Emotions

We connect to the world through our emotions.  Emotions, at least in part, play the part of the "and".  Our emotions, to a large extent, determine how we interact with people and how we interact with objects. They determine which people we want to see and eventually do see, and what things we want to do.  (And doing things, while it may involve doing things with people, also involves doing things with objects.)   If I am happy and energetic, one set of possibilities show themselves to me, and if I am depressed, another shows itself to me (i.e. staying in bed; and a bed of course is an object) Of course some of the same possibilities may show themselves to me when I'm happy and when I'm depressed, but how I regard them -or what might be called my being towards them if you're a fan of the word being, differs.

Thus, the "and" participates in emotions.  But the "or" does as well.  For in order to have an emotion, I must be other than the object or person towards whom I have an emotion.   It is axiomatic.  Even if I'm happy and "am one" with everything and everyone, I can't be removed from the equation.  An equation by its nature involves more than one variable.  Thus, emotions are self referential, and as they are self referential, they draw away from other people and objects.

So am I a Cartesian?  You bet your life I am.  It has become fashionable to trash Descartes over the last few hundred years, to blame all of philosophy's problems on this poor man.  Blame yourself. Descartes had it right.

Some simple ideas on the Andorian basis for geometry

As we recall from our halcyon years of adolescent frustration, the world of geometry starts with a point.     It progresses from there to two points, which form a line segment.  (In actuality, since a point is infinitely small, it is impossible to have a line segment consisting of two points, but we need not go there for now.)   But it is clear that the "and" is needed to unite points into a line or line segment.  Similarly, the "or" is necessary to separate the points on a line segment from all the other points on a plane.   Thus, the "and" and the "or" must work in tandem to form the basis of geometry, and they also work in tandem to constitute the basis for all geometrical shapes.  The "and" and the "or" work together to form the boundaries of a triangle.  Similarly, when we calculate the area of a triangle, we are gathering together the points within a triangle (the "and"), determining how much space they cover, and delimiting them from the area outside a triangle (the "or").   The same can be said for all geometrical shapes.

Finally, the same can be said for absolutely anything that takes up space, whether it be a desk or a person.  In giving that entity an identity, or at least a physical identity, we are gathering all the points, cells, nails or what have you (the "and") that that entity occupies or contains, and delimiting them from what exists outside that entity.

Restatement of Andorian essentialism

Essentialism in general provides that the world is what it is because things have certain essences.  Plato called these essences forms.  Aristotle, while denying that forms existed separate and apart from the physical world, went about systematically describing its essence.  We can divide the world into categories of things, and there are categories within these categories.  For instances, there is the category: clothes, and within this category, there are pants, socks, gloves and shoes, and within the category "shoes" there may be Gucci shoes.

Andorian essentialism holds that the "and" and the "or" serve as the foundation for the world of categories.  The category "shoe" exists because of the "and": we gather together all the things we use to cover and protect and in some cases showcase our feet and call them shoes. It couldn't exist without the "and".   The "or" plays an equally important role in the formation of essences by separating and delineating them from each other.   Thus, shoes are given their identity, in part, by being limited to what is placed on or under feet for protection, decoration etc.  Shoes are not socks or pants.  We give shoes their identity by delineating them, limiting their essence, separating them from the essence or definition of "socks".  As is the case with the "and", a category could not exist without the "or".   Thus, Andorian essentialism holds that the "and" and the "or" serves as the basis for all that is.  They have the highest ontological status.  And so it is.

The folly of mathematical and scientific thinking

The history of the universe, if the physicists are to be believed, traces the development of complexity.  The big bang supposedly exploded some kind of incredibly energetic super atom. From there, various subatomic particles found expression, then some of the lighter elements, then heavier elements were cooked in stars and all of this was eventually followed by the development of complex organic molecules and living organisms, such as ourselves.   Thus, we see a movement from a singularity to multiplicity, from simplicity to complexity.

When solving an equation, we see movement in the reverse, or largely in the reverse.  It may start off being of moderate length.  It may lengthen and become terribly long,  several lines or even pages, consisting of numerous pieces.   Then starts the process of simplification, in which we move numbers around, divide here and there, knock off this and that.  And we simplify and simplify, knocking off piece after piece until we arrive at THE ANSWER, THE SINGULARITY.

Thus, scientific and mathematical thinking, or a least a large chunk of it, can be seen as a specious attempt to reverse the flow of cosmic history, at least in the imagination. When this thinking moves beyond the realm of the imagination, and is used to make smokestacks and manufacture automobiles, is it any surprise that this is resulting in the destruction of our species?

