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This is bordering on semantics. What's the difference between mathematical inclination and logical inclination? The field of computer programming has made a sep

by lbrandy 18y ago

This is bordering on semantics. What's the difference between mathematical inclination and logical inclination? The field of computer programming has made a separation in alot of people's mind that simply didn't exist before. People, especially programmers, view mathematics far too narrowly because they lack historical context. George Boole was a mathematician. The logic textbooks are full of words that betray their background, e.g. the "lambda calculus". All of these things have their roots in mathematics. And before there was computer science degrees, these things -were- mathematics. I doubt, very seriously, that Djikstra would draw much of a distinction between "logical inclination" and "mathematical inclination". So while you might, the original context of the quote in question needs to be considered.

bpyne 18y ago
Agree fully with lbrandy's point. Just to add a little more, people seem to get confused between the expression of mathematical thoughts and having mathematical thoughts. Mathematical symbols are abbreviations for ideas that, if expressed in natural language, would become tedious. Mathematical thinking is something people do everyday. For example, parents have to use combinatorial optimization everyday to figure out a best strategy for running errands. Few parents are schooled to a formal expression of the mental processes they go through in determining a solution but they weigh different goals and optimize nonetheless. Oddly, a study that is all about exploration of ideas and abstraction has been narrowly defined in many people's minds. Hopefully mathematics educators can break these limited views in years to come.
potatolicious 18y ago
Maybe it's my engineering background, but I don't feel like this is semantics - it's unfair to categorize logical thinking as "mathematical" thinking. There are plenty of us from different backgrounds who are big on logic, and IMHO make great programmers. Mathematicians are far from the only ones who can think logically, and the term is at least somewhat misleading.
- donaq 18y ago
  Uh, logic is a branch of mathematics. From wikipedia: Logic is the study of the principles of valid demonstration and inference. Logic is a branch of philosophy, a part of the classical trivium, as well as a branch of mathematics.
  - carbon8 18y ago
    potatolicious has a point. In fact, in universities, logic (formal logic, with symbols) is usually taught by philosophy departments.
    - donaq 18y ago
      That raises an interesting question, doesn't it? I wonder how many mathematicians turn out to be good programmers vs how many philosophers turn out to be good programmers?
      - dkarl 18y ago
        From experience, I have concluded that whether mathematicians become good programmers depends on whether they have an engineering aesthetic. Mathematical elegance and engineering elegance are not exactly the same thing. A mathematically trivial solution can be a huge practical mess. Mathematicians with no engineering aesthetic can't see the difference and tend to produce big blobs of unmaintainable code. Mathematicians with an engineering aesthetic are some of the best programmers I've worked with. I've only worked with one philosopher. He's very creative and produces reams of working code, but new requirements always mean new reams of code. Everyone suspects there must be a lot of redundancy in his code, but then, nobody has needed to look, because it all works....
    - dkarl 18y ago
      Only by tradition, and in my experience the philosophy department only teaches the class that serves to introduce formal logic to all undergrads. Philosophers deal with words. They like to discuss the various ways a verbal problem might be reduced to logic, and they might be interested in what can be said (in terms they already use) about a system of logic, but that's the limit of their interest. If you take a graduate-level math class in logic (or metamathematics or foundations or whatever your local math department calls it) or even if you just take an upper-division set theory class, you'll learn more about mathematical logic than anyone in the philosophy department wants to know.
carbon8 18y ago
What's the difference between mathematical inclination and logical inclination? Logic is a strange area since it bridges fields, primarily math, philosophy, linguistics and computer science. In my experience, designing software more frequently taps into logic as applied to philosophical arguments and conceptual formal logic more than heavily mathematical areas of logic. The reason is that creating software is basically the process of taking something from the real world and reducing it to a series of logical components and relationships. This is pretty much the exact process for applying formal logic to philosophical questions. On the other hand, actually coding the software taps far more into the mathematical and linguistic aspects of formal logic, since it's involves piecing together units of mathematical logic to construct a logical machine. In practice, this whole process is obviously more nuanced, interconnected and filled with gray areas. It's also certainly possible to argue that all reasoning is math, but this isn't a new concept and dates back to Plato.

by lbrandy 18y ago

bpyne 18y ago

Agree fully with lbrandy's point. Just to add a little more, people seem to get confused between the expression of mathematical thoughts and having mathematical thoughts. Mathematical symbols are abbreviations for ideas that, if expressed in natural language, would become tedious. Mathematical thinking is something people do everyday. For example, parents have to use combinatorial optimization everyday to figure out a best strategy for running errands. Few parents are schooled to a formal expression of the mental processes they go through in determining a solution but they weigh different goals and optimize nonetheless. Oddly, a study that is all about exploration of ideas and abstraction has been narrowly defined in many people's minds. Hopefully mathematics educators can break these limited views in years to come.

potatolicious 18y ago

Maybe it's my engineering background, but I don't feel like this is semantics - it's unfair to categorize logical thinking as "mathematical" thinking. There are plenty of us from different backgrounds who are big on logic, and IMHO make great programmers. Mathematicians are far from the only ones who can think logically, and the term is at least somewhat misleading.

donaq 18y ago
Uh, logic is a branch of mathematics. From wikipedia: Logic is the study of the principles of valid demonstration and inference. Logic is a branch of philosophy, a part of the classical trivium, as well as a branch of mathematics.
- carbon8 18y ago
  potatolicious has a point. In fact, in universities, logic (formal logic, with symbols) is usually taught by philosophy departments.
  - donaq 18y ago
    That raises an interesting question, doesn't it? I wonder how many mathematicians turn out to be good programmers vs how many philosophers turn out to be good programmers?
    - dkarl 18y ago
      From experience, I have concluded that whether mathematicians become good programmers depends on whether they have an engineering aesthetic. Mathematical elegance and engineering elegance are not exactly the same thing. A mathematically trivial solution can be a huge practical mess. Mathematicians with no engineering aesthetic can't see the difference and tend to produce big blobs of unmaintainable code. Mathematicians with an engineering aesthetic are some of the best programmers I've worked with. I've only worked with one philosopher. He's very creative and produces reams of working code, but new requirements always mean new reams of code. Everyone suspects there must be a lot of redundancy in his code, but then, nobody has needed to look, because it all works....
  - dkarl 18y ago
    Only by tradition, and in my experience the philosophy department only teaches the class that serves to introduce formal logic to all undergrads. Philosophers deal with words. They like to discuss the various ways a verbal problem might be reduced to logic, and they might be interested in what can be said (in terms they already use) about a system of logic, but that's the limit of their interest. If you take a graduate-level math class in logic (or metamathematics or foundations or whatever your local math department calls it) or even if you just take an upper-division set theory class, you'll learn more about mathematical logic than anyone in the philosophy department wants to know.

carbon8 18y ago

What's the difference between mathematical inclination and logical inclination? Logic is a strange area since it bridges fields, primarily math, philosophy, linguistics and computer science. In my experience, designing software more frequently taps into logic as applied to philosophical arguments and conceptual formal logic more than heavily mathematical areas of logic. The reason is that creating software is basically the process of taking something from the real world and reducing it to a series of logical components and relationships. This is pretty much the exact process for applying formal logic to philosophical questions. On the other hand, actually coding the software taps far more into the mathematical and linguistic aspects of formal logic, since it's involves piecing together units of mathematical logic to construct a logical machine. In practice, this whole process is obviously more nuanced, interconnected and filled with gray areas. It's also certainly possible to argue that all reasoning is math, but this isn't a new concept and dates back to Plato.