The number of uses of X is indefinite or unknown , the different uses are unordered, are not listable, and are not deducible from one another. All biological adaptations are either affordances seized by heritable variation and selection or, far faster, by the organism acting in its world finding uses of X to accomplish Y. Based on this, we reach rather astonishing conclusions:. Brain-mind must be partly quantum—supported by increasing evidence at 6. This is supported at 5. We can and do jury-rig. Computers cannot. Beyond familiar quantum computers, we discuss the potentialities of trans-Turing systems. This short paper makes four major claims: i artificial general intelligence is not possible; ii brain-mind is not purely classical; iii brain-mind must be partly quantum; iv qualia are experienced and arise with our collapse of the wave function. These are quite astonishing claims. Even the first claim is major. Artificial Intelligence AI has made tremendous achievements since its first steps in the fifties of the last century, with Turing introducing the main concepts and questions regarding computing machines Turing, , and the enthusiastic research plan of the Dartmouth research summer project McCarthy et al. We hope to show that this is not possible for wonderful and fundamental reasons: the becoming of any world with an evolving biosphere of philosophic zombies, let alone conscious free will agents, is, remarkably, beyond any mathematics we know. The pathway to this insight depends upon a prior distinction between the degrees of freedom in physics and in an evolving biosphere. Gibson points out that a horizontal surface affords a place to sit. Affordances are both possibilities and constraints for the behaviour of organisms Jamone et al. In evolution, an existing protein in a cell used to conduct electrons also affords a structure that can be used as a strut in the cytoskeleton or to bind a ligand. Evolution has involved the evolution of behaviour. This includes Descartes, Hume, Kant and Russell. This requires ongoing interaction with the environment including other organisms.
Planning and Robotics (PlanRob 2023)
As a useful framework for the evolution of behaviour and, with it, mind, we borrow the U. How do organisms do this? We easily do this when we tinker and jury-rig. Given a leak in the ceiling, we cobble together a cork wrapped in a wax-soaked rag stuffed into the hole in the ceiling and hold it in place with duct tape Kauffman, Jury-rigging uses subsets of the causal features of each object that articulate together to solve the problem at hand. Any physical object has alternative uses of diverse causal features. It is essential that there is no deductive relation between these uses. How many uses of a screwdriver alone or with other things exist? Is the number exactly 16? Is the number infinite? How would we know? How define? No, the number of uses of a screwdriver alone or with other things is indefinite. Consider some uses of a screwdriver alone or with other things. Screw in a screw. Open a can of paint. Scratch your back. Wedge a door closed.
Scrape putty off the window. Tie to a stick and spear a fish. What is the relation between these different uses? There are four mathematical scales: nominal, partial order, interval and ratio. The different uses of a screwdriver are merely a nominal scale. This fact has profound and far-reaching consequences, as we show in the following. But we cannot prove that the indefinite and unlistable uses of a screwdriver are identical to the indefinite and unlistable uses of an engine block. No Axiom of Extensionality. We cannot get numbers. This would be the set of all objects that have exactly 0 uses. Well, no. We cannot get the integers this way. We cannot get the number 1 or the number The alternative definition of numbers is via the Peano axioms. But we cannot have a null set. And the uses of objects are unordered.
The Treaty of Guadalupe Hidalgo: Annotated
There is no successor relation. We cannot get numbers from Peano. No irrational numbers. No real line. No equations at all. No imaginary numbers and no complex plane. No manifolds. No differential equations. No topology. No combinatorics and no first order predicate logic.No quaternions, no octonions. A major implication affects computability: no non-embodied Universal Turing Machine UTM , which operates algorithmically, hence deductively Kripke, , can find new affordances not already in its logical premises. The program can then reason on this ontology and produce plans to solve a given problem. While doing this, both objects and relations can be combined by following constraints and rules in the knowledge base of the program. Nevertheless, a computer program cannot deduce new properties nor new relations. That is to say, the program cannot provide new explanations of the data it manipulates, besides the ones that can be deduced. The central reason is that, in general, there is no deductive relation between the uses of an object. From the use of an engine block as a paperweight, a computer program cannot deduce its use as a way to crack open coconuts. It can of course find the latter use if it can be deduced, i. The universe of possibilities in a computer program is like a LEGO bricks world: components with predefined properties and compositional relations that generate a huge space of possible combinations, even unbounded if more bricks can always be added. Now, let us suppose we add Scotch tape, with which we can assemble bricks without being constrained by their compositional mechanism, and a cutter, which makes it possible to cut the bricks into smaller pieces of any shape. Here rules and properties are not predefined and we have a universe of indefinite possibilities: we are no longer trapped inside the realm of algorithms. Besides deduction, other forms of logical reasoning exist, namely induction and abduction. Induction is over already identified features of the world. Induction by itself does not identify new features of the world. Abductive reasoning aims at providing an explanation of an observation by asserting a precondition that is likely to have this observation as a consequence. For example, if the corridor light bulb does not switch on, we can suppose it is broken. Abduction is differential diagnosis from a prestated set of conditions and possibilities.
