4

Who first studied "logical (ir)reversibility" philosophically?

By "logical (ir)reversibility" I mean questions like:
Why is it easier to

  1. multiply large numbers than to factorize them?
  2. understand a syllogism than to construct one?
  3. explain something (via resolutionis) than to discover it (via inventionis)?
  4. encipher something than to decipher something?
  5. destroy something than to build it?
  6. argue from effects to causes (quia reasoning) than to argue from causes to effects (propter quid reasoning)?
  7. learn logic before physics or metaphysics? (Why ∃ proper order of learning?)

What is the reason for all these asymmetries?

Perhaps one could answer "because of order". But what about order necessitates irreversibility/directionality?

  • Comment 1: point 7 really doesn't belong with the others. To the extent it does it mixes up logical and pedagogical order. Notwithstanding st Thomas and Aristotle, schools all over the world teach physics before logic. And linguists may learn a new language from the grammar but mothers don't teach their infants grammar before teaching them to speak – Rusi-packing-up Jul 5 at 6:17
  • Comment 2 You are not talking so much about logical (ir) reversability as about the asymmetry of reversible processes. – Rusi-packing-up Jul 5 at 6:21
  • 1
    Depends on what counts as "studying". Mathematicians did not really pay attention to the asymmetry between specifying a function and its inverse until the computational complexity notions were developed in 1950-s. Once a function was "given" the inverse was assumed "given" as well, in the good platonistic fashion. All ciphers used up until 1970-s were also symmetric (equally hard encryption and decryption keys), only then asymmetric (public key) ones were invented, etc. As for build/destroy, the entropic irreversibility was understood in physics already in mid-19th century. – Conifold Jul 5 at 11:08
  • 1
    In the case of 1 and 4, these are examples of algorithmic complexity theory. The complexity of an algorithm is a property that relates its computational difficulty to its size. Algorithmic complexity may be logarithmic, linear, polynomial, exponential, etc. Complexity theory was studied extensively in the 1960s and 1970s as computers became widely available. You can't easily point to any one person who was first to study it. Famously, Rivest, Shamir and Adleman were the first to show how the asymmetry between multiplication and factoring could be used to create public key cryptosystems. – Bumble Jul 5 at 22:48
  • @Bumble Yes, perhaps my question is about the philosophy of complexity theory. – Geremia Jul 5 at 22:50
2

At the root of all these asymmetries is the fact that not all relations are commutative/symmetric.

Here are some non-commutative/asymmetric relations involved in numbers

  • 1: Factors ⇒ Product
  • 2,3,6: Premises ⇒ Conclusion
  • 4: Plaintext message ⇒ Encrypted message (even in symmetric cryptography)
  • 5: Matter ⇒ Form
  • 7: Logic ⇒ Math ⇒ Physics ⇒ Morality ⇒ Metaphysics (The sciences are subalternated to each other.)

"A ⇒ B" means: "A is related to B by some relation" and "B ⇏ A by the same relation."

  • 1
    Unfortunately, saying that asymmetry is "at the root" of irreversibility does not say anything substantive, it just changes the label. What is the reason for those relations to be asymmetric/irreversible? We know a substantive answer in one case, the second law of thermodynamics, but it surely does not explain why mathematical functions display such behavior. And asymmetry itself is not enough. Encryption and decryption keys are different even in symmetric ciphers, yet their complexities are comparable, but not in the public key ones. Why? "Because asymmetric relations exist" is not an answer. – Conifold Jul 5 at 21:52
  • @Conifold I'm not "saying that asymmetry is 'at the root' of irreversibility" but that asymmetric relations are. – Geremia Jul 8 at 18:00
  • Comment space is short, so I abbreviated. From my point of view, "asymmetry" or "asymmetric relations" are just vacuous labels whose names merely restate what needs to be explained. – Conifold Jul 8 at 18:33
  • @Conifold "Relation" is vacuous? – Geremia Jul 9 at 20:57
  • Adding "relation" here does not do anything explanatorily useful that I can see. But I meant vacuous as applied to both "asymmetry" and "relations", together and separately, as explanations for "why" of irreversibility. They just name the problem. – Conifold Jul 9 at 21:04

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