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Reflexivity, Fixed Points, and Semantic Descent; How I Learned to Stop Worrying and Love Reflexivity

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Abstract

For most of the major philosophers of the seventeenth and eighteenth centuries, human cognition was understood as involving the mind’s reflexive grasp of its own contents. But other important figures have described the very idea of a reflexive thought as incoherent. Ryle notably likened the idea of a reflexive thought to an arm that grasps itself. Recent work in philosophy, psychology, and the cognitive sciences has greatly clarified the special epistemic and semantic properties of reflexive thought. This article is an attempt to give an explicit characterization of the structure of reflexive thoughts that explains those properties and avoids the complaints of its critics.

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Notes

  1. For a collection that draws together a broad range of discussions of self-representational approaches to consciousness, see Kriegel and Williford 2006. See also Kriegel 2009 and Harman 2006.

  2. Wikipedia, for example, defines self-representation as: a reflexive representation ‘a sentence or formula that refers to itself via some intermediary expression or encoding.’

  3. Perry 2001.

  4. The referential content (which Perry also refers to as the “official content”), on his account, is given by the Fregean truth conditions.

  5. I use double quotation marks for tokens like utterances and inscriptions, and square bracket for types like expressions and sentence types.

  6. That this is different from the singular proposition that January 16, 2009 is clear from the fact that one could believe the singular proposition and not realize that (C) itself occurs on that day, and likewise, one could know that (C) itself occurs on Perry’s 63 rd birthday without knowing what date that is.

  7. To see that this use of ‘the utterance itself’ presupposes the distinction between reflexive and non-reflexive characterizations of the utterance, it is enough to notice that the reflexive content wouldn’t be captured if “the utterance itself” were replaced by “the utterance made by JI at noon on Jan. 16, 2009.” In some places, Perry says is that to have a reflexive thought to have a thought whose truth conditions make reference to that very thought, ‘under the guise of identity.’

  8. See also Lehrer 1997.

  9. Some have argued that R is not a two-place relation between an element in a representational medium and object, but a three-place relation with a suppressed contextual parameter. Perhaps, but this won’t affect points here.

  10. For simplicity, I’m treating thought here as a form of subvocalized utterance.

  11. I’m making some choices here, assuming that the basic unit of self-representation is the sentence and the basic form of the self-representational sentence is P(I), i.e., [I have property P]. We might instead have taken the basic unit of self-representation as the singular term. In that case, we simply hold that reflexive sentences of the form [I have property P] should be analyzed as [the sentence that contains this token has property P]. Reasons for thinking the I of the individual thought is more basic than the token reflexive I include reasons for thinking that thoughts as wholes are more basic units of reference than their parts. It may be that the first personal [I] of the self-attribution (“I believe that p,” “I think that q”) is more basic, because it may be that the [I] only makes sense in the context of the reflexive consciousness. I believe that this is the argument in Kant. See Longuenesse, B. “Kant’s ‘I think’ versus Descartes’ ‘I am a thing that thinks’” (ms.) attributing arguments to this effect to Kant.

  12. Note that the I here is different from the first personal [I] of ordinary English, which refers to the person who utters it, and also from the token-reflexive I of Reichenbach, which doesn’t refer to the sentence in which it is contained, but only to the part of the sentence that it constitutes. See note ___ below. See my 2006 for an account of the first-personal I.

  13. That will keep the truth conditions fixed, but change the truth-value in cases like ‘I contain five words’.

  14. I assume a fixed interpretation, unless otherwise specified.

  15. Another example; consider

    • D Sentence 23 is Jenann’s (single most) favorite sentence.

    • D* “Sentence 23 is Jenann’s (single most) favorite sentence” is Jenann’s favorite sentence.

    • E The inscription in the top right corner of Jenann’s desk is Jenann’s (single most) favorite sentence.

    • E* “The inscription in the top right corner of Jenann’s desk is Jenann’s (single most) favorite sentence” is Jenann’s favorite sentence.

    If D and E are true, D* and E* are false (indeed, D and E are true iff D* and E* are false).

