Dan Robinson explores how Kant answers whether synthetic a priori judgments are possible, tying objective science and mathematics to pure intuitions of space and time.
Key Takeaways
- Kant argues that synthetic a priori knowledge is possible, grounded in the forms of space and time and the categories of the understanding.
- Objectivity in science comes from the mind's structuring of experience, which resolves the tension with subjectivism.
- Mathematics is a priori because it depends on pure intuitions of space and time.
- Natural laws are not given in sensory input; reason imposes lawfulness on nature.
- Kant's Copernican-style move reverses the assumption that cognition conforms to objects.
What the video covers
- The lecture opens with Kant's claim in the Prolegomena that pure mathematics and Euclidean geometry have objective reality only as they refer to objects of sense.
- Kant asserts objectivity for mathematical and scientific propositions while seemingly risking subjectivism, since space is described as the form of all external appearances.
- Hume's view that synthetic propositions cannot be known a priori is examined, along with C.D. Broad's observation that denying such knowledge is itself a synthetic claim.
- Kant distinguishes Aristotelian formal logic, a 'vestibule of the sciences' that preserves truth, from the objective sciences that yield real substantive knowledge.
- Kant assumes nature is lawful, grounded in Newtonian science, and argues that lawfulness cannot come from raw sensory stimulus alone.
- Robinson describes two ways cognition relates to objects: rational cognition that constructs concepts (as in mathematics) and cognition that establishes an object's reality through discovery (as in natural science).
- Kant holds that all mathematical concepts are a priori because arithmetic and geometry presuppose the pure intuitions of time and space.
- The lecture discusses Galileo and Newton, arguing reason perceives only what it produces according to its own design, and compares this to Copernican revolution reasoning.
- Robinson connects Kant's project to empiricist and Scottish philosophy influences such as Reid, and to the question of causality and simultaneity.
- The lecture concludes with a summary of how objective knowledge of external reality is secured through the model of science.
Chapters
- 00:00Kant on Synthetic A Priori Judgments and Euclidean Geometry
- 02:44Hume, Broad, and the Self-Refutation Problem
- 04:43Aristotelian Logic as Vestibule of the Sciences
- 05:13Lawfulness of Nature and Rational Cognition
- 12:00Mathematics, Pure Intuition, and Time
- 18:00Galileo, Newton, and Reason's Own Design
- 30:00Copernican Revolution and the Observer
- 38:10Canonical Summary of Kant's Project
Full Transcript — Download SRT & Markdown
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well how are a priori synthetic judgments possible in the prolagomina kant says that pure mathematics and especially euclidean geometry can have objective reality only on the condition that they refer to objects of sense now what's particularly important in
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that brief passage is that kant again as he often does refers to the objectivity of mathematical and scientific propositions this is over and against claims their current claims and frequent claims that cons metaphysics lapses into subjectivism if it does it does so over
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kant's objections but in the same passage he declares that the propositions of geometry are quote necessarily valid why because space itself is nothing other than the form of all external appearances so every time he just about every time
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he asserts the objectivity of the program he inserts something that does look like it's a road to subjectivity and so the task is to determine just how we can get objective knowledge of the external world by means of a framework that we impose
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on the external world or put in the form of a question how are synthetic propositions known to be true are priori well here's an answer to the question we might say hume's answer to the question they can't be
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now that would be the end of the story in fact most empiricists would argue but it is simply out of the question that the truth of a synthetic proposition could be established a priori you know back in the 1930s cd broad
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reflected on this this is before quine and company and he said that he said those who insist on the impossibility of our being able to know the truth of synthetic propositions are priori are surely advancing a synthetic proposition
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and it seems to be one that they take to be self-evidently true so there is this problem if you want to declare once and for all that it is out of the question that there could be synthetic propositions
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the truth of which can be established a priori if you want to deny that are you denying it as itself a synthetic proposition and do you take that synthetic proposition to be self-evidently true i leave you with that
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in the preface to the second edition kant traces the development of systematic knowledge from aristotle's logic to the mathematics and science of his own day with a lengthy pause over the achievements of galileo and newton in the preceding century
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aristotelian logic he says no surprise here constitutes the formal laws of all thought but it serves formal logic aristotle's logic he says rather pictorially it serves as quote the vestibule of the sciences and while it is necessary to enable us
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to form a correct judgment with regard to the various branches of knowledge still the acquisition of real substantive knowledge is to be sought only in the sciences properly so called that is and here's the claim again the objective sciences
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so you cannot use aristotelian logic as a mode of discovery you can use it as a truth preserving device in fact eighth week when we get to the antinomies of pure reason you'll see what happens when you attempt to use logical
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forms not merely as a method but as a mode of discovery and of course you'll end up discovering all sorts of things all of them all of them illusory so it is the objective sciences that are again the model here
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now why should anyone assume that the objective sciences are themselves able to capture the order of nature the lawfulness of nature kant begins with the assumption that nature is an orderly enterprise that it is law governed do you see
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on the strength of what does he say that well on the strength of newtonian science the laws have have been worked out well from the fact that that nature is lawful and from the fact that we have uncovered
