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5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic

[overview of what must exist to enable logic]

22 ideas
Our research always hopes that reality embodies the logic we are employing [Peirce]
     Full Idea: Every attempt to understand anything at least hopes that the very objects of study themselves are subject to a logic more or less identical with that which we employ.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], VIII)
     A reaction: The idea that external objects might be subject to a logic has become very unfashionable since Frege, but I love the idea. I'm inclined to think that we derive our logic from the world, so I'm a bit more confident that Peirce.
Logic is a fiction, which invents the view that one thought causes another [Nietzsche]
     Full Idea: The model of a complete fiction is logic. Here a thinking is made up where a thought is posited as the cause of another thought.
     From: Friedrich Nietzsche (Fragments from 1885-1886 [1886], 34[249])
     A reaction: He could almost be referring to Frege's Third Realm. Most hard core analytic philosophers seem to think that propositions have tight logical relationships which are nothing to do with the people who think them.
Logicians presuppose a world, and ignore logic/world connections, so their logic is impure [Husserl, by Velarde-Mayol]
     Full Idea: Husserl maintained that because most logicians have not studied the connection between logic and the world, logic did not achieve its status of purity. Even more, their logic implicitly presupposed a world.
     From: report of Edmund Husserl (Formal and Transcendental Logic [1929]) by Victor Velarde-Mayol - On Husserl 4.5.1
     A reaction: The point here is that the bracketing of phenomenology, to reach an understanding with no presuppositions, is impossible if you don't realise what your are presupposing. I think the logic/world relationship is badly neglected, thanks to Frege.
Phenomenology grounds logic in subjective experience [Husserl, by Velarde-Mayol]
     Full Idea: The phenomenological logic grounds logical notions in subjective acts of experience.
     From: report of Edmund Husserl (Formal and Transcendental Logic [1929], p.183) by Victor Velarde-Mayol - On Husserl 4.5.1
     A reaction: I'll approach this with great caution, but this is a line of thought that appeals to me. The core assumptions of logic do not arise ex nihilo.
Logic is concerned with the real world just as truly as zoology [Russell]
     Full Idea: Logic is concerned with the real world just as truly as zoology, though with its more abstract and general features.
     From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XVI)
     A reaction: I love this idea and am very sympathetic to it. The rival view seems to be that logic is purely conventional, perhaps defined by truth tables etc. It is hard to see how a connective like 'tonk' could be self-evidently silly if it wasn't 'unnatural'.
Logic can only assert hypothetical existence [Russell]
     Full Idea: No proposition of logic can assert 'existence' except under a hypothesis.
     From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XVIII)
     A reaction: I am prepared to accept this view fairly dogmatically, though Musgrave shows some of the difficulties of the if-thenist view (depending on which 'order' of logic is being used).
Logic can be known a priori, without study of the actual world [Russell]
     Full Idea: Logical propositions are such as can be known a priori, without study of the actual world.
     From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XVIII)
     A reaction: This remark constrasts strikingly with Idea 12444, which connects logic to the actual world. Is it therefore a priori synthetic?
Logic is highly general truths abstracted from reality [Russell, by Glock]
     Full Idea: In 1911 Russell held that the propositions of logic are supremely general truths about the most pervasive traits of reality, to which we have access by abstraction from non-logical propositions.
     From: report of Bertrand Russell (Philosophical Implications of Mathematical logic [1911]) by Hans-Johann Glock - What is Analytic Philosophy? 2.4
     A reaction: Glock says the rival views were Mill's inductions, psychologism, and Frege's platonism. Wittgenstein converted Russell to a fifth view, that logic is empty tautologies. I remain resolutely attached to Russell's abstraction view.
Russell unusually saw logic as 'interpreted' (though very general, and neutral) [Russell/Whitehead, by Linsky,B]
     Full Idea: Russell did not view logic as an uninterpreted calculus awaiting interpretations [the modern view]. Rather, logic is a single 'interpreted' body of a priori truths, of propositions rather than sentence forms - but maximally general and topic neutral.
     From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Bernard Linsky - Russell's Metaphysical Logic 1
     A reaction: This is the view which Wittgenstein challenged, saying logic is just conventional. Linsky claims that Russell's logicism is much more plausible, once you understand his view of logic.
The only classes are things, predicates and relations [Russell]
     Full Idea: The only classes appear to be things, predicates and relations.
     From: Bertrand Russell (The Principles of Mathematics [1903], §440)
     A reaction: This is the first-order logic view of reality, which has begun to look incredibly impoverished in modern times. Processes certainly demand a hearing, as do modal facts.
The propositions of logic are analytic tautologies [Wittgenstein]
     Full Idea: The propositions of logic are tautologies. Therefore the propositions of logic say nothing. (They are the analytic propositions).
