Archive for November 2005

Please, mathemasters, let the English teachers write your textbooks

November 27, 2005

The biggest problem facing Math students today, besides laziness, is the quality of the textbooks. These fellows are very intelligent, but they’ve been submerged in their secret language of letters and numbers so long they can’t even communicate with the uninitiated. Too often, you can only understand them if you already know what they’re going to say, and if you already know what they’re going to say, why are you reading the book? Examples are good, but one can lose hours trying to comprehend them if they lack sufficient explanations. Students can only take so much of this. Eventually, they give up, decide that they aren’t math people, and never do long division again. Please, masters! I want to learn! Let the peons in the Humanities departments transcribe your holy texts!


A Quality Paper

November 2, 2005

Galileo’s and Locke’s arguments about primary qualities (PQs) essentially do not differ at all.  Galileo argues that PQs are inseparable from all objects.  It is impossible to conceive of an object which does not have these traits: shape, size, mobility, quantity, physical location, and relationships with other objects.  John Locke argues that no matter how much you divide an object, no matter how imperceptibly small it becomes, it must have certain primary qualities like shape and size.  Locke’s list of PQs changes each time he mentions it, but the extended version includes all Galileo’s choices as well as solidity and texture.  Galileo would not have objected to Locke’s additions, however; he even alludes to texture in his “feather” example (see below).

Neither philosopher considers sensory data such as color, taste, and smell to be PQs.  To explain these, both propose the existence of secondary qualities (SQs), and their arguments are again quite similar.  Galileo argues that SQs, though they reside in many objects, are not essential to the conception of an object.  It is impossible to imagine an object without size or shape, but is possible to imagine an object which is colorless and tasteless.  Indeed, these SQs are not even part of the object itself; they are merely the product of the relationship between our sensory organs and the object’s PQs.  For instance, though a feather tickles us, it does not contain a “tickling” property.  It would be absurd for a feather to have “tickling” inside it.  Rather, “tickling” refers to the unique relationship between the feather’s texture and our skin.

Locke agrees with Galileo that SQs are non-essential properties which we attribute to an object but which do not actually reside in the object.  He says that SQs are ideas which PQs create in us.  For instance, we say that porphyry is red because its texture (a PQ) gives us the idea “red” (an SQ).  There are two types of SQs: the “immediately perceivable,” which stem from the relationship between us and the transmitting object (see above), and the “mediately perceivable,” which stem from our observation of the relationship between the transmitting object and another object (a fire, for example, can give us the idea “hot” by melting Descartes’s piece of wax).  Though Galileo does not share the Empiricist theory of ideas, his perception of SQs is identical to Locke’s perception of immediate SQs.  Galileo does not mention mediate SQs.

Galileo and Locke give nuanced and similar assessments of the existence of secondary qualities.  Galileo says that SQs are merely names for sensations which occur inside the perceiver’s body when it contacts an object.  These physical sensations do occur, but they are not physically present in the object which transmits them or anywhere in the physical world.  The imperceptible particles which transmit an SQ exist, but they do not resemble SQ itself.  Nothing does; nothing in the world is actually “red.”  The “real” world looks much different from the one we perceive for this reason.  An SQ would not exist without a being which could perceive it.  We do exist, however, so the SQs which we have perceived exist in our minds (and nowhere else).

Locke says that SQs are physical reactions between us and sensory organs, but they would not exist without the PQs which transmit them and the beings which perceive them.  Like Galileo, he asserts that while the imperceptible particles which transmit SQs exist in the physical world, SQs themselves do not.  He admits that he cannot explain how PQs give us SQs and notes that this reflects our fundamental ignorance about the relationships between objects and the true state of the world.  SQs are ideas, however, and any idea which a person has exists in his mind.  So, both Galileo and Locke say that SQs are not physically present in the world, but they do have mental existence because our mind registers and remembers the physical sensations for which we name SQs.