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the lawfulness of nature we must have some means by which to overcome subjectivity and reach an objective knowledge of the way things are so so much for a skepticism about our capacity for unearthing the objective facts of nature
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now kant is not taking a lead here the lead is ancient aristotle says in the physics if the art of shipbuilding were in the wood we would have ships by nature so it's been obvious for quite a long
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time that there are design features to the natural am i allowed to say intelligent design features in the natural world was professor dawkins listening well but if the art of shipbuilding were in the wood we would you'd be able to leave
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driftwood out and if you let enough time go by and had enough cows die near the driftwood perhaps an infinite time you'd be able to fashion leather sails and something like a trireme with three rows for oarsmen and you might even be able to wage a
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naval battle on egypt mind you this would take a great deal of time the very laws of the objective sciences show the sciences to have a rational character now that lawfulness is not given in the appearances the stimulus that arrives at the organs
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of sense does not carry any information regarding lawfulness with it if it's visual it's just photons do you see if it's auditory it's just air vibrations so the lawfulness must be coming from someplace other than the arriving wave of
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stimulation our scientific understandings in which lawfulness is the defining feature do find us relating to the objects of our understanding in one of two ways either by way of rational irrational cognition that determines the concept of the object this is kant
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in his most lumbering prose and it's not easier in german and if i illustrated it by giving it to you in german most of you wouldn't get um i should tell you about an incident involving one of our
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famous philosophers here no no longer here known for this kind of prose he gave a keynote address for the international philosophy meetings in moscow some years ago and this is where when you sit down you can adjust the
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dials to whatever language you speak and two minutes into his address people were fiddling with the dials trying to find a language that would render all this intelligible i i i i the same the same might might be
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said if you serve up a sentence like this but our scientific understanding in which lawfulness is the defining feature finds us relating to the objects of this understanding in one of two ways we relate to it in one of two ways
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either by way of a rational cognition that determines the concept well the pythagorean theorem this is a mode of cognition given the mode of cognition we determine the concept of a right angle triangle it's it's not that pythagoras ran around
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looking for these things it's these things were constructed by pythagoras or by way of rational cognitions that establish the very reality of an object saturn has moons so these are the two ways that we can relate our cognition to
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an objective reality either the cognition actually determines the concept itself quite characteristic of mathematics or in the natural sciences it's in some branches of the natural sciences cognitively we actually can discover things that heretofore had not been no the first form of the
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relationship between cognition and its objects is what khan says is the grounding of all theoretical sciences of which mathematics and physics are the two that are most developed but they differ in this respect in mathematics all of the concepts are a priori
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in physics some of the concepts arise from other sources such as direct observation now what does he mean when he says that all of the concepts in mathematics are a priori and i think it's fair to say contemporary mathematicians probably
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would not accept that but absent the pure intuitions of time and space can't wants to argue you could have neither arithmetic nor geometry because all arithmetic operations are sequential and sequentiality presupposes time and time is a pure intuition it's not
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something given in the stimulus so were it not for our spatio-temporal mode of apprehension we would be in a position for neither arithmetic operations nor geometric operations geometry presupposes just that spatial context that is provided by the pure intuition of space as arithmetic
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as as the pure intuition of time provides the means by which arithmetic sequential operations become possible i'm not defending this i'm attempting to clarify it arithmetic requires the pure intuition of time because it depends on succession and geometry comparably depends on
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space now in this kant pays homage to failies he thinks that one of them he says hailey's or whoever did this uh he thinks that it was in the ancient greek world that someone perhaps failies he names thales because he's
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fixated on thales and the isosceles triangle actually came to the recognition that it was he thales who was constructing out of his own conceptual resources that which then could be objectively applied to the world but in fact there was an abstract
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representation of something that is objectively real and that it is out of the cognitive resources of the mathematician that this matching becomes possible in demonstrating the properties of the isosceles triangle thales found that it was not sufficient kant says
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to meditate on the figure as it lay before his eyes or that the conception of it merely existed in his mind rather says kant and this is a quote rather says can't quote it was necessary to produce these
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properties by a positive a priori construction and that in order to arrive with certainty at a priori cognition he must not attribute to the object any other properties than those which necessarily followed from that which he himself had in
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accordance with his own concept placed in the object now physics says kant took longer to develop but it developed along comparable lines what newton and galileo realized is that reason only perceives that which it produces after its own design do you see you
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you'd have no way of launching the project of physics on entirely a posteriori grounds you already have a conceptual framework of lawfulness orderliness causality etc to put the ball in play as kant says accidental observations accidental observations made according to no preconceived plan
