In Remarks on the Foundations of Mathematics, and elsewhere, Wittgenstein made some general statements about mathematical proof which can only be described as paradoxical. What he says is directed to proofs for which there is no general method of solution such as there is for statements of the form a x b = c where a simple calculation is sufficient. His concern is with propositions for which one cannot in advance of proof describe any procedure which will demonstrate them… In an earlier study,’ ‘Proof and the Theorem Proved’, I singled out a group of propositions for which his account of proof seemed correct, and not paradoxical…. But I did not succeed in making his account of deductions of connections between established concepts paradox-free. I should like to return to his account as applied to such demonstrations, with the aim of explaining what justification there is for it, and what his account comes to.
Proof and the Theorem Proved
There is something curiously opaque about Wittgenstein’s assertions concerning the connection between proof of a proposition p, sense of the sentence ” p “, and understanding ” p “. The difficulties inherent in his account are apparent, and he has
himself mentioned them, while leaving their resolution obscure. I shall now detail them, so that it will be clear what difficulties must be got round and what clarification is required.
Perennial Idealism: A Mystical Solution to the Mind-Body Problem
Each well-known proposed solution to the mind-body problem encounters an impasse. These take the form of an explanatory gap, such as the one between mental and physical, or between micro-subjects and macro-subject. The dialectical pressure to bridge these gaps is generating positions in which consciousness is becoming increasingly foundational. The most recent of these, cosmopsychism, typically casts the entire cosmos as a perspectival subject whose mind grounds those of more limited subjects like ourselves. I review the dialectic from materialism and dualism through to panpsychism, suggesting that explanatory gaps in the latter stem from assuming foundational consciousness to be perspectival. Its renunciation may yield the notion of an aperspectival, universal, “non-dual” consciousness that grounds all manifestation and is unstructured by subject, object or any differentia. Not only is such consciousness suggestive of a natural successor to cosmopsychism, but it has also been reported to be the direct experience of mystics who claim to have transcended the individual perspective. Their purported insight — that our aperspectival conscious nature is identical to the ground of all being — has been termed “the Perennial Philosophy”. Believing this Perennial Philosophy to offer the most promising way forward in the mind-body problem, I construct from it the foundations of a metaphysical system that I call “Perennial Idealism”. This attempts to account for manifestation in terms of dispositional, imagery-bound subjects. I then address an age-old “Parmenidean” conundrum that I refer to as “the problem of the one and the many”: How can an undifferentiated substratum ground differentia without the ground itself differentiating? The proposed solution takes its cue from mystico-philosophical writings in the Advaita Vedānta tradition, known as the ajāta doctrine.
Attentional discrimination and victim testimony
Sometimes, a form of discrimination is hard to register,
understand, and articulate. A rich precedent demonstrates
how victim testimonies have been key in uncovering such
“hidden” forms of discrimination, from sexual harassment to
microaggressions. I reflect on how this plausibly goes too for
“attentional discrimination”, referring to cases where the
more meaningful attributes of one social group are made
salient in attention in contrast to the less meaningful attributes
of another. Victim testimonies understandably dominate
the “context-of-discovery” stage of research into these
initially opaque forms of discrimination; a victim’s encounter
with the gap between their experience and dominant conceptual
frameworks for understanding it is what provides an
initial foothold for analysis to begin. Some object, however,
to this methodology continuing to dominate the later “context-of-justification”
stage, where the hypothesis is rigorously
challenged. I argue that this objection underestimates not
just how other methodologies are more likely to inherit the
various mechanisms of invisibility hiding the discrimination
in question, but also how victim testimonies are distinctively
well-suited to recognize and challenge those mechanisms.
Victim testimonies, then, ought to continue playing
a dominant role into these later stages of research regarding
hidden forms of discrimination.
Japanese Provides a New Relation between Language and the Real World
In Categories and On Interpretation, Aristotle develops his view on the relation between language and the real world. However, there exist in Japanese words conflicting with the idea. This paper argues that each of the four formal classes of lexically meaningful elements of Japanese defined on their combinability with the nominative case and the tense markers consistently corresponds to the divisions of reality, and shows that the relation of words to the world cannot be predicted from their use in a sentence. Under this analysis, Aristotle’s idea, which is based on the “omoma-rhema” distinction, from which the universal “noun-verb” distinction originates, is thrown into a question.
Considerations on Logical Consequence and Natural Language
In a recent article, “Logical Consequence and Natural Language”, Michael Glanzberg claims that there is no relation of logical consequence in natural language (2015). The present paper counters that claim. I shall discuss Glanzberg’s arguments and show why they don’t hold. I further show how Glanzberg’s claims may be used to rather support the existence of logical consequence in natural language.
Structures of Matter and Patterns in Science
Inspired by the work and life of Dorothy Wrinch, 1894-1976. The proceedings of a symposium held at Smith College, Northampton, Massachusetts, September 28-30, 1977 and selected papers of Dorothy Wrinch, from the Sophia Smith Collection.
On the Structure of Scientific Inquiry
The object of this paper is the study, in some of its aspects, of the structure of scientific inquiry. The subject is a large one and covers the major part of the field of scientific methodology. We shall confine our attention more particularly to the consideration of those problems of scientific structure which occur in the case of more advanced sciences and merely outline the corresponding problems which occur primarily in sciences in the more elementary stage
Modalities: Philosophical Essays
This book is a collection of papers by Ruth Barcan Marcus, covering much ground in the development of her thought, and spanning from 1961 to 1990. Many of the papers deal with logical, semantic, metaphysical, and epistemological issues in intensional logic, and in particular, modalities. Some important themes that run through these papers are extensionality, the necessity of identity, the directly referential conception of proper names as “tags,” essentialism, substitutional quantification, and possibilia and possible worlds. What emerges from them is a robust defense of quantified modal logic in the light of a host of objections, particularly from Quine. Modalities also includes two papers on belief, which have consequences for epistemic logic and more widely for theories of rationality; two papers on ethical issues, which have consequences for deontic logic and practical reasoning; and finally, two papers on historical figures, Spinoza and Russell, dealing with the ontological proof of God’s existence, and the nature of particularity, identity, and individuation, respectively.
Distinguishing Situated Knowledge and Standpoint Theory: Defending the Achievement Thesis
Original accounts of feminist standpoint theory emphasize its fundamentally critical stance toward situated knowledge (Smith 1974; Hartsock 1983; Collins 1986). The function of a critical standpoint is not to carelessly accept the beliefs of marginalized people, but instead to interpret those beliefs in light of thoroughgoing and pervasive ideological distortions. Some formulations of standpoint theory capture this critical function in the achievement thesis. It claims that a standpoint is not obtained automatically but must be achieved through a struggle against a dominant ideology. Contrary to the standard acceptance of the achievement thesis, Bright has recently argued that the requirement of achievement can warrant the dogmatic exclusion of some perspectives from becoming standpoints. In turn, he advances an account of standpoint theory which abandons the achievement thesis. Against Bright’s non-achievement account of standpoint theory, I argue that doing away with the achievement thesis abandons standpoint theory’s original aim of being critical of the social structures which construct and legitimize situated knowledge. Further, I argue that Bright’s concern with the possible dogmatism of the achievement thesis is better addressed by a commitment to the classic account of standpoint theory rather than a revision of it.