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The Probabilistic Difference Maker Theory of Information is ontologically and conceptually circular.

Updated: Apr 24

The probabilistic difference maker theory of information seeks to solve recondite problems with the veridicality thesis for semantic information (information must be alethic or truth apt, and true) and with conceptions of information. However, there are problems with the premises of PDMT, especially its cognitivist-subjectivist premises. It conflates transmission of information with information, eliminates causation as a necessary basis for transmission, and conflates abstract information with physical information by eliminating a source token as necessary and instead making signal content about source types. What I am most interested in here, however, is a begging of the question associated with using objective background data or information as a necessary basis for defining information.


The nature of information transmission is central to theories of the nature of information, semantic information, and information dynamics (considered at various levels of abstraction). I will refer in this post only to information transmission rather than the more metaphorical and less scientifically semantically constrained concept of information flow. This concurs with Andrea Scarantino and Gaultiero Piccinini's (2011) approach, and with that of (Scarantino, 2015). ‘Information flow’ and ‘information transmission’ are not always used exactly synonymously in the philosophy of information, and the concepts of information transmission and information flow are not equivalent.


For example, in many informational logics, such as substructural relevant logics and the positive informational logic of for informational (deductive) inference[1], flow (and relational flow operators) is usually defined according to an abstractive model such as Fred Dretske’s transitive xerox principle, according to which, “if A carries[bears/receives] the information that B, and B carries [bears/receives] the information that C, then A carries [bears/receives] the information that C.” (Dretske, 1981, p. 1117). It’s implied (but usually not stated[2]) that the concept of flow in these logics somehow maps to, is grounded in, or even supervenes (strongly) upon causal transmission. Thus, transmission is still the relevant information theoretic and mathematical communication-theoretic concept to use in analysing PDMT.


Researchers, including (Scarantino 2015) sometimes equivocate on information and information transmission, or at least fail to disambiguate them. However, information is not information transmission. When referring to a source to destination and causal-channel based system, information is generated at the source, and is transmitted in an encoded signal to the receiver and destination. Transmission is a sufficient, but not necessary, condition for the obtaining of information: any causally based transmission of any pattern generated at a source structure necessarily involves information transmission. An information source or a dynamical physical process or structure is a sufficient and necessary condition for the obtaining of information. (If such existential conditions are sought, I suggest that the most important one is causal structure, which then points to a familiar structural realism debate).



Concepts of information transmission are important to Dretske’s epistemically motivated veridicality thesis for semantic information, according to which semantic information must have the property of being true, or must somehow encapsulate truth (the latter encapsulation based conception being due to Floridi). Scarantino and Piccinini (2011) specifically oppose this thesis (which I also reject) using their probabilistic conception of information and information transmission to do so (Floridi 2011, 91, 116–17, 245–46; Fresco and Michael 2016, 134; Adams 2003, 476; Dretske 1981b, 45).


According to PDMT, there are only two necessary conditions for the obtaining of information (transmission, in fact, which his conflated with information in their theory):


  1. The structure of the token signal (regarded as evidence) (Scarantino 2015, 419, 422–23).

  2. Mind-dependent mind-interpreted (Bayesian, or not) background data grounded by agent acquired knowledge of a type of signal to source correspondence

1. is regarded as sufficient for the probabilistic inferential implication of the existence a token source of origin of the requisite type or kind (regarded as a Bayesian hypothesis). However, neither the existence of such a token source, nor a state thereof, is a necessary condition for the obtaining of information transmission according to PDMT.


Our best applied scientific theories of information say there can be no information transmission without causally sustained signals in physical channels causally connected to token sources of origin. The distinction between Shannon information and physical causation is well understood, but it’s exact basis is not broadly ratified and there are significant problems with it with respect to individual signal content, semantic information, and transmission of true messages (Dretske, 1983). According to the mathematical theory of communication, transmission does necessarily involve physical causal pathways. Similarly, Shannon’s definition of the obtaining of real information has the necessary existential condition of, or is existentially dependent upon, a physical stochastic process (Cover & Thomas, 2006; Shannon, Claude E., 1948). One can get information from the lack of a signal, but this one exception also requires the presence of a physical channel with stable channel conditions (invariant physical properties constrained on a natural nomic or lawful basis) and a token source to generate the signal.


There are two main problems with PDMT:


3. Its elimination of temporal, causal, and directional in re (in a channel and source coupling) signal structure from the concept of transmission in connection with the replacement of frequentist statistics and source-signal casual pathways with Bayesian inference and confirmation, and

4.Its inclusion of mind dependence as a necessary condition of the obtaining of transmission.