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could not be united under a necessary law but it is this that reason seeks for and requires this is what reason is looking for when reason undertakes scientific inquiry he goes on to say it is only the principle of reason which can give
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to concordant phenomena the validity of laws and it is only an experiment directed by these rational principles that give them any real utility and so the question is whether metaphysics can be developed along the same lines this gets back to the
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prize competition must metaphysics uh be confined to that top and that groping around in in the dark or can it proceed along the lines of a systematic science well this leads kant to what is often referred to in the secondary literature
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as his copernican revolution kant's famous copernican revolution the problem with that rendering is that kant never uses the term copernican revolution and in fact he only mentions copernicus in the second edition of the work and there only in the preface and what
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he refers to there is den erstin gedank des copernicus copernicus's first thought he's not treating it as a copernican revolution he's not treating what he's doing as a copernican revolution rather he's very interested in how copernicus addressed a problem of some weight
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copernicus was contacted by pope leo the 10th why was that anyone what was troubling his holiness may i say his holiness what was troubling his holiness is this holy mother church had been using this calendar julius caesar's time had
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contrived a calendar well it wasn't a bad calendar oh you're off by a little bit but of course by the 14th and 15th centuries you're off by so much that the variation around easter sunday is weighing in at two and
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three weeks sometimes longer so the pope says to copernicus i wonder if you might give us a hand with this when is easter sunday copernicus writes back and says i can't be very helpful mathematicians do not agree on the length of a year
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and so then copernicus tries a thought experiment just how do things look in case i'm standing on the sun well things look quite different and in fact the length of the year gets marvelously orderly if you assume that
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the sun isn't moving and that the earth is and the important point is this what copernicus establishes is that the observer is not a passive recipient of things that just come in from the solar system he is an
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active participant in his own observations and his position and his velocity determine the model of reality that he will construct that's the main thing that kant finds in copernicus the answer to the question what was kant's copernican revolution is
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i have no idea what you're talking about so um so it may underscore what it what is important and what can't found in the motive analysis that was adopted by copernicus kant was not only fully versed in the
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science of astronomy to which he had made uh significant contributions in in the pre-critical years but there's no doubt that his reference to this first thought of copernicus who's based on something deeper than an insight into copernicus's cognitive
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processes what copernicus understood was that reality as known reflects the modes of receptivity by which events in the external world become translated into experience and copernicus knew further that it was only by testing various conjectures against the data of experience that a
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mere casting about might give way to systematic knowledge that will be valid beyond the narrow world of the individual observer now again suppose this you attempt to reduce this to some sort of subjectivity because of all copernicus was saying
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is that the model of the solar system you develop just happens to depend on where you are and how you are moving you might end up with one of these protagoras man as the measure of all things what what copernicus makes clear is that
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once you've adopted this different perspective the result is going to be universally distributed across all percipients it it's not that that that if jack and jill both go to the sun and observe events from the sun's point of view jack and jill will be in
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in in a state of subjectivity and there's no reason to believe that they will agree with each other no what is observed what is observed is is a reality that is conditional that is the representation of that reality
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is conditional on the place occupied by the observer how do we know this does not subjectify everything we know it doesn't because astronomy has developed as a science one way we know that this works i shall once more this is the last time
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i did this briefly last week i shall use an audio visual aid and this is the final time this term you were here for it all right look up don't don't be writing now this is important now there's an answer to the question of
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why that took place and the answer to the question is that all bodies attract each other with a force that's directly proportional to the product of their masses and inversely proportional to the square of the distance between them
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so that newton you know in the summer of my 23rd year i devised a calculus reflections and appreciated the relationship between the earth the moon and the other heavenly bodies when i read that i reflected on what i
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had been doing in the summer of my 23rd year oh shame where is thy blush well um well that this happens is not over and against the fact that where we happen to be positioned as observers might have some effect on the
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measurements that we make particularly for example if we start going very very rapidly if we go really very very rapidly then the assumption of mass as unchanging has to surrender to the fact that mass is going to be affected by
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velocity and that as we approach the speed of light the mass is going to approach an infinite magnitude right so what then is that subjectivity no no that's drawn from this that's drawn from the same perspective the same
