7807
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The laws of thought are true, but they are not the axioms of logic [Bolzano, by George/Van Evra]
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Full Idea:
Bolzano said the 'laws of thought' (identity, contradiction, excluded middle) are true, but nothing of interest follows from them. Logic obeys them, but they are not logic's first principles or axioms.
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From:
report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837], §3) by George / Van Evra - The Rise of Modern Logic
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A reaction:
An interesting and crucial distinction. For samples of proposed axioms of logic, see Ideas 6408, 7798 and 7797.
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9618
|
Bolzano wanted to reduce all of geometry to arithmetic [Bolzano, by Brown,JR]
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Full Idea:
Bolzano if the father of 'arithmetization', which sought to found all of analysis on the concepts of arithmetic and to eliminate geometrical notions entirely (with logicism taking it a step further, by reducing arithmetic to logic).
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From:
report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by James Robert Brown - Philosophy of Mathematics Ch. 3
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A reaction:
Brown's book is a defence of geometrical diagrams against Bolzano's approach. Bolzano sounds like the modern heir of Pythagoras, if he thinks that space is essentially numerical.
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9830
|
Bolzano began the elimination of intuition, by proving something which seemed obvious [Bolzano, by Dummett]
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Full Idea:
Bolzano began the process of eliminating intuition from analysis, by proving something apparently obvious (that as continuous function must be zero at some point). Proof reveals on what a theorem rests, and that it is not intuition.
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From:
report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by Michael Dummett - Frege philosophy of mathematics Ch.6
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A reaction:
Kant was the target of Bolzano's attack. Two responses might be to say that many other basic ideas are intuited but impossible to prove, or to say that proof itself depends on intuition, if you dig deep enough.
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17265
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Philosophical proofs in mathematics establish truths, and also show their grounds [Bolzano, by Correia/Schnieder]
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Full Idea:
Mathematical proofs are philosophical in method if they do not only demonstrate that a certain mathematical truth holds but if they also disclose why it holds, that is, if they uncover its grounds.
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From:
report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by Correia,F/Schnieder,B - Grounding: an opinionated introduction 2.3
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A reaction:
I aim to defend the role of explanation in mathematics, but this says that this is only if the proofs are 'philosophical', which may be of no interest to mathematicians. Oh well, that's their loss.
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16744
|
All powers can be explained by obvious features like size, shape and motion of matter [Descartes]
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Full Idea:
There are no powers in stones and plants that are not so mysterious that they cannot be explained …from principles that are known to all and admitted by all, namely the shape, size, position, and motion of particles of matter.
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From:
René Descartes (Principles of Philosophy [1646], IV.187), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 23.6
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A reaction:
This is an invocation of 'categorical' properties, against dispositions. I take this to be quite wrong. The explanation goes the other way. What supports the structures; what drives the motion; what initiates anything?
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5016
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Five universals: genus, species, difference, property, accident [Descartes]
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Full Idea:
The five commonly enumerated universals are: genus, species, difference, property and accident.
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From:
René Descartes (Principles of Philosophy [1646], I.59)
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A reaction:
Interestingly, this seems to be Descartes passing on his medieval Aristotelian inheritance, in which things are defined by placing them in a class, and then noting what distinguishes them within that class.
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16633
|
A substance has one principal property which is its nature and essence [Descartes]
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Full Idea:
Each substance has one principal property that constitutes its nature and essence, to which all its other properties are referred. Extension in length, breadth, and depth constitutes the nature of corporeal substance; and thought of thinking substances.
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From:
René Descartes (Principles of Philosophy [1646], I.53), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 08.3
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A reaction:
Property is likely to be 'propria', which is a property distinctive of some thing, not just any old modern property. This is quite a strikingly original view of the nature of essence. Descartes despised 'substantial forms'.
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5005
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I think, therefore I am, because for a thinking thing to not exist is a contradiction [Descartes]
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Full Idea:
There is a contradiction in conceiving that what thinks does not (at the same time as it thinks) exist. Hence this conclusion I think, therefore I am, is the first and most certain that occurs to one who philosophises in an orderly way.
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From:
René Descartes (Principles of Philosophy [1646], I.07)
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A reaction:
The classic statement of his argument. The significance here is that it seems to have the structure of an argument, as it involves 'philosophising', which leads to a 'contradiction', and hence to the famous conclusion. It is not just intuitive.
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5006
|
'Thought' is all our conscious awareness, including feeling as well as understanding [Descartes]
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Full Idea:
By the word 'thought' I understand everything we are conscious of as operating in us. And that is why not only understanding, willing, imagining, but also feeling, are here the same thing as thinking.
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From:
René Descartes (Principles of Philosophy [1646], I.09)
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A reaction:
There is a bit of tension here between Descartes' correct need to include feeling in thought for his Cogito argument, and his tendency to dismiss animal consciousness, on the grounds that they only sense things, and don't make judgements.
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5012
|
'Nothing comes from nothing' is an eternal truth found within the mind [Descartes]
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Full Idea:
The proposition 'nothing comes from nothing' is not to be considered as an existing thing, or the mode of a thing, but as a certain eternal truth which has its seat in our mind and is a common notion or axiom.
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From:
René Descartes (Principles of Philosophy [1646], I.49)
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A reaction:
There is a tension here, in his assertion that it is 'eternal', but 'not existing'. How does one distinguish an innate idea from an innate truth? 'Eternal' sounds like an external guarantee of truth, but being 'in our mind' sounds less reliable.
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9185
|
Bolzano wanted to avoid Kantian intuitions, and prove everything that could be proved [Bolzano, by Dummett]
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Full Idea:
Bolzano was determined to expel Kantian intuition from analysis, and to prove from first principles anything that could be proved, no matter how obvious it might seem when thought of in geometrical terms.
