An agent believing this statement may falsify it by taking an action B not equal to f(). Note that, since the agent is assumed to be able to compute things, f() may be determined. So, indeed, this statement does not hold as a law, either.
This contradicts a certain strong formulation of naive determinism: the idea that one’s action is necessarily determined by some known, computable function.
The contradiction is conditional on said process working. More complicated ways of looking at determinism:
Enumerated possible futures: the agent will do A or B (at time t). False if the agent does something else.*
The agent will do A (eventually). Without a time given this may be unfalsifiable.
Another agent observes A, and successfully predicts what they will do. (A is unaware of the prediction, and thus unable to falsify it intentionally.)
*If “or” enumerates ‘exclusive possibilities, then by doing more than one of the enumerated items, such a statement would be ‘false’. Also, what does time mean? You might suppose that a prophecy that you will die in the year 2000 is obviously false—but if in 2022 calendars were rolled back to a year before 2000 then such a prediction becomes something that might be true.
Here is the assumption about how the agent interacts with gravity. The agent will choose some natural number as the height of an object. Thereafter, the object will fall, while a camera will record the height of the object at each natural-number time expressed in milliseconds, to the nearest natural-number millimeter from the ground. The agent may observe a printout of the camera data afterwards.
This seems straightforward.
Some more complicated cases:
Combine the camera and the dropped object. (If this renders things too immediately difficult, add a piece of tape or create some distant marker with regular markings, or get another camera, and use the data to figure out how to convert between the two ‘frames’.)
Replace cameras with telescopes. Does the Earth go around the sun, or the sun around the earth?
(This comment might:
go better under a later post
mix up commentary and quoting, or otherwise ‘jump the gun’ (see above))
Let C be the computer that the agent is considering whether it is running on. C has, at each time, a tape-state, a Turing machine state, an input, and an output. The input is attached to a sensor (such as a camera), and the output is attached to an actuator (such as a motor).
It might have been in another post, but I remember reading about the possibility that the agent could modify C or create a machine in order to alter the tape in order to ‘falsify’ the prediction that at time t the tape would read a certain way. This seemed to point at “if “the agent is a turing machine”, that needs to include the possibility that it can be both a turing machine “t” messing with tape and a turing “t+” that includes systems of sensors, motors, etc. that will read “t” and modify it (under certain conditions).”.
Given the usual workings of physics, absent security, the agent could be a turing machine in the sense that the universe (it is in) is. (This seems to put issues/questions around “closed individualism versus alternatives” into this agent framework in a fashion that seems close to rendering the answers an empirical matter.)
The contradiction is conditional on said process working. More complicated ways of looking at determinism:
Enumerated possible futures: the agent will do A or B (at time t). False if the agent does something else.*
The agent will do A (eventually). Without a time given this may be unfalsifiable.
Another agent observes A, and successfully predicts what they will do. (A is unaware of the prediction, and thus unable to falsify it intentionally.)
*If “or” enumerates ‘exclusive possibilities, then by doing more than one of the enumerated items, such a statement would be ‘false’. Also, what does time mean? You might suppose that a prophecy that you will die in the year 2000 is obviously false—but if in 2022 calendars were rolled back to a year before 2000 then such a prediction becomes something that might be true.
This seems straightforward.
Some more complicated cases:
Combine the camera and the dropped object. (If this renders things too immediately difficult, add a piece of tape or create some distant marker with regular markings, or get another camera, and use the data to figure out how to convert between the two ‘frames’.)
Replace cameras with telescopes. Does the Earth go around the sun, or the sun around the earth?
(This comment might:
go better under a later post
mix up commentary and quoting, or otherwise ‘jump the gun’ (see above))
It might have been in another post, but I remember reading about the possibility that the agent could modify C or create a machine in order to alter the tape in order to ‘falsify’ the prediction that at time t the tape would read a certain way. This seemed to point at “if “the agent is a turing machine”, that needs to include the possibility that it can be both a turing machine “t” messing with tape and a turing “t+” that includes systems of sensors, motors, etc. that will read “t” and modify it (under certain conditions).”.
Given the usual workings of physics, absent security, the agent could be a turing machine in the sense that the universe (it is in) is. (This seems to put issues/questions around “closed individualism versus alternatives” into this agent framework in a fashion that seems close to rendering the answers an empirical matter.)