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project the same developed science that gave you this in the first instance so again and again kant's model is the achievement of physics the achievement of physics is sufficient to satisfy him that our cognitive resources are capable of unearthing lawfulness in reality
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the objective events of the external world and the question then again and again sorry to be so repetitious is how we do this given that the resources we bring to bear on the task are perceptual and cognitive so to ask how the solar system appears
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to one standing on the sun compared with what is seen by one standing on the earth is to acknowledge that the appearance itself must be grounded in non-empirical factors cognition doesn't lead then to skepticism regarding the reality of the
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sun the moon and the planets rather it establishes how that very reality will be cognized by the situated observer the position of the observer now simply becomes another element in the account and not a subjective element kant's statement that his own attempt to
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rescue metaphysics from the incessant groping of metaphysicians suggests a parallel with copernicus's efforts as with copernicus kant will he says make another trial alph annika he's going to perform a copernicus-like experiment another trial a trial of the same sort
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that copernicus has tried how is he going to do this he's going to suppose that human cognition by way of the pure categories of the understanding constitute the means by which we impose structure and lawfulness such that what we're
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going to find in our systematic observation of reality are ingredients that we have put there in just the sense that copernicus observer on the sun is now an observer that copernicus has put someplace other than we once found him
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so kant sees the project as as a kind of experiment now he says the understanding has rules which i must presuppose as being in me prior to objects being given to me and in this he's recurring both to the
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transcendental aesthetic and to the doctrine of the cognitive elements that is to say you have to stay with this keep in mind what empiricism is claiming empiricism is claiming that our ideas are fashioned out of experience that our experiences are perceptual
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transactions between an observer and the external world and that the ideas thus formed if they have any bearing on external reality simply are the result of elementary sensations being parlayed into something rather more complex and held together by some principle of
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association kant wants to make clear that on that reading you could not have a developed science you couldn't even hold together the concept of causality let alone show how it operates in the realm of physical reality so nothing in the stimulus will support
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the project of science and yet the project of science is successful so what so the necessary ingredients must be supplied by us nothing in a priori knowledge can be ascribed to objects save what the thinking subject derives from itself
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now in this kant is tracking and i i shouldn't say tracking because it suggests a dependency that would remain to be established you might include in your readings a work by manfred keane on the influence of the scottish
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enlightenment on german philosophy keane does make out a case for kant having had access to translations redactions and translations of reid's inquiry into the human mind um uh carl americ's distinguished uh khan scholar has recently argued that there are
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definitely reading resonances reading elements in uh much of the at least in some of the first critique and uh i in several places have have made the same case that there are aspects of read that match up so well with kant's argument
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that it's not a question of dependency but but here's how i i'd want you to understand this reid and kant are both troubled most by hume thus to undertake a criticism of hume at what is taken to be the weakest points in hume
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should result in no surprise if the two critics end up coming up with very similar ideas where where where what you're getting is something rather more simultaneous than than causal now when reed takes up the question of causality on which can't
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spends so much ink particularly in the second analogy when when reed takes it up he is satisfied that principles of association simply are inapplicable here that that no concept of association even if the empiricists make clear what they mean by
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it no merely associative con concept carries with it the idea of causation the constant conjunction of events could never give rise reid says could never give rise to the notion of causality except in a creature possessed of active power i want to flesh this out
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for you imagine yourself to be totally devoid of will but you do have intelligence which is to say there isn't anything you can resolve to do you don't even know the meaning of the term resolve you have no agentic power at all
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there's nothing you can do agentically or forbear from doing reed's argument is that such a creature granting that it's an intelligent creature never on the basis of experience could rise to the concept of causality concept of a cause says reed is our
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externalization of what we recognize in ourselves to be an active power as i can act and forebear from acting i understand immediately and intuitively i understand without reflection myself to be the source of events that i bring about
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it's on the strength of that that i am prepared to make an inference when i see events taking place in a patterned way in the external world that something must have brought them about so the concept of cause reid says is
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parasitic on the intuition of active power find a creature lacking active power it could not have the concept of causation now that's one way of showing how resources within the organism resources within the human being are projected onto the
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external world to create a representation of events not given by the events themselves hume is right insofar as he argues that nothing empirical not when those billiard balls collide and one moves the other and hume says i must own i do not see
