May 4, 2014

## Coffee cups and donuts

There’s a saying among mathematicians, that a topologist is someone who cannot tell the difference between a coffee cup and a donut.  I’ll discuss that in this post, and I’ll suggest implications beyond mathematics.

Usually, when we say this, we are thinking of the donut and the coffee cup as two-dimensional surfaces.  Once we go to the three-dimensional objects, nobody denies that the donut has a soft and spongy texture which makes it clearly different from a coffee cup.

### Topology

Let’s start with a brief rundown on what is topology.  It is a branch of mathematics where we discuss ideas such as continuity, convergence, etc.  A classic example of convergence is with the sequence 0.9, 0.99, 0.999, …  We can see that the sequence gets closer and closer to 1, and we say that it converges to 1.  So topology has something to do with the geometric ideas of getting closer.  But it does so without needing a notion of metric (or distance).

March 28, 2014

## Direct measurement of temperature

In an earlier post, I described the representation measurement of temperature.  In this post, I describe the direct method.  The contrast is intended to illustrate the distinction between representational theories of perception and direct theories of perception.  By using an example from science (or perception written big), we illustrate in a way that is easier to see.

### The design of the instrument

The design is almost the same as described in the earlier post.  There is one addition.  The mercury column in the capillary tube is directly calibrated in temperature.  That is to say, there are graduation markings on the thermometer, from which we can directly read off the temperature.

March 27, 2014

## Representational measurement of temperature

As indicated in the previous post, I plan to use the measurement of temperature to illustrate some ideas about perception.  This post will give a representationalist account of measurement, as an illustration of indirect perception.

The apparatus to be used is very similar to a mercury thermometer.  I shall assume that the reader is reasonably familiar with traditional analog thermometers, and how they are used.

### The design of the instrument

The thermometer uses a glass tube.  At the bottom of the tube, there is a largish bulb which can be filled with mercury.  Above the bulb, the glass tube contains only a very narrow tube of small diameter, sometimes called a capillary.

The bulb is initially filled with mercury, and the mercury extends to part way up the capillary tube.  Above the mercury, the tube is empty.  The air is pumped out, though it need not be a perfect vacuum.

March 11, 2013

## Turning epistemology upside down

Epistemology is a core area within philosophy.  It is concerned with questions of knowledge, information, description and truth.  And it is part of what I would like to see turned upside down.  That is to say, the way that I see questions of knowledge, information, description and truth is very different from what we find in the traditional literature.

### Epistemology from a design stance

As mentioned in my earlier “upside down” post, I see traditional philosophy as based on a design stance, while I would prefer a more evolutionary stance.  So let’s start by looking at how the design stance seems to work.

January 28, 2013

## HSW – Kepler’s laws are false

While my title line might seem dramatic, I want to be clear that this post is not intended as a criticism of Kepler, or of Kepler’s laws.  Rather, it is critical of the view that scientific laws are true descriptions of the world.  This post is intended as part of my series on how science works.  My aim is to describe my own understanding of Kepler’s laws.

### The basis of Kepler’s laws

In case some of my readers are not familiar with them, Kepler’s laws are an attempt to account for the motion of the planets in our solar system.  Kepler’s laws were preceded by the Ptolemaic idea that the planets moved in cycles and epicycles.  Galileo argued, instead for the idea of Copernicus, that the planets traveled in circular paths around the sun.  I presume that Kepler was looking for something a little more precise than the Copernican circles.

October 12, 2012

## On science and scientism

Coel Hellier has a new post on his blog, on the subject of scientism:

The tagline of coelsblog is “Defending Scientism” so it is no surprise that Coel is a proponent of scientism.  However, his post also brings out some points on the nature of science, and that’s what I want to discuss here.

August 13, 2012

## Symbols and categories

In earlier posts, I have preferred the Shannon notion of information, according to which information is a sequence of symbols.  And I have emphasized that symbols are abstract objects.  The symbols are usually considered to be intentional objects, because it is only on account of our intentions that we consider them to be symbols.

In this post, I want to relate the idea of symbol with that of category.  I’ll start by assuming that the readers have at least an informal idea of what we mean by category.

May 5, 2012

## A semantic conception of mind

In an earlier post, I remarked that philosophy, including philosophy of mind, appears to be a syntactic enterprise, whereas I tend to think of the mind as primarily semantic. In this post, I want to suggest a way of thinking about the mind that better fits with the idea that it is primarily semantic.

April 7, 2012

## Science and scientific theories

This is partly a comment on “The Knight’s Song, or What is a [scientific] theory?” and partly a post on my own view of science and how it differs from what philosophers of science say.

If we follow the Shannon-Weaver theory of communication, then

• we start with semantic information (the natural world, as studied by science);
• we encode that in a symbolic form (syntactic information, Shannon information, linguistic representation);
• that syntactic information can then be transmitted or recorded;
• a final receiver of the syntactic information can decode it to recover the semantic information.

With science, the method we use for symbolically encoding nature is what we call “measurement”.  This process of encoding produces the data on which science very much depends.  I also discussed this way of looking at measurement in an earlier post.