Abstract
We propose a model for belief which is free of presuppositions. Current models for belief suffer from two difficulties. One is the well known problem of logical omniscience which tends to follow from most models. But a more important one is the fact that most models do not even attempt to answer the question what it means for someone to believe something, and just what it is that is believed. We provide a flexible model which allows us to give meaning to beliefs in general contexts, including the context of animal belief (where action is usually our only clue to a belief), and of human belief which is expressed in language.
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Notes
- 1.
In Ruth Marcus (1990, 1995) describes a man and his dog in a desert, deprived of water and thirsty. When they both react the same way to a mirage, it is hard to deny that they both have the same false belief that they are seeing water. The fact that animals can experience mirages would seem to be substantiated by the fact that the Sanskrit word for a mirage is mrigajal which literally means ‘deer water,’ faux water which deer pursue to their deaths. Frans de Waal makes a much more detailed case for animal intentionality in Waal (2005).
- 2.
In Levi (1997), Isaac Levi considers the doxastic commitment we have to try to achieve logical closure of our beliefs, even when, as he admits, we cannot actually achieve such logical closure. I am sympathetic to Levi’s requirement, but in this paper, my concern is to develop a theory of actual beliefs rather than of doxastic commitments. The latter are less problematic from a purely logical point of view. If the agent’s full beliefs are consistent, then his doxastic commitments will satisfy a suitable modal logic, perhaps the logic KD4.
- 3.
This impression is surely strengthened by the remarks which Socrates makes elsewhere in Meno to the effect that if knowledge was always present then the soul must be eternal. The soul, then, as being immortal, and having been born again many times, and having seen all things that exist, whether in this world or in the world below, has knowledge of them all; and it is no wonder that she should be able to call to remembrance all that she ever knew about virtue, and about everything.
- 4.
The “conjunction fallacy” is committed when someone assigns higher probability to a conjunction than to one of the conjuncts. Gigerenzer (1996), Levi (2004) and Hintikka (2004) all dispute that the 89 % of people who responded the way indicated were actually committing the conjunction fallacy. However, I assume that the dispute is about the interpretation of this particular experiment, and that these three writers would not dispute the more general point that people do sometimes reason incorrectly.
- 5.
However, unlike Ramsey et al., we shall not try to explain probabilistic belief.
- 6.
For instance we can bet $3 on X, $3 on Y, and $2 against \(X \cup Y\). If either X or Y happens, we earn $7 (at least), and lose (at most) $5. If neither happens, we gain $8 and lose $6, so that we again make a profit – and Carol makes a loss.
- 7.
“It wasn’t until an ape saved a member of our own species that there was public awakening to the possibility of nonhuman kindness. This happened on August 16, 1996 when an eight-year old female gorilla named Binti Jua helped a three-year-old boy who had fallen eighteen feet into the primate exhibit at Chicago’s Brookfield Zoo. Reacting immediately, Binti scooped up the boy and carried him to safety.” De Waal is quite disdainful of Katherine Hepburn’s remark in The African Queen: “Nature, Mr. Allnut, is what we are put in this world to rise above.”
- 8.
Of course we need not and should not attribute to the chicken the specific belief that such caterpillars are poisonous. Davidson (1982) is right on this particular point. But we can attribute to it the belief that eating them will lead to bad consequences.
- 9.
Of course I do not personally know any logically omniscient humans, but in a limited context it is possible for a human to show full logical competence. Suppose that p stands for Pandas live in Washington DC, q stands for Quine was born in Ohio, and r stands for Rabbits are called gavagai at Harvard. Suppose that Jill believes that p is true and that q and r have the same truth values. Then she is allowing two truth valuations, v = (t, t, t), and \(v^{{\prime}} = (t,f,f)\). Given a formula ϕ on p, q, r in disjunctive normal form, she can evaluate v(ϕ) and \(v^{{\prime}}(\phi )\). If both are t she can say that she believes ϕ. If both are f, she disbelieves ϕ, and otherwise she is suspending judgment. Then Jill will be logically omniscient in this domain. But note that she will actually have to make the calculations rather than just sit back and say, “Now do I believe ϕ?” In fact if it so happens that ϕ is a complex formula logically equivalent to p, then ϕ represents the same proposition as p, and is therefore believed by Jill. And yet, Jill will not agree to ϕ because it is the same ‘proposition’ as p, but rather that she will agree to the formula ϕ whose truth value she has calculated. See also, Dennett (1985) p. 11.
- 10.
It is plausible that when a vervet monkey utters a leopard call, then it is saying, ‘Ware leopard!’, but surely nothing in the behaviour of such monkeys would justify us to think that they might utter If there were no leopards here, then this would be a wonderful spot to picnic.
- 11.
Of course, hearing a sentence is also an event, but its effect on speakers of the language goes beyond just the event. It is this second part which falls under \(\rightarrow _{s}\).
- 12.
- 13.