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From:
report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by Michael Dummett - The Philosophy of Mathematics 2.3
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A reaction:
This is characteristic of the Enlightenment Project, well after the Enlightenment. It is a step towards Frege's attack on 'psychologism' in mathematics. The problem is that it led us into a spurious platonism. We live in troubled times.
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5004
|
We can know basic Principles without further knowledge, but not the other way round [Descartes]
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Full Idea:
It is on the Principles, or first causes, that the knowledge of other things depends, so the Principles can be known without these last, but the other things cannot reciprocally be known without the Principles.
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From:
René Descartes (Principles of Philosophy [1646], Pref)
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A reaction:
A particularly strong assertion of foundationalism, as it says that not only must the foundations exist, but also we must actually know them. This sounds false, as elementary knowledge then seems to require far too much sophistication.
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5011
|
There are two ultimate classes of existence: thinking substance and extended substance [Descartes]
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Full Idea:
I observe two ultimate classes of things: intellectual or thinking things, pertaining to the mind or to thinking substance, and material things, pertaining to extended substance or to body.
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From:
René Descartes (Principles of Philosophy [1646], I.48)
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A reaction:
This is clear confirmation that Descartes believed the mind is a substance, rather than an insubstantial world of thinking. It leaves open the possibility of a different theory: that mind is not a substance, but is a Platonic adjunct to reality.
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5018
|
Even if tightly united, mind and body are different, as God could separate them [Descartes]
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Full Idea:
Even if we suppose God had united a body and a soul so closely that they couldn't be closer, and made a single thing out of the two, they would still remain distinct, because God has the power of separating them, or conserving out without the other.
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From:
René Descartes (Principles of Philosophy [1646], I.60)
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A reaction:
If Descartes lost his belief in God (after discussing existence with Kant) would he cease to be a dualist? This quotation seems to be close to conceding a mind-body relationship more like supervenience than interaction.
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17264
|
Propositions are abstract structures of concepts, ready for judgement or assertion [Bolzano, by Correia/Schnieder]
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Full Idea:
Bolzano conceived of propositions as abstract objects which are structured compounds of concepts and potential contents of judgements and assertions.
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From:
report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by Correia,F/Schnieder,B - Grounding: an opinionated introduction 2.3
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A reaction:
Personally I think of propositions as brain events, the constituents of thought about the world, but that needn't contradict the view of them as 'abstract'.
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12232
|
A 'proposition' is the sense of a linguistic expression, and can be true or false [Bolzano]
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Full Idea:
What I mean by 'propositions' is not what the grammarians call a proposition, namely the linguistic expression, but the mere sense of this expression, is what is meant by proposition in itself or object proposition. This sense can be true or false.
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From:
Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837], Pref?)
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A reaction:
This seems to be the origin of what we understand by 'proposition'. The disputes are over whether such things exists, and whether they are features of minds or features of the world (resembling facts).
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5008
|
The greatest perfection of man is to act by free will, and thus merit praise or blame [Descartes]
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Full Idea:
That the will should extend widely accords with its nature, and it is the greatest perfection in man to be able to act by its means, that is, freely, and by so doing we are in peculiar way masters of our actions, and thereby merit praise or blame.
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From:
René Descartes (Principles of Philosophy [1646], I.37)
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A reaction:
This seems to me to be a deep-rooted and false understanding which philosophy has inherited from theology. It doesn't strike me that there must an absolute 'buck-stop' to make us responsible. Why is it better for a decision to appear out of nowhere?
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6866
|
It is disturbing if we become unreal when we die, but if time is unreal, then we remain real after death [Le Poidevin]
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Full Idea:
For the A-theorists called 'presentists' the past is as unreal as the future, and reality leaves us behind once we die, which is disturbing; but B-theorists, who see time as unreal, say we are just as real after our deaths as we were beforehand.
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From:
Robin Le Poidevin (Interview with Baggini and Stangroom [2001], p.174)
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A reaction:
See Idea 6865 for A and B theories. I wonder if this problem is only superficially 'disturbing'. Becoming unreal may sound more drastic than becoming dead, but they both sound pretty terminal to me.
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15987
|
Physics only needs geometry or abstract mathematics, which can explain and demonstrate everything [Descartes]
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Full Idea:
I do not accept or desire any other principle in physics than in geometry or abstract mathematics, because all the phenomena of nature may be explained by their means, and sure demonstrations can be given of them.
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From:
René Descartes (Principles of Philosophy [1646], 2.64), quoted by Peter Alexander - Ideas, Qualities and Corpuscles 7
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A reaction:
This is his famous and rather extreme view, which might be described as hyper-pythagoreanism (by adding geometry to numbers). It seems to leave out matter, forces and activity.
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16601
|
Matter is not hard, heavy or coloured, but merely extended in space [Descartes]
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Full Idea:
The nature of matter, or body viewed as a whole, consists not in its being something which is hard, heavy, or colored, or which in any other way affects the senses, but only in its being a thing extended in length, breadth and depth.
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From:
René Descartes (Principles of Philosophy [1646], 2.4), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 04.5
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6865
|
A-theory says past, present, future and flow exist; B-theory says this just reports our perspective [Le Poidevin]
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Full Idea:
The A-theory regards our intuitive distinction of time into past, present and future as objective, and takes seriously the idea that time flows; the B-theory says this just reflects our perspective, like the spatial distinction between here and there.
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From:
Robin Le Poidevin (Interview with Baggini and Stangroom [2001], p.174)
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A reaction:
The distinction comes from McTaggart. Physics seems to be built on an objective view of time, and yet Einstein makes time relative. What possible evidence could decide between the two theories?
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