Abstract
Despite the joking title, this is not really a reply to my critics. Rather it is a response to my fellow researchers in acknowledgment of their expert contributions to this volume on information based logics. Their papers extend my work or their own, in a good way. In my responses, I try to say something interesting, maybe just to set a context, to suggest future work, to clarify something, or to make further connections to my own work.
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Notes
- 1.
It is interesting that the original formulations of implication and negation for \(\mathbf {RM}\) did have the variable sharing property, but adding conjunction or disjunction (they are interdefinable using De Morgan negation) led to the first of the implications, and the second can then be derived. Arnon has done a lot of interesting work on these implication-negation versions of \(\mathbf {RM}\) without conjunction and disjunction.
- 2.
The reader who wonders about the qualification “some” is referred to Dunn (1979a), where it is shown that Robinson’s Arithmetic blows up, whether with \(\mathbf {R}\) or \(\mathbf {RM}\), if it has 0 as primitive (but not if its numbers start with 1).
- 3.
I don’t know why but I used N to denote this third value, even though I clearly explain that it is to be understood as Both. Incidentally these three values function similarly to the three values for Graham Priest’s “Logic of Paradox” \(\mathbf {LP}\) except that implication is defined differently.
- 4.
Though Ross does talk of the “range” of A, and that is just a definition away from Carnap’s concept of “information.” The information in A is the same as the range of A.
- 5.
It might be worth pointing out that Jon Barwise and John Perry developed their “situation semantics” much later (see Barwise and Perry 1983) and while their “real” situations cannot be inconsistent although they can be partial, their “abstract” situations can be both. Also the relevantist Ed Mares still talks of situations.
- 6.
Carnap who avoided abstractions, actually used the syntactic device of “state descriptions” rather than possible worlds, where a state description can be viewed as a set containing every atomic sentence or its negation, but not both.
- 7.
Jøsang first presented this at a conference in 1997, but a more accessible source is Jøsang (2001).
- 8.
Edmund Clarke won the 2007 Turing Award for his pioneering work in using temporal modal logic in model checking. And while I have this footnote as my podium, let me use it to recommend to the reader who wants to read more on “Sinn” (not a typo but Deutsch) Alasdair Urquhart’s recent paper (Urquhart 2010).
- 9.
I am reminded of the novel Kandelman’s Krim by the mathematical physicist J. L. Synge. Nuel Belnap called my attention to this novel many years ago. It involves a philosophical discussion between a goddess, a kea, an orc, a unicorn and a plumber. The Plumber says: “I am of course perfectly well aware of the irrationality of \(\pi \), but on the job, \(\pi \) is \(3\;1/7\), or 3 if I am in a hurry.” Maybe Nuel is to be blamed for my “logics as tools” view.
- 10.
Since we all frequently travel by plane, I cannot resist mentioning that I have suggested to Larry, mostly as a joke, that he find a way to formalize “Many bags look alike.” How many of us, as we have stood waiting for our bags to arrive on the airport carousel, have wondered how to formalize this statement?
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Dunn, J.M. (2016). A “Reply” to My “Critics”. In: Bimbó, K. (eds) J. Michael Dunn on Information Based Logics. Outstanding Contributions to Logic, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-319-29300-4_19
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