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

• empiricism: the doctrine that says sense experience is the only source of knowledge
• epistemological: the science which deals with the origin, method and validity of knowledge
• experimental inference: a.k.a. induction by simple enumeration is the process of esitmating what can truly be ascribed to a whole class of things or events on the basis of what has been observed to be true of part of that class
• instrumentalism: the doctrine that ideas are instruments of response and adaptation, and that their truth is to be judged in terms of their effectiveness
• operationalism: the process of defining a concept as the operations that will measure the concept (variables) through specific observations
• posteriori: inductive; relating to or derived by reasoning from observed facts
• priori: deductive; relating to or derived by reasoning from self-evident propositions
• solipsism: the belief that the only thing a person can be absolutely sure of is that he or she exists. All other persons or objects do not exist independently and are merely projections of one’s mind. The solipsist, therefore, views his or her mind as the only thing that exists in reality. All other persons and objects are reflections of his or her consciousness.
  
• succinctly: with concise and precise brevity; to the point
• tenet: an opinion, belief, or principle held to be true by someone or especially an organization

Notes

• Empiricism means the employment of methods based on practical experience rather than on theories or assumed principles.
• The “science of man” (a study of the nature of man’s ideas and of the principle of his reasoning processes) must be founded on experience and observation for us to understand the true nature and scope of ordinary and scientific knowledge.
• Observations and experience teaches us that all thoughts are derived from past experience.
• Hume’s “impressions” are what we call sensations and feelings that are forceful and lively perceptions.
• Hume’s “ideas” are what we call thoughts that are nothing but the faint copies of impressions.
• Ideas are divided up into the simple and the complex; all complex ideas are constructions out of simple ideas, and simple ideas are copies of impressions.
• All the objects of human reason or inquiry may be divided into two kinds: relations of ideas and matters of fact.
• Examples of relations of ideas are the sciences of geometry, algebra, and arithmetic, logic, and every affirmation which is either intuitively or demonstratively certain. Propositions of this kind are discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe…(is analytic and based on the principle of noncontradiction)
• Matters of fact-e.g. physics, chemistry, everyday factual knowledg-is a posteriori, which are the second objects of human reason, are not ascertained in the same manner, nor is our evidence of their truth, however great, of a like nature with the foregoing. All reasonings concerning matter of fact seem to be founded on the relation of cause and effect.
• Hume is maintaining that all knowledge about the world is a posteriori, where a posteriori statment is one which can be confirmed or disconfirmed only by experience and observation.
• In Hume’s view, any truth discoverable by thought alone is never about the world but only about internal relations between our ideas.
• According to Hume, these are the principles of human knowledge. They set our knowledge on a firm foundation, and their application enables us to purge science and philosophy of empty metaphysical speculation.
• When Hume applied what he took to be Newton’s methods in natural science to the “science of man,” he was led, paradoxically, to the conclusion that induction, or scientific method, cannot be rationally justified. Hume was led to this conclusion when he noted that empirical generalization is founded on the principle of cause and effect and that the principle of cause and effect cannot itself be justified rationally.
• E.g. to claim that a certain virus is the cause of smallpox is to claim an invariant sequence of symptoms-preceded-by-virus.
• There are two types of legitimate inference: a priori demonstration (deduction) and a posteriori experimental inference. The inference from observed past instances to unobserved future instances clearly is not demonstrable. And to say tht this inference is experiemental is to beg the question, “for all inferences from experience suppose, as their foundation, that the future will resemble the past.” That is, because scientific method presupposes that the course of nature will not change, it can hardly be invoked to prove it. So Hume concludes that experimental inference, which is scientific method, is not rationally justifiable.
• All you can conceivably know is that there are sensations here and now and maybe that there were sensations in teh past as well.