9868
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An expression refers if it is a singular term in some true sentences [Wright,C, by Dummett]
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Full Idea:
For Wright, an expression refers to an object if it fulfils the 'syntactic role' of a singular term, and if we have fixed the truth-conditions of sentences containing it in such a way that some of them come out true.
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From:
report of Crispin Wright (Frege's Concept of Numbers as Objects [1983]) by Michael Dummett - Frege philosophy of mathematics Ch.15
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A reaction:
Much waffle is written about reference, and it is nice to hear of someone actually trying to state the necessary and sufficient conditions for reference to be successful. So is it possible for 'the round square' to ever refer? '...is impossible to draw'
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13861
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Number theory aims at the essence of natural numbers, giving their nature, and the epistemology [Wright,C]
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Full Idea:
In the Fregean view number theory is a science, aimed at those truths furnished by the essential properties of zero and its successors. The two broad question are then the nature of the objects, and the epistemology of those facts.
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From:
Crispin Wright (Frege's Concept of Numbers as Objects [1983], Intro)
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A reaction:
[compressed] I pounce on the word 'essence' here (my thing). My first question is about the extent to which the natural numbers all have one generic essence, and the extent to which they are individuals (bless their little cotton socks).
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13892
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One could grasp numbers, and name sizes with them, without grasping ordering [Wright,C]
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Full Idea:
Someone could be clear about number identities, and distinguish numbers from other things, without conceiving them as ordered in a progression at all. The point of them would be to make comparisons between sizes of groups.
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From:
Crispin Wright (Frege's Concept of Numbers as Objects [1983], 3.xv)
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A reaction:
Hm. Could you grasp size if you couldn't grasp which of two groups was the bigger? What's the point of noting that I have ten pounds and you only have five, if you don't realise that I have more than you? You could have called them Caesar and Brutus.
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17441
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Wright thinks Hume's Principle is more fundamental to cardinals than the Peano Axioms are [Wright,C, by Heck]
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Full Idea:
Wright is claiming that HP is a special sort of truth in some way: it is supposed to be the fundamental truth about cardinality; ...in particular, HP is supposed to be more fundamental, in some sense than the Dedekind-Peano axioms.
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From:
report of Crispin Wright (Frege's Concept of Numbers as Objects [1983]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 1
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A reaction:
Heck notes that although PA can be proved from HP, HP can be proven from PA plus definitions, so direction of proof won't show fundamentality. He adds that Wright thinks HP is 'more illuminating'.
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13862
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There are five Peano axioms, which can be expressed informally [Wright,C]
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Full Idea:
Informally, Peano's axioms are: 0 is a number, numbers have a successor, different numbers have different successors, 0 isn't a successor, properties of 0 which carry over to successors are properties of all numbers.
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From:
Crispin Wright (Frege's Concept of Numbers as Objects [1983], Intro)
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A reaction:
Each statement of the famous axioms is slightly different from the others, and I have reworded Wright to fit him in. Since the last one (the 'induction axiom') is about properties, it invites formalization in second-order logic.
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10140
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We derive Hume's Law from Law V, then discard the latter in deriving arithmetic [Wright,C, by Fine,K]
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Full Idea:
Wright says the Fregean arithmetic can be broken down into two steps: first, Hume's Law may be derived from Law V; and then, arithmetic may be derived from Hume's Law without any help from Law V.
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From:
report of Crispin Wright (Frege's Concept of Numbers as Objects [1983]) by Kit Fine - The Limits of Abstraction I.4
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A reaction:
This sounds odd if Law V is false, but presumably Hume's Law ends up as free-standing. It seems doubtful whether the resulting theory would count as logic.
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8692
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Frege has a good system if his 'number principle' replaces his basic law V [Wright,C, by Friend]
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Full Idea:
Wright proposed removing Frege's basic law V (which led to paradox), replacing it with Frege's 'number principle' (identity of numbers is one-to-one correspondence). The new system is formally consistent, and the Peano axioms can be derived from it.