  16. The individuation conditions for the referent depend on the individuation conditions for occurrences in a sense that depends on the medium of representation. Inscriptions are treated as objects, and their individuation conditions depend on spatial location. Utterances are treated as events and their individuation conditions depend on when they are uttered and by whom. Thoughts, likewise, depend on the identity of the thinker and time.

  17. An [I]-containing sentence presents itself as what is represented.

  18. I’ll suppress the bracketed phrase for ease.

  19. Or, perhaps, self-evidently true to users that can, respectively, see and hear. Note that this doesn’t mean that, except in special cases, they have to be true.

  20. In mathematics, a special case of a relation in which arguments that are usually distinct coincide is said to be degenerate. Degenerate cases are limiting cases in which a relation reduces to a different, usually simpler class. So, for example, since the roots of an nth degree polynomial are usually distinct, the two identical roots of the second-order polynomial make it a degenerate case.

  21. I use ‘subject matter,’ following Perry, to mean ‘referential content,’, or non-reflexive truth conditions.

  22. Lewis 1983 and 1984.

  23. This is the Tarski definition of truth for Model-Theoretic languages. There are allied definitions for reference. Tarski 1944.

  24. All languages above are assumed to be first-order. This hierarchy can be reproduced within a single language if the language is not first order by equipping it resources for semantic ascent. Restricting the presentation to first order languages highlights distinctions between semantic levels.

  25. Perhaps this is better put in negative terms, since there may be many different interpretations that make it come out true. We should say, without an independent way of identifying the intended interpretation, it will not come out false. The burden is really on the opposition to show how interpretation can be sufficiently constrained to allow it to come out false.

  26. Putnam 1983. viii.

  27. Except that Putnam wants to eliminate the analogue of a painter outside the frame whose representational intent determines the interpretation of thought. That is the point of his repeated insistence that “we interpret our languages or nothing does.” Ibid., p. xii.

  28. Precisely because “‘Dog’ refers to dogs” is true no matter how ‘dog’ is interpreted, believing “‘dog’ refers to dogs” doesn’t tell us anything about how ‘dog’ is to be interpreted.

  29. The proof is given in a first-order language without an analogue of [I].

  30. So, for example, Alice thinks that Bob is thinking something true Bob thinks that Alice is thinking something false, so that what Alice is thinking is true iff what it is false

  31. Reichenbach 1947, 284 ff. For criticism of the token-reflexive theory, see Smith 1986 and 1987.

  32. Anscombe also suggests this reading and argues that the argument founders on its inability to bridge the gap between the I of the individual thought, and the extended “I” of the first person.

  33. A thought of “I occur at t” associates the temporal term t with an event, rather than just a representation of an event. A thought of “I am the sort of image, smell, sound, or touch causally associated with such and such” associates the description “the sort of image, smell, sound or touch causally associated with such and such” with an image, smell, sound or touch, rather than a representation of one. It has been argued—I would so argue—that getting the logic of experience right requires attributing experiences this sort of reflexive content.

  34. Note, that the map needn’t be the identity. We might just as well let green represent red and red represent green. Or we might use numbers to represent them. Any one-one functions will do.

  35. How do we apply this schema to mental representation? Concepts of phenomenal properties are grounded reflexively, and other concepts are grounded by causal links to phenomenal profiles. See Ismael 2007. This requires that the causal relation is itself exemplified internally so that the concept of cause is grounded reflexively. That is something I accept.

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Acknowledgments

I would like to thank Keith Lehrer for many conversations about reflexivity over the years. This paper was written with the support of a Queen Elizabeth II grant from the Australian Research Council. I owe both great debts of gratitude.

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  1. Department of Philosophy, University of Arizona, SS213, Tucson, AZ, 85721, USA

    Jenann Ismael

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Ismael, J. Reflexivity, Fixed Points, and Semantic Descent; How I Learned to Stop Worrying and Love Reflexivity. Acta Anal 26, 295–310 (2011). https://doi.org/10.1007/s12136-011-0132-2

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