘sentence’, and SDI is thus unrelated to the possible (liar) paradoxical nature of (2). For RDSI, the situation for (1) and (2) are also similar (even though slightly more complicated); (2) may be understood as Ix & Fx. Given that Ix (x is information) implies Tx (x is true) we have an inconsistency. Thus, we have to assume ¬Ix which means that the first part of (2) is pseudo-information and the second part is information. However, since the first conjunct of (2) is false, it follows that the whole conjunction (2) is false, and thus, it is a case of pseudo-information. So far, it seems as if RDSI can solve both the simple information liar and a strengthened information liar. This certainly is a very strong argument for RDSI, while it cannot be an argument against SDI since SDI is not affected by it. Now, what about: (3) This is not information. This proposal is tricky for both approaches, but the problem inherent from it does not affect SDI. Given SDI (3) has to be false, since it is information given SDIs
B. Lundgren
requirements. This result in a contradiction, since it follows that ‘This is not information’ is information. However, given that (3) is false, it is unproblematic that (3) is contradictory. We may also note that information, given SDI, may or may not be contradictory. For RSDI, the situation becomes a bit trickier. First, (3) could not be true, since if (3) is true it satisfies all requirement of RSDI and results in an instance of non-information satisfying the criteria of information, resulting in a contradiction that is supposed to be true, T⌈Ix & ¬Ix⌉, of which one of its conjuncts also encapsules falsity. On the other hand, if we assume that (3) is false then it would be true that ‘This is not information’ is information, and given the forth requirement of RSDI, it would then follow that (3) would be true. So while the RSDI definition could solve the other information liars, it cannot deal with (3) since the resulting contradictions are actually due to the RSDI definition rather than inherent in (3). For the RSDI-definition then, there is an information liar paradox. Some might say that the result of this is expected, given that we add certain rules concerning ‘truth’, the liar paradox is solved for some instances but pops up in other situations. The problem, however, is that RSDI not only switches the context where these problems occur, it is also integrated with them. Also, SDI is completely unaffected by the liar paradox, since it does not depend on any truth-value. Therefore, it can consistently be applied in any context without the risk of causing any paradoxes. Neither is it affected by the normal liar paradox, (0). Thus, in this sense, the SDI definition is a neutral definition of information. However, since RSDI is concerned with truth-values, it will have to deal with these problems. One suggestion might be that the RSDI definition applies some technical (or philosophical) solution to solve the informal liar paradox. However, RSDI cannot use just use any previous technical solution to the liar paradox to solve the information liar paradox since the truth assignment is integrated into the definition of DOS information, e.g. the problem cannot be solved with a hierarchical truth-notion. This ought to be obvious, since in order assign truth to (3) we must know if it is the case that it is ‘not information’ which itself is dependent on the assignment of its truth-value. Thus, I do not claim that in order to propose RSDI as a definition for DOS information, one must solve the liar paradox. What I am saying is that one must solve the technical problems resulting from using RSDI as a definition for DOS information (technical problems that are very similar to the structure of the liar paradox and tightly connected to the truth(fulness) requirement of RSDI). The problem is, however, not merely a question of having to propose new technical (or philosophical) solutions. It is also another type of problem since sentence (3), above, seems much more intuitively unproblematic then, e.g. sentence (0) or any other classic liar. Thus, while we could accept that there are problems with sentences like (0), similar problems with sentence (3) seem highly unintuitive. Concluding I would say that even though I am very sympatic towards Floridi’s idea that semantic information must be truthful, it is connected with serious philosophical and technical problems that have to be solved before RSDI can be accepted as a definition of DOS information. So while Floridi has moved on to upgrading semantic information to knowledge, declaring a partial success of truth-requirement:
The Information Liar Paradox
Admittedly, the analysis—according to which semantic information encapsulates truth, exactly as knowledge does—has attracted some criticisms for being too restrictive. Nevertheless, such criticisms have been proved unjustified and, as a result, there is now a growing consensus about the following approach (Floridi 2012:432). It is, however, obvious that such a declaration of partial success is too soon and that any definition ‘according to which semantic information encapsulates truth’ necessarily needs to deal with the problems here expounded.
References Floridi, L. (2005). Is semantic information meaningful data? Philosophy and Phenomenological Research, 70, 351–70. Floridi, L. (2012). Semantic information and the network theory. Synthese, 184, 431–54.