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> Classical logic has always made the most sense to me, because accepting the law of excluded middle leads to a neater world of arguments to me. What use is a

> Classical logic has always made the most sense to me, because accepting the law of excluded middle leads to a neater world of arguments to me. What use is a neat argument if it is divorced from reality? LoEM tricks us into viewing ontologies as static, leading to subtle but drastic errors in thinking. LoEM/classical logic should always be employed as a conscious assumption, with awareness of its drawbacks. Leave room for dialectical reasoning as well.

amw-zero 5y ago
It is very fair to say that this is: a) far too extreme of a position to be useful to anyone b) not true in any sense of the word Classical logic has been behind the bulk of mathematical results in the last 100 years or so. It may not be perfect, but no system is.
- pphysch 5y ago
  By far the bulk of pure mathematical results in the last 100 years have no demonstrated real world function. They are logically sound--and utterly divorced from reality. And any useful innovations tend to come about from dialectical reasoning, because classical logic is incapable of genuine ontological generation. For example, infinitesimal calculus was not "embedded" somewhere in the existing mathematics, waiting to be logically deduced by an expert logician; Newton developed new methods of mathematically modeling unquantifiable quantities to address contradictions in the application of traditional mathematics to physical systems.
  - amw-zero 5y ago
    > By far the bulk of mathematical results in the last 100 years have demonstrated no real world function How absolutely arrogant and unappreciative of you to say. You are very divorced from reality. That much is clear - normally I don’t like to get personal, but really. I’m sure you hear this all the time which ferments your bitterness. “It is not the critic who counts”
    - pphysch 5y ago
      I have a degree in mathematics and (PhD) friends who are still in the system. Event they admit that pure mathematics is largely an illusion. But it pays, if you're lucky. Mathematics in general, and logic, are extraordinarily useful tools when applied to real systems. I use them frequently when developing software. However, like every tool, they can metastatize beyond their use. In my opinion that describes the vast bulk of "pure" mathematics and "pure" logic (and "pure" programming).
drdeca 5y ago
Everything I’ve seen be called “dialectics” has either seemed like something trivial wrapped up in fancy language, or seemed to be something bunk [edit: or I didn’t understand it enough to have an evaluation of it]. I’m skeptical that it is a useful concept. I mean, there’s game semantics, but as far as I’ve seen, there’s no reason to confuse the idea of that by appealing to “dialectics”. Are there any examples of an insight which is uncontroversially regarded as an insight, and uncontroversially regarded as being first made as a result of viewing things in terms of “dialectics”? Also, do you mean the law of the excluded middle, or the law of non-contradiction? [edit: I removed a part I said here because I realized I didn’t know what I was talking about with it. It referenced Kierkegaard, but, again, I didn’t know what I was saying.] Refraining from affirming the law of the excluded middle can be useful at times, but I cannot accept the rejection (or non-affirmation) of the law of non-contradiction. If one thinks that one has a true contradiction, one is simply confused.
- pphysch 5y ago
  > If one thinks that one has a true contradiction, one is simply confused. Consider the time just before the concept of negative numbers was widely accepted. There were natural numbers, perhaps zero as well, and the operation of addition. Someone realized you could reverse the process of addition and yield subtraction. Yet when you applied this "reverse addition" to some pairs of numbers, you would get an impossible result, a number that doesn't exist. This represents a contradiction in the method. A reasonable logician would stop there and simply avoid doing contradictory subtraction. A super smart and reasonable logician would go further and reject subtraction altogether since its "not closed over N", "not safe", etc. However, a "confused" accountant might see the value in such impossible values. He's balancing payments for dozens of deals and finds that his calculations are much smoother if he temporarily allows the impossible values, as long as he marks them as "impossible", like with a small horizontal line. His increased efficiency brings him success and his methods spread, and eventually "negative numbers" becomes a core component of virtually all mathematics. All because this one accountant was "confused" and pragmatic.
  - drdeca 5y ago

amw-zero 5y ago

It is very fair to say that this is: a) far too extreme of a position to be useful to anyone b) not true in any sense of the word Classical logic has been behind the bulk of mathematical results in the last 100 years or so. It may not be perfect, but no system is.

pphysch 5y ago
By far the bulk of pure mathematical results in the last 100 years have no demonstrated real world function. They are logically sound--and utterly divorced from reality. And any useful innovations tend to come about from dialectical reasoning, because classical logic is incapable of genuine ontological generation. For example, infinitesimal calculus was not "embedded" somewhere in the existing mathematics, waiting to be logically deduced by an expert logician; Newton developed new methods of mathematically modeling unquantifiable quantities to address contradictions in the application of traditional mathematics to physical systems.
- amw-zero 5y ago
  > By far the bulk of mathematical results in the last 100 years have demonstrated no real world function How absolutely arrogant and unappreciative of you to say. You are very divorced from reality. That much is clear - normally I don’t like to get personal, but really. I’m sure you hear this all the time which ferments your bitterness. “It is not the critic who counts”
  - pphysch 5y ago
    I have a degree in mathematics and (PhD) friends who are still in the system. Event they admit that pure mathematics is largely an illusion. But it pays, if you're lucky. Mathematics in general, and logic, are extraordinarily useful tools when applied to real systems. I use them frequently when developing software. However, like every tool, they can metastatize beyond their use. In my opinion that describes the vast bulk of "pure" mathematics and "pure" logic (and "pure" programming).

drdeca 5y ago

Everything I’ve seen be called “dialectics” has either seemed like something trivial wrapped up in fancy language, or seemed to be something bunk [edit: or I didn’t understand it enough to have an evaluation of it]. I’m skeptical that it is a useful concept. I mean, there’s game semantics, but as far as I’ve seen, there’s no reason to confuse the idea of that by appealing to “dialectics”. Are there any examples of an insight which is uncontroversially regarded as an insight, and uncontroversially regarded as being first made as a result of viewing things in terms of “dialectics”? Also, do you mean the law of the excluded middle, or the law of non-contradiction? [edit: I removed a part I said here because I realized I didn’t know what I was talking about with it. It referenced Kierkegaard, but, again, I didn’t know what I was saying.] Refraining from affirming the law of the excluded middle can be useful at times, but I cannot accept the rejection (or non-affirmation) of the law of non-contradiction. If one thinks that one has a true contradiction, one is simply confused.

pphysch 5y ago
> If one thinks that one has a true contradiction, one is simply confused. Consider the time just before the concept of negative numbers was widely accepted. There were natural numbers, perhaps zero as well, and the operation of addition. Someone realized you could reverse the process of addition and yield subtraction. Yet when you applied this "reverse addition" to some pairs of numbers, you would get an impossible result, a number that doesn't exist. This represents a contradiction in the method. A reasonable logician would stop there and simply avoid doing contradictory subtraction. A super smart and reasonable logician would go further and reject subtraction altogether since its "not closed over N", "not safe", etc. However, a "confused" accountant might see the value in such impossible values. He's balancing payments for dozens of deals and finds that his calculations are much smoother if he temporarily allows the impossible values, as long as he marks them as "impossible", like with a small horizontal line. His increased efficiency brings him success and his methods spread, and eventually "negative numbers" becomes a core component of virtually all mathematics. All because this one accountant was "confused" and pragmatic.
- drdeca 5y ago