Copyright © 2013
Avello Publishing Journal
ISSN: 2049 - 498X
Issue 1 Volume 3:
Principia Mathematica
Jason Wakefield
University of Cambridge
Review: Modal Logic as Metaphysics (2013) Williamson, T. Oxford University Press.
This is an excellent first impression of a new publication from the current Wykeham Professor of
Logic at the University of Oxford. His previous publications include Vagueness (1994) which
includes an epistemic solution to the vagueness of predicates that Mellor advocated on the 16th
January 2006 at the annual conference of the Philosophical Society of Southern Africa at Rhodes
University. Mellor also agreed with Williamson on the crucial semantic difference between set and
sums in this paper on the limits of composition. Mellor's semantics are unfortunately omitted by
Williamson in favour of Stalnaker's quantified modal logic with identity in this new book. Logic is
analysed in terms of orthodox and unorthodox semantics, however the clearest part of the book is
about the semantic conditions in the Barcan and converse Barcan formulas in Kripke's model
theory:
As Kripke emphasizes, BF and CBF are valid in his model theory only over very restricted
classes of models. He points out that BF fails at a world w when something in the domain of
w is not in the domain of w, and that CBF fails at w when something in the domain of w is
not in the domain of a world accesible from w. He provides simple counter-models to the
formulas in each case. (Williamson 2013: 124)
This is made precise when an inhabited frame is called non-increasing if and only if no new
inhabitants appear when one goes to a counterfactual possibility. 'In a non-decreasing frame, no old
inhabitants disappear when one goes to a counterfactual possibility' (Williamson 2013: 124). This is
a reading of Kripke's 'Semantical Considerations on Modal Logic' originally published in Acta
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Philosophica Fennica, 16, p. 83-94 9 (1963).1Burgess, Carnap, Dummett, Kaplan, Lewis and
Salmon are also accurately read with precision by Williamson, however he seems unsure of his
consistent self – referencing. This is an exceptional single – authored monograph, however if it is to
become a central structural core to any scientific theories, his abductive methodological afterword
should not have concluded by asking his opponents to to use his own methodological higher – order
necessitist logic. Williamson's modalist view is defended well by him, concluding with a simple
formula to support his radical contingency. He works this out by formulating formal semantic
theories with quantification over worlds in an extensional metalanguage that absorbs Kripke's
possible worlds model theory advancements in modal logic quantification without the problematics
of Carnap's approach. A book review does not have sufficient space to analyse Kripke's solution to
Carnap's approach in detail on the members of non-empty sets and atomic formulas, thus readers
should turn to my single – authored monograph The Question of Non- Being? A Pragmatic
Methodology of Casino Contingency (2013).
Kripke also helped clarify the semantics of modal logic, binary relations of relative
possibility between worlds and its modalities metalinguistically in Naming and Necessity (1980);
however Williamson is strictly focused on the accessibility between worlds, comprehension
principles for plurals, domains and identity in terms of Leibniz's Law. The proofs of BF in KB and
S5 rely on principles of quantified modal logic according to Williamson. This is argued
convincingly, as this book's central application of higher-order modal logic is not confined to
natural language semantics, but to logic and metaphysics. He uses restricting Leibniz's Law for
indentity as an example of pathetically weak logic. To clarify, a logic restricted to natural properties
and relations is not the best logic we can attain.
Some readers may feel that Leibniz's Law and Quinean logic is ground that is too well trodden
at international Mind Association, Royal Institute of Philosophy and Wittgenstein Symposiums,
1 Part II: Non-normal modal propositional calculi was later published in 1965.
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however when these ideas are combined with Williamson's modal dimensions - the logic is
refreshed! Other readers will decline to purchase this book who already have responded extensively
in writing and at conferences to Williamson's 'Truthmakers and the converse Barcan formula',
Dialectica, 53, p. 253-70 (1999). My recommendation is that Modal Logic as Metaphysics is an
excellent addition to other new products on the market such as Plural Logic by Oliver and Smiley
also published by Oxford University Press. These books are both very similar to each other,
because they are both of a similar size, price and format; and both appeal to mathematicians,
linguists, logicians and scientists interested in plural quantification. The main differences are that
Plural Logic analyses plural terms ('Whitehead and Russell'), plural predicates ('are consistent') and
plural quantification ('some things'); whilst Modal Logic as Metaphysics is more focused on modal
plural logic, comprehension principles for plurals and plural pointed models as defended by the
terminology of Bricker, Fine and Kaplan.
In conclusion, this book does not answer the question of whether or not there are such things
as merely possible people and future people, who have not yet been conceived. The reason why the
consent of human beings is not asked for - to implant secret microchips in to the civilians of
Cambridge, Oxford and London (by ex – RAF service men and women) is because military
organisations are creating the human interrogation technology of the future. This is a deep issue
about the nature of being human and its logical relation with change that Williamson's reading of
Prior misses. The Ministry of Defence's secret black budget is financing implants as a form of
covert identification of unwitting people. The top thinkers in the fields of modal and plural logic in
both Cambridge and Oxford are being considered as targets for implants so that MI5 has the best
possible test-subjects for experiments in bio-physics and cognitive computing. Neuroscience has
now matured to the extent where we can now extract and clone every single neuron and every
single tissue connection between neurons in human brains. Thus when people die now we can
preserve their experiences and memories as data extracted directly from a connectome (the
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complete map of the neural connections in a brain) to a computer.
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