Erudite Relics of Loc Huu Ho

Definitions

• adept: is an individual identified as having attained a specific level of knowledge, skill, or aptitude in doctrines relevant to a particular author or organization
• axiomatic: evident without proof or argument; of or pertaining to an axiom; obvious (layman)
  
• exegetical: related to an exegesis, which is the interpretation and understanding of a text on the basis of the text itself
• gnomon: pronounced NO-mon, a Greek word meaning “the one who knows.” The gnomon is the pointer on a sundial, the part of the sundial that “knows” the time
• interlocutor: a person who takes part in a conversation
• par excellence: being the best of its kind; being a quintessential example of the kind in question
• truth-value: a proposition’s truth-value is its being true or its being false

Notes

• Mathematics, or at least geometry, provides a straightforward instance of the gap between the flawed material world around us and the serene, ideal perfect world of thought.
• Plato believed that the propositions of geometry are objectively true or false, independent of the human mind, language, and so on of mathematicians. He believed that geometrical objects are like Forms and are in the world of Being where it is not physical, and that they are eternal and unchanging. He would thus reject the above suggestion that geometric objects exist in physical space.
• Refer to the end of Book 6 of the Republic Plato gives a metaphor of a divided line: the divisions are unequal, with the Forms getting the largest space. The following double proportion holds: Forms are to mathematical objects as physical objects are to reflections, as Being (i.e. Forms plus mathematical objects) is to Becoming (i.e., physical objects and reflections). Although Plato does not mention this, it follows that the ‘mathematical objects’ segment is exactly the same size as the ‘physical objects’ segment.
• Geometry is not about anything in the physical world, the world of Becoming, and we do not apprehend geometric objects via the senses. With the exception that some physical objects approximate Euclidean figures, but geometric theorems do not apply to these approximations.
• We are in position to better understand Plato’s remark in the passage from Book 7 of the Republic, quoted in chapter 1:

[The] science [of geometry] is in direct contradiction with the language employed by its adepts…Their language is most ludicrous…for they speak as if they were doing something and as if all their words were directed toward action…[They talk] of squaring and applying and adding and the like…whereas in fact the real object of the entire subject is… knowledge…of what eternally exists, not of anything that comes to be this or that at some time and ceases to be. (Plato, 1961, 527a in the standard numbering)

(510d) You…know how [geometers] make use of visible figures and discourse about them, though what they really have in mind is the originals of which these figures are images. They are not reasoning, for instance, about this particular square and diagonal which they have drawn, but about the Square and the Diagonal; and so in all cases. The diagrams they draw and the models they make are actual things, which may have their shadows or images in water; but now they serve in their turn as images, while the student is seeking to behold those realities which only thought can comprehend.

• Most Platonists maintained that geometrical knowledge is a priori, independent of sensory experience. It may be that some sensory experience is necessary to grasp the relevant concepts, or we may need drawn diagrams as a visual aid to the mind, or perhaps to awaken our minds to the eternal and unchanging geometric realm of Euclidean space.
• The details of Plato’s views concerning arithmetic and algebra are not as straightforward as his account of geometry, but the overall picture is the same. We see that arithmetic, like geometry, applies to the material world only approximately, or only to the extent that objects can be distinguished from each other.
• Several ancient sources distinguish the theory of numbers (world of Being), called ‘arithmetic’ from the theory of calculations (world of Becoming), called ‘logistic’.
• It is through the study of the numbers themselves, and the relations among numbers, that the soul is able to grasp the nature of numbers as they are in themselves.

