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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 di

by 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
  Calling this a "contradiction" is, imo, unjustified. It is not the accountant who I am calling (more) confused (though if the accountant believes what they are doing to be "impossible" they are still somewhat confused). It is the person who asserts that the thing which they know exists, "is impossible", who is confused. If you have a partial function that takes in a beardnacle and a frompulin and (where it is defined) returns a brimwich, and one has some conditions under which, in the cases it is defined, certain patterns have been shown to hold, and one has found a number of cases in which, it seems as if, if the function were defined at some of the places it isn't, and the value fit with the patterns which have been shown to hold where it is defined, in that other things are consistent with that, even though no brimwich can actually satisfy those properties, a logician can perfectly well ask "well, can we define a concept which generalizes the concept of a brimwich, in order to make this partial function into a total function, in a way that keeps the patterns we have shown?" . This does not involve any contradictions. There are no contradictions here. And yet, this is doing the same kind of thing as generalizing the natural numbers to the integers. You are either using a notion of "contradiction" which is quite unlike the everyday concept (and, if it differs, also quite far from the mathematical concept), or you are mistaken in thinking that there is a contradiction. Like, what is the alleged contradiction? "I want to subtract these two numbers, but there is no natural number which is the result of that subtraction"? That's not a contradiction in the sense that [people who aren't talking about dialectics] use. If you couldn't use it in order to derive False in a theorem prover that allows the relevant statements to be expressed, then it isn't a contradiction-in-the-ordinary-sense. "John is married" and "John is not married" are contradictory. "Smith has 6 apples" and "Smith has fewer than 3 apples" are contradictory. "John has a banana, but Gerald really hates bananas and wishes John didn't have a banana." is not a contradiction-in-the-ordinary-sense. It may be a conflict, which may be resolved in some way, but it isn't a contradiction.
  - pphysch 5y ago
    The pre-negative-number contradiction here is between the "obviously" true propositions: A) "undefined quantities can't/don't exist" (practically a tautology) B) "subtraction sometimes produces an undefined quantity" The first proposition contradicts any proposition that asserts the existence of undefined/impossible/negative numbers. Keep in mind that, before negative numbers, there would be no valid symbols to express the result of the expression "one minus two"; it is irreducible. The root of the problem is that classical logic doesn't have good tools for dealing with ontological deficits, in this case, the lack of a well-defined concept of "negative numbers". All of Plato's classic "laws of thought" presume the existence of a well-defined universal set of things/ideas/truths that they can operate over, which is usually a flawed assumption. In reality, the baseline is that everyone has their own ontology derived from personal experience and it takes serious collective effort (or pedagogical browbeating) to establish shared ontologies on which systems of communication can be built. On the other hand, a core feature of dialectical reasoning is resolving contradictions through the synthesis of novel orthogonal concepts.

by drdeca 5y ago

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
Calling this a "contradiction" is, imo, unjustified. It is not the accountant who I am calling (more) confused (though if the accountant believes what they are doing to be "impossible" they are still somewhat confused). It is the person who asserts that the thing which they know exists, "is impossible", who is confused. If you have a partial function that takes in a beardnacle and a frompulin and (where it is defined) returns a brimwich, and one has some conditions under which, in the cases it is defined, certain patterns have been shown to hold, and one has found a number of cases in which, it seems as if, if the function were defined at some of the places it isn't, and the value fit with the patterns which have been shown to hold where it is defined, in that other things are consistent with that, even though no brimwich can actually satisfy those properties, a logician can perfectly well ask "well, can we define a concept which generalizes the concept of a brimwich, in order to make this partial function into a total function, in a way that keeps the patterns we have shown?" . This does not involve any contradictions. There are no contradictions here. And yet, this is doing the same kind of thing as generalizing the natural numbers to the integers. You are either using a notion of "contradiction" which is quite unlike the everyday concept (and, if it differs, also quite far from the mathematical concept), or you are mistaken in thinking that there is a contradiction. Like, what is the alleged contradiction? "I want to subtract these two numbers, but there is no natural number which is the result of that subtraction"? That's not a contradiction in the sense that [people who aren't talking about dialectics] use. If you couldn't use it in order to derive False in a theorem prover that allows the relevant statements to be expressed, then it isn't a contradiction-in-the-ordinary-sense. "John is married" and "John is not married" are contradictory. "Smith has 6 apples" and "Smith has fewer than 3 apples" are contradictory. "John has a banana, but Gerald really hates bananas and wishes John didn't have a banana." is not a contradiction-in-the-ordinary-sense. It may be a conflict, which may be resolved in some way, but it isn't a contradiction.
- pphysch 5y ago
  The pre-negative-number contradiction here is between the "obviously" true propositions: A) "undefined quantities can't/don't exist" (practically a tautology) B) "subtraction sometimes produces an undefined quantity" The first proposition contradicts any proposition that asserts the existence of undefined/impossible/negative numbers. Keep in mind that, before negative numbers, there would be no valid symbols to express the result of the expression "one minus two"; it is irreducible. The root of the problem is that classical logic doesn't have good tools for dealing with ontological deficits, in this case, the lack of a well-defined concept of "negative numbers". All of Plato's classic "laws of thought" presume the existence of a well-defined universal set of things/ideas/truths that they can operate over, which is usually a flawed assumption. In reality, the baseline is that everyone has their own ontology derived from personal experience and it takes serious collective effort (or pedagogical browbeating) to establish shared ontologies on which systems of communication can be built. On the other hand, a core feature of dialectical reasoning is resolving contradictions through the synthesis of novel orthogonal concepts.