     From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.1)
Whether a modal claim is true depends on how the object is described [Quine, by Fine,K]
     Full Idea: Quine says if ∃x□(x>7) makes sense, then for which object x is the condition rendered true? Specify it as '9' and it is apparently rendered true, specify it as 'the number of planets' and it is apparently rendered false.
     From: report of Willard Quine (Three Grades of Modal Involvement [1953]) by Kit Fine - Quine on Quantifying In p.105
     A reaction: This is normally characterised as Quine saying that only de dicto involvement is possible, and not de re involvement. Or that that all essences are nominal, and cannot be real.
Logical languages are rooted in ordinary language, and that connection must be kept [Quine]
     Full Idea: A logical language is not independent of ordinary language. It has its roots in ordinary language, and these roots are not to be severed.
     From: Willard Quine (Mr Strawson on Logical Theory [1953], V)
     A reaction: Music to my ears. When you study logic, no one has to teach you what the words 'or' and 'if-then' mean, but they are disambiguated by the symbolism. The roots of logic are in ordinary talk of 'and', 'or' and 'not', which is the real world.
Unfashionably, I think logic has an empirical foundation [Putnam]
     Full Idea: Today, the tendency among philosophers is to assume that in no sense does logic itself have an empirical foundation. I believe this tendency is wrong.
     From: Hilary Putnam (Philosophy of Logic [1971], Ch.9)
     A reaction: I agree, not on the basis of indispensability to science, but on the basis of psychological processes that lead from experience to logic. Russell and Quine are Putnam's allies here, and Frege is his opponent. Putnam developed a quantum logic.
Logicians like their entities to exhibit a maximum degree of purity [Kaplan]
     Full Idea: Logicians like their entities to exhibit a maximum degree of purity.
     From: David Kaplan (Transworld Heir Lines [1967], p.97)
     A reaction: An important observation, which explains why the modern obsession with logic has often led us down the metaphysical primrose path to ontological hell.
Logical space is abstracted from the actual world [Stalnaker]
     Full Idea: Logical space is not given independently of the individuals that occupy it, but is abstracted from the world as we find it.
     From: Robert C. Stalnaker (Anti-essentialism [1979], p.85)
     A reaction: I very much like the second half of this idea, and am delighted to find Stalnaker endorsing it. I take the logical connectives to be descriptions of how things behave, at a high level of generality.
Logic is a mathematical account of a universe of relations [Badiou]
     Full Idea: Logic should first and foremost be a mathematical thought of what a universe of relations is.
     From: Alain Badiou (Briefings on Existence [1998], 14)
A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos]
     Full Idea: One may be of the opinion that no sentence ought to be considered as a truth of logic if, no matter how it is interpreted, it asserts that there are sets of certain sorts.
     From: George Boolos (On Second-Order Logic [1975], p.44)
     A reaction: My intuition is that in no way should any proper logic assert the existence of anything at all. Presumably interpretations can assert the existence of numbers or sets, but we should be able to identify something which is 'pure' logic. Natural deduction?
In first-order we can't just assert existence, and it is very hard to deny something's existence [Bach]
     Full Idea: In standard logic we can't straightforwardly say that n exists. We have to resort to using a formula like '∃x(x=n)', but we can't deny n's existence by negating that formula, because standard first-order logic disallows empty names.
     From: Kent Bach (What Does It Take to Refer? [2006], 22.2 L1)
Either logic determines objects, or objects determine logic, or they are separate [Shapiro]
     Full Idea: Ontology does not depend on language and logic if either one has the objects determining the logic, or the objects are independent of the logic.
     From: Stewart Shapiro (Philosophy of Mathematics [1997], 6.4)
     A reaction: I favour the first option. I think we should seek an account of how logic grows from our understanding of the physical world. If this cannot be established, I shall invent a new Mad Logic, and use it for all my future reasoning, with (I trust) impunity.
Maybe mathematical logic rests on information-processing [Ladyman/Ross]
     Full Idea: It is claimed that mathematical logic can be understood in terms of information-processing.
     From: J Ladyman / D Ross (Every Thing Must Go [2007], 3.7.5)
     A reaction: [They cite Chaitin 1987] I don't understand how this would work, but it is still worth quoting. This would presumably make logic rest on processes rather than on entities. I quite like that.
We can use truth instead of ontologically loaded second-order comprehension assumptions about properties [Halbach]
     Full Idea: The reduction of 2nd-order theories (of properties or sets) to axiomatic theories of truth may be conceived as a form of reductive nominalism, replacing existence assumptions (for comprehension axioms) by ontologically innocent truth assumptions.
     From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.1)
     A reaction: I like this very much, as weeding properties out of logic (without weeding them out of the world). So-called properties in logic are too abundant, so there is a misfit with their role in science.