Definitions

• rationalism: platonism; branch of philosophy which emphasizes reason or intellect, rather than observation or sensory perception, as the basis for knowledge and truth.
• secular: of or relating to the doctrine that rejects religion and religious considerations

Notes

• The problems that occupied mathematicians for centuries, culminating more than 2,000 years later with the result that there are no solutions-the tasks to obtain exact solutions are impossible.
• Thomas Kuhn’s influential Structure of Scientific Revolutions (1970) speaks of revolutions and ‘paradigm shifts’ that make it difficult to understand scientific works of the past. I.e., to understand previous work we have to unlearn our current science and try to immerse ourselves in the overturned world-view.
• However, there’s an exception of this when mathematics is concerned. A contemporary mathematicians does not have to do much (if any) conceptual retooling in order to read and admire Euclid’s Elements.
• Plato stands at the head of a long tradition in philosophy sometimes called rationalism or ‘Platonism’

Definitions

• obstensive: represented or appearing as such; pretended
• reductio ad absurdum: assume as true for the sake of argument what you actually take to be false

Notes

• Contemporary empiricism begins with the rejection of Hume’s assumption that what we directly experience are always our own sensations.
• Physical things actually constitute the objects of perception, where “physical things” is all the other sorts of objects common within the natural world.
• We perceive not the natural world, but only mental images of it.
• You cannot ask other people whether you are consistent, for that is ruled out: your language is supposed to be intelligible to you alone.
• Private sense impressions are the objects of direct perception with the view that publicly observable physical things are the objects of perception.
• The contemporary empiricist holds that a priori knowledge is analytic; he holds that observation-now of publicly observable things-together with memory is the only source of empirical or a posteriori knowledge; he holds that any reasoning taking us beyond this source, i.e., any nondemonstrative (nondeductive) reasoning is basically empriical generalization from observations; and he holds that all meaningful ideas must ultimately come from experience.
• Every genuine descriptive word must be definable in terms of ostensive words. An obstensive word cannot be defined verbally but only by pointing out examples of what it is to which the word applies. Thus one understands a descriptive word only if one knows the observable situations to which it can correctly apply.
• Strict empiricist standards oblige contemporary empiricists to conclude that theoretical talk is a kind of convenient shorthand fiction for talk about the behavior of such genuinely real and observable things as the movement of a meter-pointer or the path of a streak in a Wilson cloud chamber. We cannot see or touch an individual electron for precisely the same reason that we cannot see or shake hands with the average man.

Definitions

• ad infinitum: for ever, without limit, to infinity
• Calcutta: Largest city in India, located in the eastern part of the country on the Hooghly River.
• phenomenalism: the view that physical objects do not exist as things in themselves but only as perceptual phenomena or sensory stimuli (e.g. redness, hardness, softness, sweetness, etc.) situated in time and in space

Notes

• According to this phenomenalism theory, anticipated by Hume and George Berkeley, a physical thing is a kind of construction out of our experiences.
• According to the phenomenalist, to have a visual experience of a real physical thing is to have an experience of a real physical thing is to have an experience which belongs to a certain kind of group of experiences. This kind of set of experiences has a constancy and a rich and complex coherence that is lacking in the set of expereinces of which halluncinations are a part.
• The phenomenalist affirms also that all we can possibly mean in speaking of these things is confined to our experiences.
• Hume’s criterion states that every idea-and thus the idea of an “external” thing-is ultimately derived from sense impressions alone.
• The phenomenalist phase of post-Humean empiricism ended by the 1940s, for by that time it had become evident that statements about physical things could not be translated into propositions about actual and possible sense data.

RECORDING THE FINDINGS

Record primary research findings by a medium that suits your purpose.
Record secondary research findings as notes.

• Taking Notes (decide what to record and how to record the item; Record the sources of all internet-based material)
• Quoting the Work of Others (avoid plagiarism by correctly citing your sources; it is better to paraphrase your borrowed material to draw your conclusions from other works)
• Paraphrasing the Work of Others (to express the original idea in a clear, simple, direct, or emphatic way without distorting the idea and giving full credit to the source)

• Elements of an effective paraphrase:

reference to the author early in the paraphrase, to indicate the beginning of the borrowed passage

keywords retained from the original, to preserve the meaning

original sentences restructured and combined, for emphasis and fluency

needless words from the original deleted, for conciseness

your own word and phrases that help explain the author’s ideas, for clarity

a citation (in parentheses) of the exact source, to mark the end of the borrowed passage and to give full credit

preservation of the author’s original intent

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