Clearly Lois Lane will react differently to the sentences Superman flew over the Empire State Building, and Clark Kent flew over the Empire State Building. Similarly, Kripke’s Pierre (1979) will react differently to the questions, Would you like a free trip to Londra? and Would you like a free trip to London? Indeed in the second case he might offer to pay in order not to go to London!
- 14.
See, however, Alchourron et al. (1985) where more complex kinds of reactions to sentences heard are described.
- 15.
To see this, if \(\pi (P) \subseteq \vert \vert \phi \vert \vert\), and \(\pi (P) \subseteq \vert \vert \psi \vert \vert\) then clearly \(\pi (P) \subseteq \vert \vert \phi \vert \vert \cap \vert \vert \psi \vert \vert = \vert \vert \phi \wedge \psi \vert \vert\). The proof for the other case is similar using the fact that \(\vert \vert \phi \rightarrow \psi \vert \vert = (C -\vert \vert \phi \vert \vert ) \cup \vert \vert \psi \vert \vert\). Since π(P) is contained in | | ϕ | | , it is disjoint from C − | | ϕ | | . Hence it can be contained in \((C -\vert \vert \phi \vert \vert ) \cup \vert \vert \psi \vert \vert\) if and only if it contained in | | ψ | | .
- 16.
The use of the letter u for utility is not meant to suggest that we have a formal notion of utility in mind; only a rough one.
- 17.
- 18.
It may seem to the reader as if I am endorsing a representational theory after all, but not so. First, the stock may not literally exist, but may simply refer to those sentences which the agent assents to quickly. Secondly, the agent’s beliefs need not be restricted to this stock – just as earlier, the bookseller Jill was not restricted to selling sets of books which were in her store as a set.
- 19.
We might compare entertaining a proposition as a bit like entering a building. If Ann and Bob enter the same building through different doors, they need not be in the same spot, and indeed they might never meet. But what makes it the same building is that they could meet without going out into the street. Thus if Ann and Bob are apt to assent to sentences \(s,s^{{\prime}}\) respectively where we know that \(s,s^{{\prime}}\) are equivalent; then it need not follow that there is a sentence they share. But they could through a purely deductive process, and without appealing to any additional facts, be brought to a situation where Ann assents to \(s^{{\prime}}\) and Bob to s (unless one of them withdraws a belief, which may also happen).
References
Alchourron, C., Gärdenfors, P., & Makinson, D. (1985). On the logic of theory change: Partial meet contraction and revision functions. The Journal of Symbolic Logic, 50, 510–530.
Artemov, S., & Nogina, E. (2005). On epistemic logics with justifications. In R. Meyden (Ed.), Theoretical aspecits of rationality and knowledge (pp. 279–294). Singapore: University of Singapore press.
Aumann, R. (1976). Agreeing to disagree. Annals of Statistics, 4, 1236–1239.
van Benthem, J. (1976). Modal correspondence theory. Doctoral dissertation, University of Amsterdam.
Bicchieri, C. (1997). Learning to co-operate. In C. Biccheri, R. C. Jeffrey, & B. Skyrms (Eds.), The dynamics of norms (pp. 17–46). Cambridge: Cambridge University Press.
Brandom, R. (1994). Unsuccessful seminatics. Analysis, 54, 175–178.
Davidson, D. (1982). Rational animals. Dialectica, 36, 318–327.
Dennett, D. (1985). Brainstorms (2nd ed.). MIT, cf. page 11. Singapore.
Dennett, D. (1996). The Intentional Stance (6th printing), Cambridge, Massachusetts: The MIT Press.
Fagin, R., Halpern, J. Y., Moses, Y., & Vardi, M. (1995). Reasoning about knowledge. Cambridge: MIT.
de Finetti, B. (1937). Foresight: Its logical laws, its subjective sources. Annales de l’Institut Henri Poincare, 7. (Trans.: Kyburg, H. (1980). Studies in subjective probability, Kyburg and Smokler (Eds.), (pp. 53–118). Krieger Publishing.)
Fitting, M. (2004). A logic of explicit knowledge. Logica Yearbook, 11–22.
Gaifman, H. (2004). Reasoning with limited resources and assigning probabilities to arithmetical statements. Synthese, 140, 97–119.
Gettier, E. (1963). Is justified true belief knowledge? Analysis, 23, 121–123.
Gigerenzer, G. (1996). On narrow norms and vague heuristics: A reply to Kahneman and Tversky (1996). Psychological Review, 103, 592–596.
Hayek, F. A. (1948). Individualism and economic order (See especially chapters II and IV). Chicago: University of Chicago Press.
Hintikka, J. (2004). A fallacious fallacy? Synthese, 140, 25–35.
Hume, D. (1988). A treatise of human nature, (L. A. Selby-Brigge (Ed.), pp. 176–179). New York: Oxford University Press.
Kahneman, D. (2002). Maps of Bounded Rationality, Nobel prize lecture.
