Maverick Philosopher

Footnotes to Plato from the foothills of the Superstition Mountains

Category: Logica Docens

  • Excluded Middle and Future-Tensed Sentences: An Aporetic Triad

    Do you remember the prediction, made in 1999, that the DOW would reach 36,000 in a few years?  Since that didn't happen, I am inclined to say that Glassman and Hasset's prediction was wrong and was wrong at the time the prediction was made.  I take that to mean that the content of their prediction…

  • Atomic Sentences and Syncategorematic Elements

    According to Fred Sommers (The Logic of Natural Language, p. 166), ". . . one way of saying what an atomic sentence is is to say that it is the kind of sentence that contains only categorematic expressions." Earlier in the same book, Sommers says this: In Frege, the distinction between subjects and predicates is not…

  • The Aporetics of Singular Sentences

    I should issue a partial retraction.  I wrote earlier,"The TFL representation of singular sentences as quantified sentences does not capture their logical form, and this is an inadequacy of TFL, and a point in favor of MPL."  ('TFL' is short for 'traditional formal logic'; 'MPL' for 'modern predicate logic with identity.' ) The animadversions of Edward the…

  • Nota Notae Est Nota Rei Ipsius and the Ontological Argument

    (By popular demand, I repost the following old Powerblogs entry.) "The mark of a mark is a mark of the thing itself." I found this piece of scholasticism in C. S. Peirce. (Justus Buchler, ed., Philosophical Writings of Peirce, p. 133) It is an example of what Peirce calls a   'leading principle.' Let's say you…

  • On the TFL (Mis)Representation of Singular Propositions as General

    The following is a valid argument: 1. Pittacus is a good man2. Pittacus is a wise man—–3. Some wise man is a good man. That this argument is valid I take to be a datum, a given, a non-negotiable point. The question is whether traditional formal logic (TFL) is equipped to account for the validity…

  • Inferences Involving Singular Propositions

    In Modern Predicate Logic (MPL), logical quantity comes in three 'flavors,' universal, particular, and singular. Thus 'All bloggers are self-absorbed' and 'No bloggers are self-absorbed' are universal; 'Some bloggers are self-absorbed' and 'Some bloggers are not self-absorbed' are particular; 'Bernie is self-absorbed' and 'Bernie is not self-absorbed' are singular. Traditional Formal Logic (TFL), however, does…

  • Being as the Apotheosis of the Copula: Frege’s Eliminativism in his Dialogue with Pünjer on Existence

    Some time before 1884, Gottlob Frege had a discussion about existence with the Protestant theologian Bernard Pünjer (1850-1885). A record of the dialogue was found in Frege's Nachlass, and an English translation is available in Gottlob Frege: Posthumous Writings, eds. Hans Hermes et al., University of Chicago Press, 1979. Herewith, some critical commentary on part…

  • Burden of Proof in Philosophy?

    1. The question this post raises is whether it is at all useful to speak of burden of proof (BOP) in dialectical situations in which there is no judge or tribunal to lay down and enforce rules of procedure.  By a dialectical situation I mean a context in which orderly discussion occurs among two or more competent…

  • Notes on Burden of Proof and Defeasible Presumption

    Since I don't understand this topic very well, I blog about it.  Nescio, ergo blogo!  Caveat lector!  The following notes are a blend of what I have gleaned from Nicholas Rescher and Douglas Walton and my own reflections. 1. Burden of Proof and Defeasible Presumption are correlative notions.  If there is a defeasible presumption in…

  • Burden of Proof in Philosophy: Preliminary Thoughts

    A reader asks about burden of proof in philosophy.  I really ought to have a worked-out theory on this, but I don't.  Here are some very tentative remarks. 1. In the law it is clear where the burden of proof lies: on the plaintiff in a civil case and on the prosecutor in a criminal…

  • The Rabbit of Real Existence and the Empty Hat of Mere Logic

    Consider again this curious piece of reasoning: 1. For any x, x = x.  Ergo:2. a = a.  Ergo:3. (Ex)(x = a). Ergo:4. a exists. This reasoning is curious because it seems to show that one can deduce the real existence of an individual a from a purely formal principle of logic, the Law of…

  • Deducing John McCain from the Principle of Identity

    What, if anything, is wrong with the following argument:    1. (x)(x = x) (Principle of Identity)   Therefore   2. John McCain = John McCain (From 1 by Universal Instantiation)   Therefore   3. (Ex)(x = John McCain) (From 2 by Existential Generalization)   Therefore   4. John McCain exists. (From 3 by translation into ordinary idiom) The initial premise…

  • Does Any Noncontingent Proposition Entail a Contingent Proposition?

    This post continues the discussion in the comment thread of an earlier post.   Propositions divide into the contingent and the noncontingent.  The noncontingent divide into the necessary and the impossible.  A proposition is contingent iff it is true in some, but not all, broadly logical possible worlds, 'worlds' for short.   A proposition is necessary iff it…

  • Butchvarov on Metaphysical Realism and Logical Nonrealism

    This post is a  stab at a summary and evaluation of Panayot Butchvarov's "Metaphysical Realism and Logical Nonrealism" which is available both online and in R. M. Gale, ed., The Blackwell Guide to Metaphysics (Oxford: Blackwell 2002), pp. 282-302.  Page references are to the Blackwell source. The ComBox stands open if readers have some informed commentary…

  • ‘Material’ as *Alienans* in ‘Material Implication’

    The topic of conditionals is ancient, not as ancient as Aristotle and logic itself, but damn near: hard thinking on this topic began with the Dialectical School which featured such worthies as Philo the   Logician and Diodorus Cronus, circa late 4th to mid-3rd centuries B.C. In nuce, those gentlemen had wrapped their minds around what…