February 1, 2015
Penelope Maddy was recently interviewed by 3am magazine (h/t Brian Leiter). I found the interview interesting.
Maddy is a philosopher of mathematics. In the past I have read some of her work related to set theory. I very much disagreed with her philosophy, but her work was still worth reading. She was very much into questions such as whether axioms are true. That’s sometimes called “mathematical realism” because it is based on the idea that mathematics is saying something about the real world.
For myself, I could never make sense of mathematical realism. As I saw it, axioms were neither true nor false. I saw axioms as just useful assumptions whose consequences interested the mathematician.
It seems that Maddy has now moved away from that realism, so is adopting a view a bit closer to mine. She now also doubts the Quine-Putnam indispensability thesis (that mathematical platonism is indispensable to physics). Again, that is closer to my view.
I’m not at all sure that one’s philosophy of mathematics affects how one does mathematics. But I did find it interesting to read of this evolution in her thinking. And I’ll put this down as recommended reading for those interested in the philosophy of mathematics.
January 31, 2015
I noticed this yesterday:
Structure, it’s all imposed. We impose order and narrative on everything in order to understand it. Otherwise, there’s nothing but chaos.
It’s from actress Julianne Moore. I only noticed it, because it was quoted in a post by Hemant Mehta.
I agree with Moore, and appreciate her insight. But I do wonder why I am hearing this from an actress. Why am I not seeing it discussed by philosophers?
Maybe it is being said by some philosophers, but not by most of them. When I say or write something along those lines, philosophers seem to react as if I have said something that is obviously wrong.
I expect to write more on the idea of structuring in future posts. So this will serve as a light introduction to the topic.
January 22, 2015
Note that the “heretic” in the title refers to me, and comes from this blog’s title.
I have long considered myself a scientific realist. At least, on some definitions, a scientific realist is one who believes that science provides the best available descriptions of the natural world. And, in that sense, I surely am a scientific realist.
I’ve been noticing that some people have been suggesting that I am an instrumentalist or an anti-realist. So they must be using a different notion of “scientific realism.” There’s a post, today, at Scientia Salon which gets into such an account of scientific realism:
Here, I will discuss that post and where I have difficulty with the way that it looks at science. My own view of science, and how it works, should be apparent from that discussion. And I think it will be clear that my own view is non-standard (and, in that sense, heretical). Continue reading
January 21, 2015
My second example of why I don’t like ontology, is a TEDx talk by Kit Fine (h/t Brian Leiter). In that talk, Fine discusses what is the fundamental nature of the being of numbers.
It’s a puzzle to me that anyone would suppose that numbers have any fundamental being. It seems obvious that they do not.
Fine gives three possible versions of the nature of numbers. The first is due to Frege and Russell, the second to von Neumann, the third to Cantor. The only one of those that I find useful is von Neumann’s. But I do not take it as being about the nature of numbers. Rather, I take it as a useful way to model arithmetic within set theory. I have always assumed (perhaps wrongly) that was why von Neumann proposed that definition.
Kit Fine seems to think that there are puzzles about numbers and mathematics, that can be resolved by understanding the nature of numbers. He suggests that there is a puzzle as to why mathematics is so useful in science. Others apparently also see that as a puzzle. Fine asks (about numbers):
How can they be so far removed from the familiar world, yet so intimately connected to it?
Presumably, he thinks that understanding the fundamental nature of numbers will answer that question.
Numbers have no fundamental nature. Perhaps knowing that will help Fine.
The usefulness of numbers and of mathematics is explained by how we use them, not by what they are. The usefulness of numbers in science is explained by how scientists use them.
January 21, 2015
I’ve been critical of metaphysics in the past. When I suggest that there is a problem with metaphysics, philosophers seem to come out of the woodwork to tell me how wrong I am.
Well, never mind that. I’ll continue to call them as I see them.
I’m told that ontology is the main part of metaphysics. I’ve recently come across some examples of ontology that illustrate my viewpoint.