A supplemental note on the Andorian basis for mathematics

Much like the study of chemical reactions, which has been discussed in an earlier post, mathematical reasoning, or at least a great deal of mathematical reasoning, involves an elaborate "and/or" dance.   It is often necessary to begin with what appear to be interminably long equations.  Variables are shifted around, moved from one side of the equation to the other, actualizing the "and" on one side of the equation, the "or" on the side of the equation that is losing a variable.  It is lengthened and shortened until, lo and behold, an answer has been arrived at, which is generally one number.   A lengthy equation with numerous constituent parts, is eventually peeled away until all has been compressed into one number.   Thus, while the "and" and "or" is involved in mathematical problem solving, we can say that the "and" eventually triumphs when a solution is arrived at.  Or is it a triumph of the "or", with a solution being reached by a peeling away of layers.  Most likely a fine balance, as is required for good health.  Problem solving, like health, requires a balance of the "and" and the "or".

A brief transition from mathematics to physics

And we can say that because the laws of physics are expressed in equations, the "and" is present in all the laws of physics.  And unlike mathematical equations, equations expressing the laws of physics are not entirely self referential.  Rather, they connect to the world.  And the "and" is present in their connection to the world.

Thus, the "and" is present in Newton's law, Force = Mass times Acceleration, Distance = 1/2 acceleration times time squared, etc.     Thus, the "and" connects Force to Mass, Force to Acceleration, and Mass to Acceleration (for Force divided by Mass = Acceleration.    Each member of each equation is in some way connected.

But the "or" is also present in each law, for the quantity described by each member is not the same, and the "or" separates differences in quantity (see last post).  Thus, Force does not equal Acceleration, it equals Mass times Acceleration.

Thus, the "and" and the "or" are present in each of the laws of physics.

Everything is related. Everything is different.

Some more (simple) philosophy of mathematics

We have already said that the "and" is what makes possible the operations of addition and multiplication, while the "or" underlies subtraction and division.

Similarly, the "and" underlies all quantity, or all numbers greater than one. The number two would not be possible without the "and" conjoining separate units.  While the "and" makes quantity possible, the "or" makes possible differences in quantity.

We can take that all of this a step further, and say that mathematics consists largely of equations.  And equations, in their simplest form, consist of two sides, a left side and a right side separated by an "=" sign.  Statements of equality essentially join together the two sides, saying their the same.   Thus, we can say that the "and" makes possible all mathematical equations.

Now, there are different schools of thought concerning what mathematical equations really say.  It has been said that they don't say anything about the world.  Rather, they are entirely self referential, with the statement on one side simply being another way of expressing the statement on the other.  And if the two sides of an equation are not really different but are really the same thing, then we are arguably not tying together two different things, and the "and" is not operative, for in order for the "and" to be operative, there must be at least two things.

While there may be some validity to this point of view, we cannot say the "and" is not present at all, as the "and" underlies all quantity.  Moreover, while the quantity on each side of an equation maybe the same, we can't say that all ways of naming the same quantity have the same meaning.  The quantity (4+2) may be the same as (5+1) but it is hard to argue that we mean the same thing when we say (4+2) as when we say (5+1). At the very least, it would seem, an equation would would tie together two putatively different quantities by showing that they are in fact the same.  And once again, in this tying together of putatively different meanings, the "and" is present.

It can also be argued that an equation ties together two different sets, one on each side of the equation.   This is a relatively dynamic picture of what happens in an equation.  In the equation 4 plus two equals six, according to this school of thought, you have a set of six units on the right side of the equation, and two sets on the left side, one consisting of four units and the other of two.  These two sets are joined together, and when you count the total number of units on the left side (6), you see that the quantity is the same as what is on the right side.  The "and" is prominently featured in this conception, and as noted above, it is dynamic.  Things are happening. Things are being joined together or, in the case of subtraction, wrenched apart.

While we usually think of mathematics consisting of statements of equality, it can also consist of statements of inequality, such as four plus two does not equal 7, or 4+2<7.  The "or" would appear to be present in such statements, distinguishing between the different quantities.

We can attempt to compare the strength of the "and" and the "or" in the mathematical realm by asking whether there are more possible statements of equality or inequality.  It would appear at first blush that there are more possible statements of inequality.  Four plus two can only equal 6.  It can't equal 7, 8, 9 etc.  Thus, it may seem that for each statement of equality, the number of statements of inequality is infinite.   However, there are an infinite number of numbers that add up to 6 (3 plus 3, 2 1/2 + 3 1/2, 2 1/3 + 3 2/3 etc.)   And if we wished to compare the number of statements of inequality with the number of statements of equality by mapping each statement of inequality to a statement of equality, since the number of both is infinite, it is always possible to find a statement of equality to map against a statement of inequality.

Thus, we can say that the "and" and the "or" are equally strong in the mathematical realm.  And there we have another statement of equality!!

Similarly, we can say that the "and" is always present in a statement of inequality.  For even when we say that two numbers are different, we are linking them together when we compare them.