Category: Logica Docens
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The Notion of a Cumulative Case
In a comment thread Tony Hanson asked me if I had written a post on cumulative-case arguments. After some digging, I located one that I had written 24 August 2004. Here it is for what its worth. …………… Suppose you have a good reason R1 to do X. Then along comes a second good…
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De Dicto/De Re
In the course of thinking about the de dicto/de re distinction, I pulled the Oxford Companion to Philosophy from the shelf and read the eponymous entry. After being told that the distinction "seems to have first surfaced explicitly in Abelard," I was then informed that the distinction occurs: . . . in two main forms:…
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On Falsely Locating the Difference Between Deduction and Induction
One commonly hears it said that the difference between deductive and inductive inference is that the former moves from the universal to the singular, while the latter proceeds from the singular to the universal. (For a recent and somewhat surprising example, see David Bloor, "Wittgenstein as a Conservative Thinker" in The Sociology of Philosophical Knowledge,…
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Validity, Invalidity, and Contravalidity
If a deductive argument is valid, that does not say much about it: it might still be probatively worthless. Nevertheless, validity is a necessary condition of a deductive argument's being probative. So it is important to have a clear understanding of the notion of validity. An argument is valid if and only if one of…
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My Lately Posted Logic Problem Pondered . . .
. . . and pondered well by David Parker over at Pondering the Preponderance. I challenged the reader to spot what is wrong in the following argument, an argument I thought was interesting because it is fairly seductive, as compared to the stock examples in logic texts: The Argument1. A necessary truth is true.2. Whatever is true…
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A Logic Problem
Consider this argument: 1. A necessary truth is true. 2. Whatever is true is possibly true. 3. Whatever is possibly true could be false. Therefore 4. A necessary truth could be false. A sound argument is one that satisfies two conditions: its premises are all true, and the reasoning it embodies is correct. Is the…
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Logic’s Limit
Logic is not to be denigrated, nor is it to be overestimated. It is an excellent vehicle for safe travel among concepts and propositions. It will save us from many an error and perhaps even lead us to a few truths. But it cannot move us beyond the plane of concepts and propositions and arguments.…
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Collective Inconsistency and Plural Predication
We often say things like 1. The propositions p, q, r are inconsistent. Suppose, to keep things simple, that each of the three propositions is self-consistent. It will then be false that each proposition is self-inconsistent. (1), then, is a plural predication that cannot be given a distributive paraphrase. What (1) says is that the three…
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A Problem With the Multiple Relations Approach to Plural Predication
Consider 1. Sam and Dave are meeting together. 2. Al, Bill, and Carl are meeting together. 3. Some people are meeting together. Obviously, neither (1) nor (2) can be decomposed into a conjunction of singular predications. Thus (2) cannot be analyzed as 'Al is meeting together & Bill is meeting together & Carl is meeting…
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Irreducibly Plural Predication: ‘They are Surrounding the Building’
Let's think about the perfectly ordinary and obviously intelligible sentence, 1. They are surrounding the building. I borrow the example from Thomas McKay, Plural Predication (Oxford 2006), p. 29. They could be demonstrators. And unless some of them have very long arms, there is no way that any one of them could satisfy the predicate,…
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Necessitas Consequentiae versus Necessitas Consequentiis
Take the sentence, 'If I will die tomorrow, then I will die tomorrow.' This has the form If p, then p, where 'p' is a placeholder for a proposition. Any sentence of this form is not just true, but logically true, i.e., true in virtue of its logical form. Now every sentence true in virtue of its…
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Amphiboly
Amphiboly is syntactic ambiguity. "The foolish fear that God is dead." This sentence is amphibolous because its ambiguity does not have a semantic origin in the multiplicity of meaning of any constituent word, but derives from the ambiguous way the words are put together. On one reading, the construction is a sentence: 'The foolish/ fear…
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Is There a Paradox of Conjunction?
There are supposed to be paradoxes of material and strict implication. If there are, why is there no paradox of conjunction? And if there is no paradox of conjunction, why are there paradoxes of material and strict implication? With apologies to the friends and family of Dennis Wilson, the ill-starred original drummer of the Beach…
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Geach on Assertion
The main point of Peter Geach's paper, "Assertion" (Logic Matters, Basil Blackwell, 1972, pp. 254-269) is what he calls the Frege point: A thought may have just the same content whether you assent to its truth or not; a proposition may occur in discourse now asserted, now unasserted; and yet be recognizably the same proposition.…
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Five Grades of Self-Referential Inconsistency: Towards a Taxonomy
Some sentences, whether or not they are about other things, are about themselves. They refer to themselves. Hence we say they are 'self-referential.' The phenomenon of sentential self-referentiality is sometimes benign. One example is 'This sentence is true.' Another is 'Every proposition is either true or false.' Of interest here are the more or less…