This post will comment on the first of those examples. It is a blog post
As an example of “fundamental ontology” it mentions:
First, what is the nature of being – is it all one substance diversified into different entities, or do the entities themselves have qualitatively, perhaps even quantitatively, separate substances?
I presume some people see that as an important question. To me, it looks as if some words have been strung together so as to match the syntactic form of a question. But it still reads as word salad.
Now maybe I have just picked one sentence out of that blog post. So go read the whole thing. To me, it all seems silly.
So I see ontology as nonsense. Epistemology should be done without ontology. If you don’t think that epistemology can be done without ontology, then you are doing it wrong. Lots of people are doing epistemology wrongly. (And that’s why I am a heretic).
January 2, 2015
This is mostly a reaction to a recent post at Scientia Salon:
Apparently some philosophers, including the author Massimo Pigliucci, are seriously arguing that philosophy does not depend on intuition.
I had to check my calendar. It seems far to early in the year for an April Fools joke. The argument presented seems to suggest a staggering lack of self-awareness among philosophers.
Mathematics and intuition
I’ll start with where I see intuition as important. And, quite frankly, I could not do mathematics or science without intuition. Skeptics often criticize the use of intuition, but I’m inclined to think that when I am expressing skepticism, that skepticism is partly based on intuition.
Mathematics can be said to have a formal structure that is independent of intuition. We make definitions and prove theorems based on those definitions. Thus the conclusions are formal consequences of the definitions and other assumptions, so technically they are not dependent on intuition.
However, in order to do mathematics without any intuition, I would be forced to rely on a mathematical philosophy of formalism. Yet mathematics, seen as logical manipulation of formal symbols, seems sterile. Almost everything that I value about mathematics depends on intuition. My ability to use mathematics to solve real world problems depends on intuition. My ability to think of numbers as if they were actual entities rather than formal meaningless symbols, is dependent on mathematical intuition.
December 29, 2014
The WordPress.com stats helper monkeys prepared a 2014 annual report for this blog.
Here’s an excerpt:
The concert hall at the Sydney Opera House holds 2,700 people. This blog was viewed about 14,000 times in 2014. If it were a concert at Sydney Opera House, it would take about 5 sold-out performances for that many people to see it.
Click here to see the complete report.
December 29, 2014
I just heard the announcement on my local NPR station. They will be interviewing President Obama on the question of whether racism has gotten worse during his term.
Presumably, the interview is on tape. They have not yet played it at my local station. But, from the announcement, it looks as if Obama will be saying that actually things have been improving.
I look at this partly from the vantage of a university professor (now retired), and partly as a member of the community. From what I have seen, there is more interracial friendship, more mingling. Overall, I agree that things have been getting better. This has been particularly noticeable over the last 15-20 years and the improvement of racial relations continues.
So why are we hearing so much about racial issues on the news? I believe that to be a backlash from the more racist members of our society. Racism is deeply engrained among some groups. Others have been trying to overcome their racism. But, for people raised during a racist era, that can be difficult.
Our younger folk have grown up in an era of change. And we are seeing that change. There is now far more recognition of the unfairness that minorities often face. And that increasing consciousness of the problem is also part of why we are hearing so many news reports on racial issues.
I’ll ask those of minority groups to be heartened by these changes. I don’t ask them to be patient. I understand their impatience. Change has been far too slow. I naively thought that racism would end with the civil rights legislation of the 1960. But changing laws is easy, compared to changing people and changing cultures. Yet there is ongoing change. Your children will experience less racism than you experienced.
December 24, 2014
Merry Christmas everybody. Happy holidays to all.
And, for balance, here’s a link to a word from the grinch.
December 18, 2014
I was brought up with the idea that God is love. This was the centerpiece of Christianity.
Judging by what some conservative Christians have been saying, this is now changed to “God is torture” (see this recent slacktivist post).
There doesn’t seem to be much Christianity remaining. Thankfully, Fred Clark’s “slacktivist” blog still makes a case for the “God is love” view.