• PL Olcott
    524
    ---One such principle in truthmaker theory is the entailment principle: if X is a truthmaker for Y,
    ---then X is a truthmaker for anything entailed by Y.

    ---While seemingly quite plausible, the entailment principle runs into an immediate difficulty:
    ---the problem of trivial truthmakers for necessary truths. ‘Socrates is a philosopher’ also
    ---entails ‘2 + 2 =4’, at least when entailment is thought of on the model of necessary truth
    ---preservation. https://iep.utm.edu/truth-ma/

    The author of this article is quite brilliant and very well established in this field. How could he possibly construe: {‘Socrates is a philosopher’ also entails ‘2 + 2 =4’} ?
  • Leontiskos
    1.4k
    This seems like a general problem with the truth functional approach, in this case the truth functional approach to entailment. Teleology crops up like weeds. ...Or crops!
  • Banno
    23.4k
    It's never the case that two and two is not four. So we are only considering implications in which the consequent is true. In all such cases, the implication is also true.

    I don't see an issue.

    KiJ8A.png

    Rows one and three.
  • Leontiskos
    1.4k
    I don't see an issue.Banno

    Here's an introduction:

    An oddity [of material implication] pointed out early by MacColl (1908) is the observation that of any two sentences of the form “not A or B” and “not B or A”, at least one must be true. Assuming the equivalence with the material conditional, this implies that either “if John is a physician, then he is red-haired” or “if John is red-haired, then he is a physician” must be true. Intuitively, however, one may be inclined to reject both conditionals. Similar complications, known as the paradoxes of material implication, concern the fact that for any sentences A and B, “if A then B” follows from “not A”, but also from “B”, thereby allowing true and false sentences to create true conditionals irrespective of their content (C. I. Lewis 1912). Another peculiarity looms large: the negation of “if A then B” is predicted to be “A and not B”, but intuitively one may deny that “if God exists, all criminals will go to heaven” without committing oneself to the existence of God (cited in Lycan 2001).

    A fourth complication is that conditional sentences in natural language are not limited to indicative conditionals (“if I strike this match, it will light”), but also include subjunctive conditionals used to express counterfactual hypotheses (“if I had struck this match, it would have lit”). All counterfactual conditionals would be vacuously true if analyzed as material conditionals with a false antecedent, as pointed out by Quine (1950), an obviously inadequate result, suggesting that the interplay of grammatical tense and grammatical mood should also be of concern to understand the logic of conditionals.

    To a large extent, the development of conditional logics over the past century has thus been driven by the quest for a more sophisticated account of the connection between antecedent and consequent in conditionals.
    SEP | The Logic of Conditionals
  • PL Olcott
    524
    It's never the case that two and two is not four. So we are only considering implications in which the consequent is true. In all such cases, the implication is also true.Banno

    You see these things exactly the same way that I do.
  • PL Olcott
    524
    To a large extent, the development of conditional logics over the past century has thus been driven by the quest for a more sophisticated account of the connection between antecedent and consequent in conditionals.SEP | The Logic of Conditionals

    When we require that the consequent be a necessary semantic consequence of its antecedent all of the issues go away. A ⇒ B then becomes A ⊨ B and we quit using the former.

    We could do as
    So we are only considering implications in which the consequent is true. In all such casesBanno
    suggests yet limit the use of ⇒ to propositional logic.
  • Banno
    23.4k
    Yep. Been there.

    For what it's worth, given that 2+2 is 4, "Socrates is a fish" entails 2+2=4.

    The truth or falsehood of the antecedent makes no different to the truth of the entailment, if the consequent is true.
  • Leontiskos
    1.4k


    What is at stake here is the nature of implication, not the meaning of material implication. We are questioning whether material implication is an adequate account of implication. No one is confused about how material implication works.
  • PL Olcott
    524
    What is at stake here is the nature of implication, not the meaning of material implication. We are questioning whether material implication is an adequate account of implication. No one is confused about how material implication works.Leontiskos

    The same author says this later on in the same article.

    For example, one might think that some sort of relevance notion of entailment is at stake (for example, Restall 1996); the hope is to develop a conception of entailment that maintains that while ‘Socrates is a philosopher’ en-tails ‘Someone is a philosopher’, it does not entail ‘2 + 2 =4’.
  • Banno
    23.4k
    Ah, you are looking for the essence of implication... :wink:
  • Leontiskos
    1.4k
    I'm going to find an essence one of these days, I swear! :sweat:
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