I hope that after a long weekend holiday you have time to come to the
meeting this Sunday to discuss: How fundamental is mathematics?
I know it is not an easy subject but don't forget we are doing
philosophy and not mathematics; hence the issues are quite different. So
Sunday's meeting is not a maths tertulia for that you need to follow
For us, as I have outlined in my few ideas below, what is important is
why do we find it so difficult to define mathematics and yet it is so
fundamental in our lives. And secondly, can mathematics show us what is
ethical like it can show us a lot about other things in the universe? I
argue that philosophy has already solved the first problem, but the second?
In the meantime Ruel has sent us a link to his essay and the photos from
the meeting of two weeks ago.
APOLOGIES I POSTED THE WRONG LINK
How fundamental is mathematics?
This question needs further clarification; indeed it needs a context.
For our purpose we can provide three possible contexts: the social
context, the individual context and the natural context, whether human
or everything else.
It is evident that a society, by which we can mean people today living
together, or a primitive tribe, do require mathematics and mathematics
is fundamental for the function of a society. Of course, the maths
required by a 60 odd member tribe in a tropical jungle, might be very
different from the maths in a mega big city such as Vienna, Paris or New
York. For society I would say that mathematics and knowledge of
mathematics are necessary conditions for a society to survive.
Individual knowledge of mathematics might be very useful and desirable
in city but I would not describe it as fundamental. Some knowledge of
maths, or arithmetic, would be sufficient to operate in a city and in
the jungle as long as someone can count the number of lions in the
distance and navigate by the stars that would be enough.
Nature by contrast, does not need mathematics and mathematics is neither
a necessary nor sufficient condition for nature. I know, this looks like
blasphemy for some, but it's not. Despite the chaotic impression of the
world or even universe around us, nature is a well ordered well balanced
place. But nature, although this should be the universe, as a whole does
not need to understand itself, it only needs to exist. Only we, as a
subset of this universe need to understand our parent set, i.e. the
So far I have made many statements about mathematics without defining
what mathematics is. This is the problem, no one really knows what
mathematics is, or rather there are so many definitions of mathematics
that your guess is as good as mine. But for a philosopher, when a
definition of something is elusive and imprecise alarm bells start
ringing in our head.
Our philosophical instinct will tell us that the problem is either a
language problem or a concept problem. I would argue that the reason why
a definition of mathematics is so elusive is because of a two step flaw
in our thinking. First, our brains, having been born and survived the
devastation of Cartesian dualism, are now infected with this meme that
creates the perception that the world is made up of two things. The
intelligent part, for example in our case mathematics, and the physical
part of the universe, for example the Fibonacci pattern distribution of
the seeds in a sunflower.
So the first philosophical flaw is that we assume that there are two
necessary conditions for the existence of something we perceive when in
reality there is only one thing, i.e. the sunflower. In other words, we
commit a naturalistic type of fallacy that was identified by GE Moore
with the word "good", by ascribing some extra property to the sunflower,
such as a mathematical property, when in reality there is only an
efficient distribution of seeds on a sunflower. There isn't this
ingredient called mathematics that makes part of the sunflower.
The second step is a form of the "Ghost in the machine argument" put
forward by G Ryle against Cartesian dualism as well. Our brain, having
been tainted by Cartesian dualism and having identified a mathematical
pattern, say in the distribution of sunflower seeds, ascribes
mathematics as a necessary property for the existence of the sunflower.
So we first identify the property of mathematics in the pattern of seeds
in a sunflower and then we ascribe this property of mathematics as a
necessary conditions for the existence of the sunflower. However, I hear
you say, but the seeds of the sunflower do flow in a Fibonacci series
therefore mathematics is found in the flower. Yes, but the Fibonacci
series is our way of understanding the distribution of the sunflower
seeds but maths is not a plan the flower follows. The sunflower does
not look up in some big maths reference book as decide to distribute its
seeds in a Fibonacci series, we do that. What has happened is that this
particular plant has evolved with its seeds being distributed in a
Fibonacci patter because it is more efficient for it to evolve this
way. The Fibonacci series of seed distribution is not an ingredient in
making of a sunflower.
So the word and concept of mathematics seems to be elusive to define
because we make the same linguistic and conceptual mistake we commit
with "good" and "mind". Having said that, definitions that define
mathematics is terms of "quantity" or "measurement" (see Wikipedia) seem
to be on the right tracks since this ascribes maths to our ability and
need to understand and not some property in the universe. Sure we are a
subset of the universe, but that won't help us much if what we want to
know is whether the roof of our house is strong enough to protect us
during the night or not.
So as long as we are still around or there are people like us
mathematics is fundamental because we will always need to understand our
environment, interact with it or just simply curious. My bottom line
argument is that mathematics is a function of our brain and not an
ingredient nature mixes to create things in the universe; mathematics is
not like the plum in a plum cake. This means that mathematics is not out
there in the universe but in here in our brain.
It should not come as surprise that mathematics is so useful and
fundamental for our needs and survival. The stability of the universe is
a fine balance of equilibrium and existence on the one hand and
who-knows-what-the-universe-would-be-like if that equilibrium never
happened. Mathematics helps us to understand this universe around and
more importantly make predictions about it. But our ability to represent
the universe in terms of mathematics is no different than bats making
sense of their universe using ultrasound or butterflies using ultra
It is no wonder that scientists justifiably believe that our first
contact with other sentient beings in our galaxy would be through
mathematical exchanges. While this assumption is reasonable to make it
does not follow that alien life, even carbon based, must be familiar
But if mathematics can give us access to the universe and other beings
can it also give us access to what is ethical and moral for rational
beings to follow? I think that maths can take us a long way to establish
what is ethical and what is moral; for example by being able to
mathematically model a healthy and happy human being we can say what is
or isn't ethical to do to human beings. The scientific method is based
on mathematical modelling of our universe including medicine and human
interactions. Therefore, we already know a lot about what it ethical to
do to other human beings but what is ethical and what is political might
not always coincide.
To answer our question mathematics is fundamental for us because it
opens the doors to the truth about the universe, but it is also true that
it is our task to consult the books given that neither mathematics nor
the truth grow on trees.
Open Tertulia in English every
From: January 15 at Triskel in c/San Vicente Ferrer 3.
Time: from 19:30 to 21h
from Lawrence, SUNDAY PhiloMadrid meeting at 6:30pm: How fundamental is