What is Projectibility?


Thomas Hill, Emerald Bay, Lake Tahoe (1864)

The "New Riddle Of Induction" has amassed an enormous literature since the publication of Nelson Goodman's classic essays in the 1940s and 1950s [1]. These works have introduced a very peculiar term to anglo-american philosophy: 'projectibility'.

An odd word

Although sharing etymology, this neologism does not have any deep semantic overlap with the set-theoretical term 'projection' employed in many fields of mathematics. It has greater affinity with the looser uses of 'projection' that we may find in science, often interchangeably with (or in the context of) prediction and forecast.

Dissent starts at the grammatical level. The built-in dictionary called for spellchecking as I write this entry does not recognize 'projectible' and 'projectibility'. Some authors prefer to use what seem to be more natural derivations of the verb 'to project', i.e., 'projectable' and 'projectability'.

Prima facie, trivia like this may seem unimportant, but I believe that lack of grammatical consensus in philosophical jargon is often symptomatic of weak conceptual standing. It wouldn't be problematic if the concept was deployed consistently and rigorously in the literature, but this is not the case. As a homage to Goodman, the predicate 'projectible' itself does not seem to have been sufficiently well entrenched.

A place and purpose for projectibility

What is the role played by the projectibility concept? Why do we need it at all?

Projectibility is typically deployed in discussions concerning the rationality of inductive inferences and the role of positive empirical confirmation in theoretical predictions.

Stated informally, the default and most general account is something like this: projectibility is a property of some component (or components) of inductive inferences that is shared by all inductive inferences deemed rationally legitimate. It aims to separate good inductions from bad inductions, if we are to accept the rationality of at least some inductions (I'll leave the topic of which are the bearers of the projectibility property for another entry).

This picture is probably what Goodman had in mind, according to the exegesis of Remi Israel [2]; projectibility specifies legitimate inductive inferences.

Nonetheless, this characterization seems to beg the question of projectibility being a non-disjunctive property. Perhaps there are very different ways by which inductive inferences can be rational.

Samir Okasha [3] states that Goodman’s project was descriptive, that is, it purported to isolate the class of rational inductive inferences, not to justify the practice of inductive inferences - that would be the Old Riddle of Induction. This is reiterated by Peter Turney [4] in the context of the curve-fitting problem in statistics.

It is not clear if such a through and through separation between description and justification is possible. Grounding the original program of Goodman (and the 'Riddle' it posed) lie certain logical theories of confirmation and epistemological theories of evidential credibility inherited from Jean Nicod and Carl Hempel; what characterizes rational inductive inferences may very well be what justifies their rationality, the constraints themselves being uncontroversially normative epistemically.

Probing the structure of confirmation

A deep investigation of Goodman-esque projectibility requires at first a careful delineation of the theory of confirmation that exists in the background - an endeavor that can be very arid. Before considering how empirical evidence may increase or decrease the credibility of a given hypothesis, one must answer if such a relation is held exclusively between linguistic/representational entities or if the empirical world ends up somehow as one of the relata. This is needed to shed light on the bearers of the Goodman property, what kinds of entities are projectible at all.

References

[1] N. Goodman, Fact, fiction, and forecast, Harvard University Press, 1955.
[Bibtex]
@book{Goodman1955a,
author = {Goodman, Nelson},
citeulike-article-id = {12534797},
posted-at = {2013-07-30 07:13:11},
priority = {2},
publisher = {Harvard University Press},
title = {Fact, Fiction, and Forecast},
year = {1955}
}
[2] R. Israel, "Projectibility and explainability or how to draw a new picture of inductive practices," Journal for general philosophy of science, vol. 37, iss. 2, pp. 269-286, 2006.
[Bibtex]
@article{Israel2006a,
author = {Israel, Rami},
citeulike-article-id = {12534792},
journal = {Journal for General Philosophy of Science},
number = {2},
pages = {269--286},
posted-at = {2013-07-30 07:13:10},
priority = {2},
title = {Projectibility and Explainability or How to Draw a New Picture of Inductive Practices},
volume = {37},
year = {2006}
}
[3] S. Okasha, "What does goodman's 'grue' problem really show?," Philosophical papers, vol. 36, iss. 3, pp. 483-502, 2007.
[Bibtex]
@article{Okasha2007a,
abstract = {No abstract},
author = {Okasha, Samir},
citeulike-article-id = {13531605},
journal = {Philosophical Papers},
number = {3},
pages = {483--502},
posted-at = {2015-03-02 22:50:45},
priority = {2},
publisher = {Taylor \& Francis},
title = {What Does Goodman's 'Grue' Problem Really Show?},
volume = {36},
year = {2007}
}
[4] P. Turney, "The curve fitting problem: a solution," The british society for the philosophy of science, vol. 41, iss. 4, pp. 509-530, 1990.
[Bibtex]
@article{Turney1990a,
author = {Turney, Peter},
citeulike-article-id = {13112819},
journal = {The British Society for the Philosophy of Science},
number = {4},
pages = {509--530},
posted-at = {2014-03-21 00:50:00},
priority = {2},
title = {The Curve Fitting Problem: A Solution},
volume = {41},
year = {1990}
}

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