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But first, for those that enjoy a dabbling in philosophy... and from a reading (Floridi) in the 4th year "Information Technology and Society" course I'm taking at the moment (more on this in the actual Fermilab post to come)...
The Inverse Relationship Principle (IRP) states there is an inverse relationship between the probability of p — where p may be a proposition, a sentence of a given language, an event, a situation, or a possible world — and the amount of semantic information [meaning] carried by p. The IRP states that information goes hand in hand with unpredictability (Shannon’s "surprise factor"). So, the higher the probability of p occurring (as a piece of data), the less informative it is. If P(p) = 1 (that is, the probability of p happening is 100%, like suppose you say "tomorrow, it will rain, or it won't"... your prediction has a 100% chance of happening), it is tautological (includes all possibilities) and is thus non-informative. It is data, but not semantic information (information with meaning). From classic logic: Q is deducible from a finite set of premises, P1, ... , Pn, if and only if [P1 and P2, and ... Pn imply Q] is a tautology. Since tautologies carry no information, "no logical inference can yield an increase of information". So deductions extracted logically from tautologies also yield no information. But... for any logical deduction, the information contained in the conclusion must already be contained in the premises used for the deduction (logical and mathematical inferences are "analytical"), and therefore logic and mathematics must be "utterly uninformative", and this is known as the "scandal of deduction". The fact that we seem to have more collective knowledge after having solved a logic or mathematics problem, flies in the face of the argument that solving such systems conveys no meaning. This remains a huge unsolved bugbear in the philosophy of mathematics and logic.
As with all paradoxes, it usually means that the question being asked or the tools being used to generate the paradoxical conclusion are fundamentally flawed. One of my favourites is Zeno's Paradox of motion: to reach an end-point (say, shooting an arrow at a target), it must cross half the distance first. It must then cross half the remaining distance, and then half of the remaining distance after that, etc. with the implication that, logically, the end-point will never be reached. You can go all shmancy and say, well quantum electrodynamics says it's actually photons that mediate the actions of one object on another and so the objects will interact before the atoms get close to each other. Back to the arrow, the arrow will stop its motion because of photons hitting it from the target, and push atoms of the target out of the way using photons (this is really how the universe works, btw, you never actually "touch" anything, the virtual swarm of photons in your hand interacts with the virtual swarm of photons in the object you "touch" and it pushes your hand away as though there was a solid surface you are touching... kinda fries the ol' noodle to think about), and kathunk, arrow in target... but you can make the same argument that you will need to traverse half the distance required for the photons to be effective and then half that distance, etc. Going deeper doesn't help. Since we know we get to the grocery store when we set out or that we touch (given the definition above) things, what is the solution to the paradox (because it poses a valid question)?
The Inverse Relationship Principle (IRP) states there is an inverse relationship between the probability of p — where p may be a proposition, a sentence of a given language, an event, a situation, or a possible world — and the amount of semantic information [meaning] carried by p. The IRP states that information goes hand in hand with unpredictability (Shannon’s "surprise factor"). So, the higher the probability of p occurring (as a piece of data), the less informative it is. If P(p) = 1 (that is, the probability of p happening is 100%, like suppose you say "tomorrow, it will rain, or it won't"... your prediction has a 100% chance of happening), it is tautological (includes all possibilities) and is thus non-informative. It is data, but not semantic information (information with meaning). From classic logic: Q is deducible from a finite set of premises, P1, ... , Pn, if and only if [P1 and P2, and ... Pn imply Q] is a tautology. Since tautologies carry no information, "no logical inference can yield an increase of information". So deductions extracted logically from tautologies also yield no information. But... for any logical deduction, the information contained in the conclusion must already be contained in the premises used for the deduction (logical and mathematical inferences are "analytical"), and therefore logic and mathematics must be "utterly uninformative", and this is known as the "scandal of deduction". The fact that we seem to have more collective knowledge after having solved a logic or mathematics problem, flies in the face of the argument that solving such systems conveys no meaning. This remains a huge unsolved bugbear in the philosophy of mathematics and logic.
As with all paradoxes, it usually means that the question being asked or the tools being used to generate the paradoxical conclusion are fundamentally flawed. One of my favourites is Zeno's Paradox of motion: to reach an end-point (say, shooting an arrow at a target), it must cross half the distance first. It must then cross half the remaining distance, and then half of the remaining distance after that, etc. with the implication that, logically, the end-point will never be reached. You can go all shmancy and say, well quantum electrodynamics says it's actually photons that mediate the actions of one object on another and so the objects will interact before the atoms get close to each other. Back to the arrow, the arrow will stop its motion because of photons hitting it from the target, and push atoms of the target out of the way using photons (this is really how the universe works, btw, you never actually "touch" anything, the virtual swarm of photons in your hand interacts with the virtual swarm of photons in the object you "touch" and it pushes your hand away as though there was a solid surface you are touching... kinda fries the ol' noodle to think about), and kathunk, arrow in target... but you can make the same argument that you will need to traverse half the distance required for the photons to be effective and then half that distance, etc. Going deeper doesn't help. Since we know we get to the grocery store when we set out or that we touch (given the definition above) things, what is the solution to the paradox (because it poses a valid question)?