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some third term betwixt them quite so there is no empirical source of causal dependency so hume is right again when he says that that if you're looking for the locus of causality well let me just say it's somewhere
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between our ears or wherever we we do these things but how do we do these things even between our ears how would it be possible merely on the basis of constant conjunction ever to arise at the notion of causal
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dependency reid says it's not possible that the notion of causal dependency is parasitic on the intuitive recognition of oneself as an agent so there's the scottish common sense version of the cognitive and volitional resources of the observer now constituting the
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grounds for causal attributions in contexts in which the external world could provide no cue at all recall reid's comment about no two events have been as constantly conjoined in human experience as day and night but that no man come of years has ever
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regarded day as the cause of night or night because of day and you can hear resonances of this when contacts up the question of simultaneity so again it's back into the observer back into the cognizer that we must go to find the sources
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of these representations these representations of objective objective reality so asserted here when khan says that nothing in a priori knowledge can be ascribed to objects save what the thinking subject derives from itself if you wanted to translate that into the
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reading critique of hume's notion of causality you you would say that that nothing in the external event carries with it the concept the notion even the grounding of causality except insofar as there is a precipitate who's up whose resources are such that
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on a priori grounds is able to represent able to cognize lawful dependencies causal dependencies and distinguish them from merely constant conjunctions again understanding human understanding has rules which i must presuppose as being in me prior to objects being given to me
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well here again the pure concepts of the understanding were they not in place and were you simply the creature that that a radical empiricism would have you be what's the basis upon which you you'd even connect something like
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this fuzzy white thing blue tablecloth hand in the air etc how these connections may see on the empiricist account of associationism the associations we form are not willy-nilly though why aren't they you understand that when when i well i can't get it now i think
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it fell someplace may i use another one uh but but you're looking at this which is selectivity there's a tremendous amount going on as that's going on why aren't you looking at this why not this why not my spectacles
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why not this rather attractive tie that i put on this morning so you are already tuned selectively to bring to bear a certain order on the external world such that some things will be associated and others will be relegated
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to background considerations shall i bring this to life for you the neonatal rhesus monkey at three hours is shown to have cells in the auditory cortex that respond selectively to the distress cries of that species that's what i mean by an a priori
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selectivity of perception as reed would argue were we not thus constituted you couldn't get across the street for goodness sake the problem with radical empiricism is that you can't get across the street you can't even get a street
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well surely hume wasn't fooled no well you look you don't have to be let's here's a way to be foolish while being extremely intelligent have a theory um and and then defend it against all john stewart mill was doing
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greek at eight and thought that the series of positive integers was in fact an empirical achievement this is a serious person thinks that you got there by counting but or something like counting this is a serious person he he actually
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represented oxford for one term it's an imperfect world but that mill got elected at all as a miracle but that he only lasted one term was inevitable um so so on the reading account quote even the lowly caterpillar will
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crawl across a thousand leaves until it finds the one that's right for its diet is the manner in which reed illustrates a principle of common sense reed is a sort of pre darwinian a providential creator has fitted creatures out to be able to negotiate
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the requirements of life on earth and when philosophers set out to explain how somehow that's all impossible uh their systems are reduced to a source of laughter kant in a much more meticulous metaphysically rich way wants to make the same kind of argument
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that that the rational structure of science is at once created by the cognitive resources of an intelligent being our priori resources that must be in place for order itself to be cognized and at the same time that apparatus generates representations
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of external reality in a manner that is objective and the model is the model of science well this permits me a very brief canonical summary of a very difficult passage in kant and that has to do with how we're going
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to answer the question how synthetic propositions can be known to be true our priori the answer is how could they not be thank you you see if we've put it there then how could it be otherwise how could it
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be otherwise you're stunned the answer to the question how can we know the truth of our synthetic a priori propositions is that in fact the propositions to the extent that they constitute a reality that we have framed that has
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been structured by the pure concepts of the understanding will have reason finding its own grounding in the very phenomena that it's setting out to to explain it is on the basis of the a priori resources of the cognizer
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that a lawful reality is made possible in the first instance so the trick then is not to establish how uh a priori synthetic propositions can be known to be the case the trick is how they can be known to be
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the case by way of resources that do not conduce to subjectivity and it's on that that khan's critics and kant supporters continue to argue so that's all i've got for today
Topics:KantCritique of Pure Reasonsynthetic a prioritranscendental idealismHumeNewtonGalileospace and timephilosophy lectureepistemology











