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22353
|
One view says objectivity is making a successful claim which captures the facts [Reiss/Sprenger]
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Full Idea:
One conception of objectivity is that the facts are 'out there', and it is the task of scientists to discover, analyze and sytematize them. 'Objective' is a success word: if a claim is objective, it successfully captures some feature of the world.
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From:
Reiss,J/Spreger,J (Scientific Objectivity [2014], 2)
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A reaction:
This seems to describe truth, rather than objectivity. You can establish accurate facts by subjective means. You can be fairly objective but miss the facts. Objectivity is a mode of thought, not a link to reality.
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22356
|
An absolute scientific picture of reality must not involve sense experience, which is perspectival [Reiss/Sprenger]
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Full Idea:
Sense experience is necessarily perspectival, so to the extent to which scientific theories are to track the absolute conception [of reality], they must describe a world different from sense experience.
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From:
Reiss,J/Spreger,J (Scientific Objectivity [2014], 2.3)
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A reaction:
This is a beautifully simple and interesting point. Even when you are looking at a tree, to grasp its full reality you probably need to close your eyes (which is bad news for artists).
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22359
|
Topic and application involve values, but can evidence and theory choice avoid them? [Reiss/Sprenger]
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Full Idea:
There may be values involved in the choice of a research problem, the gathering of evidence, the acceptance of a theory, and the application of results. ...The first and fourth do involve values, but what of the second and third?
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From:
Reiss,J/Spreger,J (Scientific Objectivity [2014], 3.1)
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A reaction:
[compressed] My own view is that the danger of hidden distorting values has to be recognised, but it is then possible, by honest self-criticism, to reduce them to near zero. Sociological enquiry is different, of course.
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22360
|
The Value-Free Ideal in science avoids contextual values, but embraces epistemic values [Reiss/Sprenger]
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Full Idea:
According to the Value-Free Ideal, scientific objectivity is characterised by absence of contextual values and by exclusive commitment to epistemic values in scientific reasoning.
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From:
Reiss,J/Spreger,J (Scientific Objectivity [2014], 3.1)
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A reaction:
This seems appealing, because it concedes that we cannot be value-free, without suggesting that we are unavoidably swamped by values. The obvious question is whether the two types of value can be sharply distinguished.
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22362
|
Value-free science needs impartial evaluation, theories asserting facts, and right motivation [Reiss/Sprenger]
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Full Idea:
Three components of value-free science are Impartiality (appraising theories only by epistemic scientific standards), Neutrality (the theories make no value statements), and Autonomy (the theory is motivated only by science).
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From:
Reiss,J/Spreger,J (Scientific Objectivity [2014], 3.3)
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A reaction:
[They are summarising Hugh Lacey, 1999, 2002] I'm not sure why the third criterion matters, if the first two are met. If a tobacco company commissions research on cigarettes, that doesn't necessarily make the findings false or prejudiced.
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22364
|
Thermometers depend on the substance used, and none of them are perfect [Reiss/Sprenger]
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Full Idea:
Thermometers assume the length of the fluid or gas is a function of temperature, and different substances yield different results. It was decided that different thermometers using the same substance should match, and air was the best, but not perfect.
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From:
Reiss,J/Spreger,J (Scientific Objectivity [2014], 4.1)
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A reaction:
[summarising Hasok Chang's research] This is a salutary warning that instruments do not necessarily solve the problem of objectivity, though thermometers do seem to be impersonal, and offer relative accuracy (i.e. ranking temperatures). Cf breathalysers.
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10170
|
While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price]
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Full Idea:
While truth can be defined in a relative way, as truth in one particular model, a non-relative notion of truth is implied, as truth in all models.
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From:
E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4)
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A reaction:
[The article is actually discussing arithmetic] This idea strikes me as extremely important. True-in-all-models is usually taken to be tautological, but it does seem to give a more universal notion of truth. See semantic truth, Tarski, Davidson etc etc.
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8083
|
Boole applied normal algebra to logic, aiming at an algebra of thought [Boole, by Devlin]
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Full Idea:
Boole proposed to use the entire apparatus of a school algebra class, with operations such as addition and multiplication, methods to solve equations, and the like, to produce an algebra of thought.
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|
From:
report of George Boole (The Laws of Thought [1854]) by Keith Devlin - Goodbye Descartes Ch.3
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|
A reaction:
The Stoics didn’t use any algebraic notation for their study of propositions, so Boole's idea launched full blown propositional logic, and the rest of modern logic followed. Nice one.
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8686
|
Boole made logic more mathematical, with algebra, quantifiers and probability [Boole, by Friend]
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Full Idea:
Boole (followed by Frege) began to turn logic from a branch of philosophy into a branch of mathematics. He brought an algebraic approach to propositions, and introduced the notion of a quantifier and a type of probabilistic reasoning.
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|
From:
report of George Boole (The Laws of Thought [1854], 3.2) by Michèle Friend - Introducing the Philosophy of Mathematics
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|
A reaction:
The result was that logic not only became more mathematical, but also more specialised. We now have two types of philosopher, those steeped in mathematical logic and the rest. They don't always sing from the same songsheet.
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10175
|
Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price]
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Full Idea:
In second-order logic there are three kinds of variables, for objects, for functions, and for predicates or sets.
