S'I'R'L'S' University of Arizona

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

• Miss information and Mis-transfer of Information
• Martin Frické

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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

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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

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3 Assumptions

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

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4 Semantic Signaling

• Semantic Bar Hillel, Carnap (Frické, Floridi)
• Signaling Shannon
• Signaling Dretske, CSLI, Barwise

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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

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6 First order logic emp preds

• General/universal (Lindstrom, Manzano)
• Information measure defined over all contingent
  empirical statements
• Measure Do we want Inf(Prop) (?gt0), if Prop
  true Inf(Prop) 0, if Prop false ?

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7 Inf(Prop) 0, if Prop false ?

• No, dont want this
• Conjunction argument (continuity argument)
• Universal argument

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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

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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 !

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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)

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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

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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

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13 Dretske IV Fallibility

• does not buy into probabilistic world view
• of course, he is a fallibilist (of sorts)
• irrelevant alternatives

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14 Dretske V probabilities

• Notation
• General Prob(Baseball see Baseball) lt 1
• Particular Prob(Baseball (see Baseball not
  drugged paying attention etc.)) 1

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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

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16 Dretske VI But, improvable?

• Quantum physics
• Unlikely (runs against fallibilism)

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17 Proper conclusion

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

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18 Others CSLI

• Situation theory Israel, Perry, Barwise
• Infomorphisms Barwise, Seligman
• Same Cond Prob 1 and exception barring

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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.

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20 Solid conflict

• Dretske, Situations, Infomorphisms -gt 1, no
  communication of information at all otherwise
• Shannon -gt 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.

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21 Conclusion

• Abandon correctness
• false statements, high verisimilitude
• do not insist on conditional probabilities of 1
  for information transfer

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22 End last years dinner