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From:
report of Crispin Wright (Frege's Concept of Numbers as Objects [1983]) by Michčle Friend - Introducing the Philosophy of Mathematics 3.7
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A reaction:
The 'number principle' is also called 'Hume's principle'. This idea of Wright's resurrected the project of logicism. The jury is ought again... Frege himself questioned whether the number principle was a part of logic, which would be bad for 'logicism'.
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17440
|
Wright says Hume's Principle is analytic of cardinal numbers, like a definition [Wright,C, by Heck]
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Full Idea:
Wright intends the claim that Hume's Principle (HP) embodies an explanation of the concept of number to imply that it is analytic of the concept of cardinal number - so it is an analytic or conceptual truth, much as a definition would be.
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From:
report of Crispin Wright (Frege's Concept of Numbers as Objects [1983]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 1
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A reaction:
Boolos is quoted as disagreeing. Wright is claiming a fundamental truth. Boolos says something can fix the character of something (as yellow fixes bananas), but that doesn't make it 'fundamental'. I want to defend 'fundamental'.
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13870
|
We can't use empiricism to dismiss numbers, if numbers are our main evidence against empiricism [Wright,C]
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Full Idea:
We may not be able to settle whether some general form of empiricism is correct independently of natural numbers. It might be precisely our grasp of the abstract sortal, natural number, which shows the hypothesis of empiricism to be wrong.
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From:
Crispin Wright (Frege's Concept of Numbers as Objects [1983], 1.i)
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A reaction:
A nice turning of the tables. In the end only coherence decides these things. You may accept numbers and reject empiricism, and then find you have opened the floodgates for abstracta. Excessive floodgates, or blockages of healthy streams?
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13899
|
The Peano Axioms, and infinity of cardinal numbers, are logical consequences of how we explain cardinals [Wright,C]
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Full Idea:
The Peano Axioms are logical consequences of a statement constituting the core of an explanation of the notion of cardinal number. The infinity of cardinal numbers emerges as a consequence of the way cardinal number is explained.
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From:
Crispin Wright (Frege's Concept of Numbers as Objects [1983], 4.xix)
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A reaction:
This, along with Idea 13896, nicely summarises the neo-logicist project. I tend to favour a strategy which starts from ordering, rather than identities (1-1), but an attraction is that this approach is closer to counting objects in its basics.
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13895
|
The standard objections are Russell's Paradox, non-logical axioms, and Gödel's theorems [Wright,C]
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Full Idea:
The general view is that Russell's Paradox put paid to Frege's logicist attempt, and Russell's own attempt is vitiated by the non-logical character of his axioms (esp. Infinity), and by the incompleteness theorems of Gödel. But these are bad reasons.
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From:
Crispin Wright (Frege's Concept of Numbers as Objects [1983], 4.xvi)
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A reaction:
Wright's work is the famous modern attempt to reestablish logicism, in the face of these objections.
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13877
|
Singular terms in true sentences must refer to objects; there is no further question about their existence [Wright,C]
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Full Idea:
When a class of terms functions as singular terms, and the sentences are true, then those terms genuinely refer. Being singular terms, their reference is to objects. There is no further question whether they really refer, and there are such objects.
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From:
Crispin Wright (Frege's Concept of Numbers as Objects [1983], 1.iii)
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A reaction:
This seems to be a key sentence, because this whole view is standardly called 'platonic', but it certainly isn't platonism as we know it, Jim. Ontology has become an entirely linguistic matter, but do we then have 'sakes' and 'whereaboutses'?
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12189
|
Logical necessity involves a decision about usage, and is non-realist and non-cognitive [Wright,C, by McFetridge]
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Full Idea:
Wright espouses a non-realist, indeed non-cognitive account of logical necessity. Crucial to this is the idea that acceptance of a statement as necessary always involves an element of decision (to use it in a necessary way).
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From:
report of Crispin Wright (Inventing Logical Necessity [1986]) by Ian McFetridge - Logical Necessity: Some Issues §3
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A reaction:
This has little appeal to me, as I take (unfashionably) the view that that logical necessity is rooted in the behaviour of the actual physical world, with which you can't argue. We test simple logic by making up examples.