Kripke, S. (1979). A puzzle about belief. In A. Margalit (Ed.), Meaning and use. Dordrecht/Boston: Reidel
Levi, I. (1997). Rationality and commitment. In The covenant of reason. Cambridge/New York: Cambridge University Press.
Levi, I. (2004). Jaakko Hintikka. Synthese, 140, 37–41.
Marcus, R. (1990). Some revisionary proposals about belief and believing. Philosophy and Phenomenological Research, 50, 133–153.
Marcus, R. (1995). The anti-naturalism of some language centere accounts of belief. Dialectica, 49, 112–129.
Millikan, R. (2006). Styles of rationality. In M. Nudds & S. Hurley (Eds.), Rationality in animals (pp. 117–126). Oxford: Oxford University Press.
Milner, R. (1989). Communication and concurrency. New York: Prentice Hall.
Moses, Y. (1988). Resource bounded knowledge. In M. Vardi (Ed.), Proceedings of the 2nd Conference on Theorectical Aspects of Reasoning About Knowledge (pp. 261–276). San Francisco: Morgan Kaufmann.
Parikh, R. (1987). Knowledge and the problem of logical omniscience. In International symposium on methodology for intelligent systems (ISMIS- 87), Charlotte (pp. 432–439). North Holland.
Parikh, R. (1991). Finite and infinite dialogues. In Moschovakis (Ed.) Proceedings of a Workshop on Logic from Computer Science (pp. 481–498). Berlin: Springer/MSRI Publications.
Parikh, R. (2001). Propositions, propositional attitudes and belief revision. In K. Segerberg, M. Zakharyaschev, M. de Rijke, & H. Wansing (Eds.), Advances in modal logic (Vol. 2). Stanford: CSLI Publications.
Parikh, R. (1995). Logical omniscience. In Leivant (Ed.), Logic and computational complexity (Lecture notes in computer science, Vol. 960, pp. 22–29). Berlin/New York: Springer.
Parikh, R., & Ramanujam, R. (2003). A knowledge based semantics of messages. Journal of Logic, Language and Information, 12, 453–467.
Park, D. (1981). Concurrency and automata on infinite sequences. In P. Deussen (Ed.), Proceedings of the 5th GI-Conference Karlsruhe. Berlin/Heidelberg: Springer.
Pepperberg, I. (2004). Talking with Alex: Logic and speech in parrots; exploring intelligence. Scientific American Mind, August 2004.
Plato. Meno. (380 BC). (trans. Benjamin Jowett). Available online at http://classics.mit.edu//Plato/meno.html
Ramsey, F. P. (1990). Facts and propositions. In D. H. Mellor (Ed.), Philosophical papers (pp. 34–51). Cambridge/New York: Cambridge University Press.
Ramsey, F. P. (1931). Truth and probability. In The foundations of mathematics (pp. 156–198). London: Routledge and Kegan Paul.
Savage, L. J. (1954). The foundations of statistics. New York: Wiley.
Schwitzgebel, E. (2002). A phenomenal, dispositional account of belief. Nous, 36:2, 249–275.
Schwitzgebel, E. (2006, Fall). Belief. In E. N. Zalta (Ed.), The stanford encyclopedia of philosophy (Fall 2006 ed.). http://plato.stanford.edu/archives/fall2006/entries/belief/.
Searle, J. (1994). Animal minds. In P. French & H. Wettstein (Eds.), Philosophical naturalism, midwest studies in philosophy (XIX, pp. 206–219). Notre Dame: University of Notre Dame Press.
Stalnaker, R. (1999). Context and content. Oxford/New York: Oxford University Press.
de Waal, F. (2005). Our inner ape. Penguin. Singapore.
Whyte, J. T. (1990). Success semantics. Analysis, 50, 149–157.
Wittgenstein, L. (1958). Philosophical investigations. New York: MacMillan.
Acknowledgements
We thank Sergei Artemov, Can Başkent, Samir Chopra, Horacio Arló Costa, Juliet Floyd, Haim Gaifman, Isaac Levi, Mike Levin, Larry Moss, Eric Pacuit, Catherine Wilson, and Andreas Witzel for comments. The information about chess came from Danny Kopec. This research was supported by a grant from the PSC-CUNY faculty research assistance program. Earlier versions of this paper were given at TARK-05, ESSLLI-2006, at the Jean Nicod Institute, at a seminar in the philosophy department at Bristol University, and at the Philosophy Colloquium at the City University Graduate Center. Some of the research for this paper was done when the author was visiting Boston University and the Netherlands Institute for Advanced Study. A very preliminary version of some of the ideas was presented at Amsterdam, and published as Parikh (2001). This research was partially supported by grants from the PSC-CUNY program at the City university of New York.
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Parikh, R. (2016). Sentences, Belief and Logical Omniscience, or What Does Deduction Tell Us?. In: Arló-Costa, H., Hendricks, V., van Benthem, J. (eds) Readings in Formal Epistemology. Springer Graduate Texts in Philosophy, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-20451-2_31
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