S.I.R.L.S. University of Arizona

1. S.I.R.L.S.University of Arizona Miss information and Mis-transfer of Information Martin Frické

2. 1: Questions • What is information? • How much information is there? • What is information transfer? • How much information has been transferred? ____________________________________________ • information vs information transfer • what vs how much

3. 2: No one single definition • ‘The word “information” has been given different meanings by various writers in the general field of information theory. It is likely that at least a number of these will prove sufficiently useful in certain applications to deserve further study and permanent recognition. It is hardly to be expected that a single concept of information would satisfactorily account for the numerous possible applications of this general field. [Shannon]’

4. 3: Assumptions • information is propositional (ie conveyed in propositions) • empirical (about the world) • objective facet (no one need be informed)

5. 4: Semantic & Signaling • Semantic: Bar Hillel, Carnap (Frické, Floridi) • Signaling: Shannon • Signaling+: Dretske, CSLI, Barwise

6. 5: Correctness conditions • Semantic: true • Yes! No! Well, (cf. Borat) not so much! • Modify to truthlike, to permit false statements to have a non-zero information measure • Signaling: conditional probability of 1 • No! • Accommodate fallibility • Probabilistic world view

7. 6: First order logic + emp preds • General/universal (Lindstrom, Manzano) • Information measure defined over all contingent empirical statements • Measure: Do we want Inf(Prop)= (?>0), if Prop true Inf(Prop)= 0, if Prop false ?

8. 7: Inf(Prop)= 0, if Prop false ? • No, don’t want this • Conjunction argument (continuity argument) • Universal argument

9. 8: Truthlikeness, Verisimilitude • Philosophy of Science • for statements stronger than literals • notion well identified and characterized, but formal analysis recalcitrant • can say what it is, at a hand waving level, but cannot measure it • compare with Carnap and Bar-Hillel and with Floridi

10. 9: Signaling, Shannon • Probabilistic. Theory of tokens, marks, or signs. No content, no intentionality (aboutness) • Conditional probabilities, both ways • Equivocation and Noise • Conditionals always less than 1 • Averages, entropy. But also error correction of single individual signals !

11. 10: Dretske, generalizing Shannon • Shannon about averages, we need to deal with particular signals/indicators to get aboutness/intentionality • “To a person with prior knowledge k, r being F carries information that s is G if and only if the conditional probability of s being G given that r is F is 1 (and less than 1 given k alone). (1983)” • Correctness value 1 (also relativized to individual)

12. 11: Dretske II: Mistake about averages • “… information, as ordinarily understood, is a semantic not a statistical quantity… “ pp.73-4 • but… Shannon on error correction

13. 12: Dretske III: Why cond prob = 1? • Information needs to be true • Television, Iraq. Might be ‘informed’ about something that did not happen ie something false

14. 13: Dretske IV: Fallibility • does not buy into probabilistic world view • of course, he is a fallibilist (of sorts) • [irrelevant alternatives]

15. 14: Dretske V: probabilities • [Notation] • General: Prob(Baseball | see Baseball) < 1 • Particular: Prob(Baseball | (see Baseball & not drugged & paying attention etc.)) = 1

16. 15: Dretske V • “Probabilities, in so far as they are relevant to practical affairs, are always computed against a set of circumstances that are assumed to be fixed or stable. The conditional probability of s, an event at a source, given r, the condition at the receiver is really the probability of s, given r within a background of stable or fixed circumstances B. To say that these circumstances are fixed or stable is not to say that they cannot change. It is only to say that for the purposes of reckoning conditional probabilities, such changes are set aside as irrelevant. They are ignored .... The communication of information depends on there being, in fact, a reliable channel between a source and receiver. It doesn't require that this reliability itself be necessary. “ 2008 p.45-6

17. 16: Dretske VI: But, improvable? • Quantum physics • Unlikely (runs against fallibilism)

18. 17: Proper conclusion • The appropriate conclusion to draw here is that a theory should not insist on conditional probabilities of 1 for information transfer.

19. 18: Others CSLI • Situation theory Israel, Perry, Barwise • Infomorphisms Barwise, Seligman • Same Cond Prob 1 and ‘exception barring’

20. 19: What Shannon has done • How to deal with fallibility • Error correct. Arbitrarily close to 1. • [NB: these are not ‘exceptions’, they are the ordinary run of things.]

21. 20: Solid conflict • Dretske, Situations, Infomorphisms -> 1, no communication of information at all otherwise • Shannon -> never 1 (in practical cases) • But, fallibilism + error correction • Need to side with Shannon on this • Probabilistic world view [Bayes, Jeffreys, Jeffrey, Jaynes, etc.] Truth at both ends, high probability, know, know that you know etc.

22. 21: Conclusion • Abandon ‘correctness’ • false statements, high verisimilitude • do not insist on conditional probabilities of 1 for information transfer

23. 22: End [last year’s dinner]