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7320
|
Holism cannot give a coherent account of scientific methodology [Wright,C, by Miller,A]
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Full Idea:
Crispin Wright has argued that Quine's holism is implausible because it is actually incoherent: he claims that Quine's holism cannot provide us with a coherent account of scientific methodology.
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From:
report of Crispin Wright (Inventing Logical Necessity [1986]) by Alexander Miller - Philosophy of Language 4.5
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A reaction:
This sounds promising, given my intuitive aversion to linguistic holism, and almost everything to do with Quine. Scientific methodology is not isolated, but spreads into our ordinary (experimental) interactions with the world (e.g. Idea 2461).
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13885
|
If apparent reference can mislead, then so can apparent lack of reference [Wright,C]
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Full Idea:
If the appearance of reference can be misleading, why cannot an apparent lack of reference be misleading?
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From:
Crispin Wright (Frege's Concept of Numbers as Objects [1983], 2.xi)
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A reaction:
A nice simple thought. Analytic philosophy has concerned itself a lot with sentences that seem to refer, but the reference can be analysed away. For me, this takes the question of reference out of the linguistic sphere, which wasn't Wright's plan.
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6217
|
Natural law is supplied to the human mind by reality and human nature [Cumberland]
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Full Idea:
Some truths of natural law, concerning guides to moral good and evil, and duties not laid down by civil law and government, are necessarily supplied ot the human mind by the nature of things and of men.
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From:
Richard Cumberland (De Legibus Naturae [1672], Ch.I.I)
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A reaction:
I agree that some moral truths have the power of self-evidence. If you say they are built into the mind, we now ask what did the building, and evolution is the only answer, and hence we distance ourselves from the truths, seeing them as strategies.
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6221
|
If there are different ultimate goods, there will be conflicting good actions, which is impossible [Cumberland]
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Full Idea:
If there be posited different ultimate ends, whose causes are opposed to each other, then there will be truly good actions likewise opposed to each other, which is impossible.
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From:
Richard Cumberland (De Legibus Naturae [1672], Ch.V.XVI)
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A reaction:
A very interesting argument for there being one good rather than many, and an argument which I don't recall in any surviving Greek text. A response might be to distinguish between what is 'right' and what is 'good'. See David Ross.
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5954
|
All inventions of the mind aim at pleasure, and those that don't are worthless [Metrodorus of Lamp., by Plutarch]
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Full Idea:
Metrodorus says that all the wonderful, ingenious and brilliant inventions of the mind have been contrived for the sake of pleasure of the flesh or for the sake of looking forward to it, and any accomplishment not leading to this end is worthless.
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From:
report of Metrodorus (Lamp) (fragments/reports [c.291 BCE], Fr 6) by Plutarch - 74: Reply to Colotes §1125
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A reaction:
It is very hard to think of counterexamples! Would anyone bother to work out the theorems of number theory if they didn't enjoy doing it? Would any sensible person make great sacrifices if they didn't think that increased happiness would result?
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6220
|
The happiness of all contains the happiness of each, and promotes it [Cumberland]
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Full Idea:
The common happiness of all contains the greatest happiness for each, and most effectively promotes it. …There is no path leading anyone to his own happiness, other than the path which leads all to the common happiness.
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From:
Richard Cumberland (De Legibus Naturae [1672], Ch.I.VI)
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A reaction:
I take this as a revolutionary idea, which leads to utilitarianism. It is doing what seemed to the Greeks unthinkable, which is combining hedonism with altruism. There is no proof for it, but it is a wonderful clarion call for building a civil society.
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6216
|
Natural law is immutable truth giving moral truths and duties independent of society [Cumberland]
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Full Idea:
Natural law is certain propositions of immutable truth, which guide voluntary actions about the choice of good and avoidance of evil, and which impose an obligation to act, even without regard to civil laws, and ignoring compacts of governments.
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From:
Richard Cumberland (De Legibus Naturae [1672], Ch.I.I)
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A reaction:
Not a popular view, but I am sympathetic. If you are in a foreign country and find a person lying in pain, there is a terrible moral deficiency in anyone who just ignores such a thing. No legislation can take away a person's right of self-defence.
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