(3.) is the core thesis of PDMT:


[T]he transmission of natural information entails nothing more than the truth of a probabilistic claim…signals carry natural information by changing the probability of what they are about…On this view, spots carry natural information about measles not because all and only patients with spots have measles but because patients with spots are more likely to have measles than patients without spots. (Scarantino and Piccinini 2011, 70; Martinez and Sequoiah-Grayson 2019, sec. 2.2-3.1, 29)

The ‘nothing more’ claim has been multiply opposed by philosophers of information (Lloyd, 1989, p. 64; Lombardi, 2004, pp. 113–117; Millikan, 2013, pp. 141–142; Shea, 2007, p. 421; Stegmann, 2015, pp. 874–877). Scarantino is interested in this premise and principle because he opposes Fred Dretske’s veridicality thesis: that information requires truth (a thesis upheld by Luciano Floridi). Scarantino wants information to have a probabilistic basis, and not require veridicality. This is more in keeping with Shannonian classical information theory and avoids some of the pitfalls of the Dretskian approach (the requirement of p=1 or statistical certainty about the state of a source for the signal and message received from a channel). I happen to agree with the rejection of the veridicality thesis because I regard information as a truthmaker rather than a truth bearer. However, it does not follow from the truth of necessary proportionality of transmission that a token causally connected source is not required for information transmission.


PDMT’s primary revision is thus the replacement of combined statistical and causal grounds of transmission with Bayesian probabilistic inference alone. It regards the signal structure as evidence in a Bayesian statistical framework. The (state of the) source is mapped to a Bayesian hypothesis such that the probability that the source, conditional upon evidence at the signal, and given mind dependent and psychologically interpreted propositional background data, is the information content. This constitutes information according to PDMT. However, it’s really a (revisionary and flawed) conception of transmission, and, as already noted, transmission is not identical to information, since it’s information that is transmitted.


An immediate response to this observation might be that information is the transmission of a signal that results in the objective reduction in uncertainty at the destination about the source. However, Shannon’s theory also talks about information being generated at a source, and if that is to be taken seriously in ontological terms, then information is not a reduction in uncertainty alone (or perhaps at all) as probabilism about the nature of information would have it. Moreover, it would preclude information being encapsulated by structures in algorithmic information theory, and this is too quick, at best.


PDMT is multiply revisionary with respect to the classical conception of transmission, but its subjectivist and cognitivist revisions that make the obtaining of information dependent upon propositional mind-dependent background data that are the most troublesome. Mind-dependence prevents PDMT information[3] from being an objective commodity as Scarantino claims, because the mind dependence is ineliminable from the establishment of, and agent access to, the background information or data:


“[I]nformation is transmitted relative to the background data available to hypothetical recipients…information transmission would not take place in the absence of potential interpretative processes on the part of recipients, which violates Dretske’s own requirement that information is ‘out there’ independently of its ‘actual or potential use by some interpreter’. I emphasize that, although mind-dependent, natural information as PDMT understands it should still be understood as an objective commodity, in the same sense in which the confirmation of hypotheses by evidence is an objective affair…Once we have established what the background data are, the natural information transmitted by a signal relative to such data is objectively determined, independently of what anyone may think on the matter. (Scarantino 2015, 432)

It’s a straightforward problem of petitio principii or begging the question. Background data are information. They must be. You cannot use reference to meaning as part of the basis (or part of the premises) for a definition of meaning, reference to knowledge as part of a basis for defining knowledge, or reference to belief to define belief, and so on. Likewise, you cannot use information, or reference to information as part of the basis for a definition of information. PDMT does this. Objective (Bayesian or otherwise) background data constitutes part of the basis for the propositional mental content that is a necessary condition for the obtaining of information in a signal. This background data is required to track and refer to information sources types, since information source tokens are not required for information to obtain according to PDMT.


Some might allege that this claim is due to a failure to understand or account for the nature of Bayesian (or else non-Bayesian) background data. However, as salutary and relevant as interpretations of probability and associated disagreements about how Bayesian probability works (subjective versus objective interpretations) – they have little bearing on this question. Whatever background data is, it’s information, even if is objectively determined. However, according to PDMT it cannot be objectively determined at all, since information is necessarily mind-dependent. The problems caused by the circularity are even more apparent in these terms.





Notes


[1] (Barwise et al., 1995; D’Alfonso, 2014; Restall, 1996, pp. 466–467; Sequoiah-Grayson, 2009) [2] Note that only the term ‘flow’, but never the term ‘transmission’ is used in (Aucher, 2014; Restall, 1996, 2018) [3] Or transmission, since PDMT seems to equivocate on information and information transmission.

Bibliography

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