13337
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A language: primitive terms, then definition rules, then sentences, then axioms, and finally inference rules [Tarski]
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Full Idea:
For a language, we must enumerate the primitive terms, and the rules of definition for new terms. Then we must distinguish the sentences, and separate out the axioms from amng them, and finally add rules of inference.
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From:
Alfred Tarski (The Establishment of Scientific Semantics [1936], p.402)
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A reaction:
[compressed] This lays down the standard modern procedure for defining a logical language. Once all of this is in place, we then add a semantics and we are in business. Natural deduction tries to do without the axioms.
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13335
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Semantics is the concepts of connections of language to reality, such as denotation, definition and truth [Tarski]
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Full Idea:
Semantics is the totality of considerations concerning concepts which express connections between expressions of a language and objects and states of affairs referred to by these expressions. Examples are denotation, satisfaction, definition and truth.
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From:
Alfred Tarski (The Establishment of Scientific Semantics [1936], p.401)
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A reaction:
Interestingly, he notes that it 'is not commonly recognised' that truth is part of semantics. Nowadays truth seems to be the central concept in most semantics.
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10529
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If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K]
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Full Idea:
Neo-Fregeans have thought that Hume's Principle, and the like, might be definitive of number and therefore not subject to the usual epistemological worries over its truth.
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From:
Kit Fine (Precis of 'Limits of Abstraction' [2005], p.310)
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A reaction:
This seems to be the underlying dream of logicism - that arithmetic is actually brought into existence by definitions, rather than by truths derived from elsewhere. But we must be able to count physical objects, as well as just counting numbers.
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10530
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Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K]
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Full Idea:
The fundamental difficulty facing the neo-Fregean is to either adopt the predicative reading of Hume's Principle, defining numbers, but inadequate, or the impredicative reading, which is adequate, but not really a definition.
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From:
Kit Fine (Precis of 'Limits of Abstraction' [2005], p.312)
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A reaction:
I'm not sure I understand this, but the general drift is the difficulty of building a system which has been brought into existence just by definition.
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14292
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Dispositions seem more ethereal than behaviour; a non-occult account of them would be nice [Goodman]
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Full Idea:
Dispositions of a thing are as important to us as overt behaviour, but they strike us by comparison as rather ethereal. So we are moved to enquire whether we can bring them down to earth, and explain disposition terms without reference to occult powers.
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From:
Nelson Goodman (Fact, Fiction and Forecast (4th ed) [1954], II.3)
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A reaction:
Mumford quotes this at the start of his book on dispositions, as his agenda. I suspect that the 'occult' aspect crept in because dispositions were based on powers, and the dominant view was that these were the immediate work of God.
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18749
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Goodman argued that the confirmation relation can never be formalised [Goodman, by Horsten/Pettigrew]
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Full Idea:
Goodman constructed arguments that purported to show that a satisfactory syntactic analysis of the confirmation relation can never be found. In response, philosophers of science tried to model it in probabilistic terms.
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From:
report of Nelson Goodman (Fact, Fiction and Forecast (4th ed) [1954]) by Horsten,L/Pettigrew,R - Mathematical Methods in Philosophy 4
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A reaction:
I take this idea to say that Bayesianism was developed in response to the grue problem. This is an interesting light on 'grue', which never bothered me much. The point is it scuppered formal attempts to model induction.
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10527
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An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]
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Full Idea:
If an abstraction principle is going to be acceptable, then it should not 'inflate', i.e. it should not result in there being more abstracts than there are objects. By this mark Hume's Principle will be acceptable, but Frege's Law V will not.
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From:
Kit Fine (Precis of 'Limits of Abstraction' [2005], p.307)
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A reaction:
I take this to be motivated by my own intuition that abstract concepts had better be rooted in the world, or they are not worth the paper they are written on. The underlying idea this sort of abstraction is that it is 'shared' between objects.
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4794
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We don't use laws to make predictions, we call things laws if we make predictions with them [Goodman]
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Full Idea:
Rather than a sentence being used for prediction because it is a law, it is called a law because it is used for prediction.
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From:
Nelson Goodman (Fact, Fiction and Forecast (4th ed) [1954], p.21), quoted by Stathis Psillos - Causation and Explanation §5.4
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A reaction:
This smacks of dodgy pragmatism, and sounds deeply wrong. The perception of a law has to be prior to making the prediction. Why do we make the prediction, if we haven't spotted a law. Goodman is mesmerised by language instead of reality.
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