Does a rock implement every Finite-State Automaton? by David Chalmers

Putnam’s Claim and its consequences

· Every ordinary open system is a realization of every finite automaton.
· If the above statement and the claim of artificial intelligence are true it implies even a rock has mind.


Chalmers Objections

· Putnam’s argument requires “unnatural physical states involving arbitrary disjunctions.
· Putnam’s system does not satisfy the right kind of state-transition conditionals.


Conditionals

· Conditionals are "if . . then . . "claims.
· The standard form for a material conditional is as follows: If P then Q.
· The truth functional characteristics of the material conditional are defined by the following table.


Problem with material conditionals

· Material conditionals can be true even when there is clearly no connection between the antecedent and the consequent, for example "If grass is green then the sky is blue".
· For this reason, material conditionals have often been thought to be an inadequate way of representing the causal connection between antecedent and consequent.


Counterfactuals

· As an example of why counterfactual conditionals are important, consider an event A causing an event B. Now, minimally if A really caused B then A and B must have actually occurred, and that entails the truth of the material conditional "If A then B". But the material conditional does not capture the sense in which there is supposed to be some connection between A's occurrence and B's occurrence.
· That fact is captured by the truth of the following counterfactual conditional "If, all else being equal, A had not occurred, then B would not have occurred".


Putnam’s system does not satisfy the right kind of strong conditionals.

· There are two ways in which Putnam’s system fails to satisfy the strong conditionals:

(a) First concerns the state-transitions that are actually exhibited.
(b) Second concerns the uninhibited state-transitions.


The state-transitions that are actually exhibited.

· Consider the transition from p to q. For the system to be true implementation, this transition must be reliable. But Putnam’s system is open to all sorts of environmental influences.
· The construction is entirely specific to the environmental conditions as they were during the time period in question.
· Slight change in environmental circumstances may lead to a different state.


Unexhibited state transitions

· To qualify as an implementation, it is not only required that are manifested on this run are mirrored in the structure of the physical system.
· It is required that every state transition be so mirrored, including the many that may not be manifested on a particular run.


Possible reply
· To overcome the first objection – It is required that the system reliably transits through a sequence of states irrespective of environmental conditions. A system containing a clock will satisfy this objection. (HOW?)
· To overcome the second objection – It is required that there are extra states to map unexhibited states in a particular run. This can be ensured if the system has a subsystem with an arbitrary number of different states.
· Thus, Putnam’s result is preserved only in a slightly weakened form.
· Further, Chalmers argues that all this has demonstrated is that inputless FSAs are an inappropriate formalism.
· Then he introduces a notion of combinatorial state automaton or CSA.
· Only advantage it has is that states are not monadic but have some internal structure.
· But for every CSA there is an FSA that can implement it.