https://m.media-amazon.com/images/M/MV5BNzMxYzI0NTctMTA5Yi00YjNkLWJiNDYtZDBiYmZlZGVjZDQ2XkEyXkFqcGdeQXVyMzQ5Njc1Nw@@._V1_FMjpg_UX1000_.jpgConnecting the dots: social networks in the classroom and white matter connections in the brain
When implemented in computer programs, these kinds of reasoning nonetheless cannot add new symbols to represent new possibilities and new meanings. Abductive reasoning can only work with explanations already in its knowledge base. In other words, new symbols—along with their grounding in real objects—are outside of the ontology of the system. The perhaps astonishing implication of this is that we humans and other organisms learn novel features of the world all the time, but cannot do so by deduction, induction or abduction by using previous categories. Our conclusion is supported by remarkable recent work Devereaux, showing that no modeller within the universe can have a complete model of the universe. This work demonstrates that no finite list of true-false propositions and their truth values can exhaust the real world. New features of the world always exist and perhaps can be found and used. Open-ended behaving and doing in the world, therefore, cannot be limited to mere induction, deduction and abduction. We can conclude from all of the above that non-embodied UTMs cannot find new affordances. Nor can such interacting UTMs mutually create novel affordances. If finding and creating new affordances outside of the ontology of the UTM are necessary conditions for passing the Turing test, then non-embodied UTMs will never pass the Turing test. Moreover, besides the capability of reasoning and learning, an Artificial General Intelligence AGI should also be capable of using common sense knowledge, dealing with ambiguity and ill-defined situations, and creating new knowledge representations Roli et al. All these capabilities rely on the ability of finding affordances beyond the algorithmic predefined space, therefore AGI in non-embodied UTMs is ruled out. Because affordances characterize actions in the physical world, a fundamental question arises as to whether and how robots, which are embodied UTMs, can find and exploit novel affordances. Robots interact with the physical world through their sensors and actuators, and they can be capable of learning, therefore they can possibly discover new sensory-motor patterns useful for their goals. Nevertheless, two unresolved issues come into play: first, the symbol grounding problem Harnad, , i. No algorithmic way of tackling this issue is therefore possible. Consider a case of a robot using an engine block as a paper weight and the solution to achieving its goal is to use the engine block to crack open coconuts. To do so, the robot must acquire information on the relevant causal features of the engine block to crack open coconuts. The robot can move and sense its world via its sensors: what must occur such that the robot can discover the use of the engine block to crack open coconuts?Achieving the final goal may require connecting several relevant coordinated causal features, none of which can be deduced from the others. It is clear that indefinitely many other ways to use the engine block to crack open coconuts also are possible, hence these are also affordances. More, for any one such sequence of actions it is critical that there is no way for the robot to determine that it is actually improving over the successive and incremental steps of its search. The robot cannot accumulate successes until it happens upon the final success. Even a first step is a search in an undefined space. Taking this first step, and each successive step, to reaching the goal is blind luck with some timescale for each, or perhaps many, step s. A passage of time is required because the robot must use the real physical object if it is to discover new novel but non-deducible features of the object. Therefore, we conclude that even an embodied UTM can rarely find a concatenated set of novel affordances on some very long timescale compared to the time available to the robot to accomplish the task. Computers cannot jury-rig in novel ways. The evolving biosphere can and does jury-rig in ever-creative ways by jury-rigged Darwinian pre-adaptations such as the evolution of the swim bladder from the lungs of lungfish Kauffman, Cells do thermodynamic work to construct themselves. The evolution of hominid technology for the past 2. Life and mind are not algorithms.
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