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From:
E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5)
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|
A reaction:
It is interesting that a predicate seems to be the same as a set, which begs rather a lot of questions. For those who dislike second-order logic, there seems nothing instrinsically wicked in having variables ranging over innumerable multi-order types.
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22277
|
Boole's method was axiomatic, achieving economy, plus multiple interpretations [Boole, by Potter]
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Full Idea:
Boole's work was an early example of the axiomatic method, whereby intellectual economy is achieved by studying a set of axioms in which the primitive terms have multiple interpretations.
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|
From:
report of George Boole (The Laws of Thought [1854]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 02 'Boole'
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A reaction:
Unclear about this. I suppose the axioms are just syntactic, and a range of semantic interpretations can be applied. Are De Morgan's Laws interpretations, or implications of the syntactic axioms? The latter, I think.
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10164
|
Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price]
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Full Idea:
A common formulation of Peano Arithmetic uses 2nd-order logic, the constant '1', and a one-place function 's' ('successor'). Three axioms then give '1 is not a successor', 'different numbers have different successors', and induction.
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|
From:
E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2)
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|
A reaction:
This is 'second-order' Peano Arithmetic, though it is at least as common to formulate in first-order terms (only quantifying over objects, not over properties - as is done here in the induction axiom). I like the use of '1' as basic instead of '0'!
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10167
|
Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price]
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Full Idea:
Structuralism has emerged from the development of abstract algebra (such as group theory), the creation of axiom systems, the introduction of set theory, and Bourbaki's encyclopaedic survey of set theoretic structures.
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|
From:
E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2)
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A reaction:
In other words, mathematics has gradually risen from one level of abstraction to the next, so that mathematical entities like points and numbers receive less and less attention, with relationships becoming more prominent.
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10169
|
Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price]
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|
Full Idea:
Relativist Structuralism simply picks one particular model of axiomatised arithmetic (i.e. one particular interpretation that satisfies the axioms), and then stipulates what the elements, functions and quantifiers refer to.
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|
From:
E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4)
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|
A reaction:
The point is that a successful model can be offered, and it doesn't matter which one, like having any sort of aeroplane, as long as it flies. I don't find this approach congenial, though having a model is good. What is the essence of flight?
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10179
|
There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price]
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Full Idea:
The term 'structure' has two uses in the literature, what can be called 'particular structures' (which are particular relational systems), but also what can be called 'universal structures' - what particular systems share, or what they instantiate.
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|
From:
E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §6)
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|
A reaction:
This is a very helpful distinction, because it clarifies why (rather to my surprise) some structuralists turn out to be platonists in a new guise. Personal my interest in structuralism has been anti-platonist from the start.
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10182
|
There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price]
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|
Full Idea:
There are four main variants of structuralism in the philosophy of mathematics - formalist structuralism, relativist structuralism, universalist structuralism (with modal variants), and pattern structuralism.
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|
From:
E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §9)
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|
A reaction:
I'm not sure where Chihara's later book fits into this, though it is at the nominalist end of the spectrum. Shapiro and Resnik do patterns (the latter more loosely); Hellman does modal universalism; Quine does the relativist version. Dedekind?
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10168
|
Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price]
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|
Full Idea:
Formalist Structuralism endorses structural methodology in mathematics, but rejects semantic and metaphysical problems as either meaningless, or purely formal, or as inference relations.
|
|
From:
E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §3)
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|
A reaction:
[very compressed] I find the third option fairly congenial, certainly in preference to rather platonist accounts of structuralism. One still needs to distinguish the mathematical from the non-mathematical in the inference relations.
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|
10178
|
Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price]
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|
Full Idea:
It is tempting to take a modal turn, and quantify over all possible objects, because if there are only a finite number of actual objects, then there are no models (of the right sort) for Peano Arithmetic, and arithmetic is vacuously true.
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|
From:
E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5)
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|
A reaction:
[compressed; Geoffrey Hellman is the chief champion of this view] The article asks whether we are not still left with the puzzle of whether infinitely many objects are possible, instead of existent.
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|
10177
|
Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price]
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|
Full Idea:
Universalist Structuralism is eliminativist about abstract objects, in a distinctive form. Instead of treating the base element (say '1') as an ambiguous referring expression (the Relativist approach), it is a variable which is quantified out.
|
|
From:
E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5)
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|
A reaction:
I am a temperamental eliminativist on this front (and most others) so this is tempting. I am also in love with the concept of a 'variable', which I take to be utterly fundamental to all conceptual thought, even in animals, and not just a trick of algebra.
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22357
|
The 'experimenter's regress' says success needs reliability, which is only tested by success [Reiss/Sprenger]
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|
Full Idea:
The 'experimenter's regress' says that to know whether a result is correct, one needs to know whether the apparatus is reliable. But one doesn't know whether the apparatus is reliable unless one knows that it produces correct results ...and so on.
|
|
From:
Reiss,J/Spreger,J (Scientific Objectivity [2014], 2.3)
|
|
A reaction:
[H. Collins (1985), a sociologist] I take this to be a case of the triumphant discovery of a vicious circle which destroys all knowledge turning out to be a benign circle. We build up a coherent relationship between reliable results and good apparatus.
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