TheSim

The conclusions drawn by the scientific method are independent of one's definition of personal identity. Therefore science has nothing to say about the truth of mortality or immortality. Instead we must instead turn to conceptual analysis, where it becomes clear , at least to my mind, that whatever one's conclusions are regarding the truth of mortality or immortality, one's conclusions are nothing more than a restatement of one's definition of personal identity.

Sure there is no bijection between a set and it's powerset in the case of finite sets since this result can be directly constructed. But Cantor's theorem is a so-called 'proof' by way of contradiction that begs the law of excluded middle without right in order to lead to his desired conclusion. He seems to argue that since N -> P(N) cannot be a surjective function without leading to a contradiction, that it must therefore be the case that N->P(N) isn't a surjection, thereby concluding that |P(N)| > |N|. But he has no right to do this because he hasn't shown that P(N) is a set. Obviously Cantor's theorem is expressible as a theorem of ZF since the rules of classical logic are permitted there. But as Skolem's Paradox demonstrates this leads to a contradiction regarding its intended interpretation. This is why it is probably better to abandon ZF for a constructive set theory.

Second order logic has certainly been used to create a sentence that has traditionally been called "completeness of the reals", but to 'prove' completeness of the reals in second-order logic requires assuming the very existence of uncountable and non-computable sets of real-numbers that are in question. At best all you have is an empty axiom of syntax called "completeness of the reals" that cannot be meaningfully interpreted. And if non-constructable sets are dropped from second-order logic, it collapses into first order logic. Cantor's so-called "proof" of the existence of uncountable sets is merely a conditional statement saying that if the power-set of natural numbers exists then it cannot be enumerated. But we have no way of constructing this power-set, since only a countable number of subsets of N are recursively enumerable, that is to say, can be generated by an algorithm. Sure, we can define the phase "Uncountable sets exist" to refer to Cantor's proof, but this result is merely an empty and circular parlour game of syntactical gibberish without physical or practical significance. It might be a fun parlour game, but i don't see how it leads to philosophical clarity.

But it HAS been proven. See Skolem's paradox. Every countable axiomatisation of set theory in first-order logic, if it is consistent, has a model that is countable. This result should only be surprising to those who literally believe in non-computable reals.

Perhaps it would solve the philosophical confusion if a line is defined to be a set of ordered constructable points, where a point is a computable total function by at least one terminating algorithm. That way there is explicit clarity that there are no "holes" in our field of entities - except perhaps for the partial functions corresponding to non-terminating algorithms that cannot be ordered by their outputs - and that there is only a countable number of entities describable by mathematics.

Your problems appear to be with regard to the soul being conceived as a substance. But not of all our indispensable concepts are backed by substances.

Universal statements of the form "Every X has property Y" where X has unlimited scope, are best understood to be policies for generating empirically verifiable finite propositions of the form " precisely n X's have property Y", where in order to generate a proposition the variable n must be substituted for any finite number. It is analogous to infinite FOR loops in programming languages. Whenever a programmer uses an infinite FOR loop, he isn't implying that the algorithm will never ever be stopped, he is merely deferring the termination of the FOR loop to the external operating environment of the program and has nothing else to state about the matter. Likewise, so-called universal "laws" of science are better understood to be policies for generating verifiable and finite propositions that we deem to be permissible in light of our current observations. Here, the "stopping conditions" of a policy of science are the fulfilment of falsification criteria for one of it's generated propositions . As with a non-terminated infinite FOR loop, a non-terminated policy of science implies nothing empirical whatsoever, positive or negative, concerning the eventuality of it later stopping due to falsification of one of it's verifiable propositions. Put another way, science is empirically constructive and expresses a finite amount of information concerning what has happened and what can be envisaged to happen, but science implies nothing empirical about what cannot ever happen, despite occasional appearances to the contrary. For example, take the so-called law that "Nothing can accelerate faster than the speed of light". On the surface, it looks as if if it were a meaningful negative empirical statement that universally forbids a genuine empirical possibility. But what it is really saying is that "an object accelerating faster-than the speed of light" is a nonsensical sentence in the language-game of relativity that isn't even a proposition. It is a statement of grammar, rather than a statement of empirical fact.

Is scientific truth inferred via replication, or is scientific truth equivalent to replication? A problem with the former realist conception of truth is that it understands justified true belief in terms of predictive accuracy. But this is problematic, because our identification of predictive behaviour is relative to our cultural conventions. For example, ordinarily we might consider buying a lottery ticket to constitute a lottery prediction. But what has a mere guess concerning tomorrow's lottery numbers got to do with tomorrow's actual lottery outcome? If the answer is "physically nothing" then our pairing of predictions with their physical outcomes is purely decided post-hoc after the outcome has physically occurred, according to cultural convention. Does the realist really want to say that "he was wrong in his prediction" is merely a figure of speech of post-hoc linguistic convention? On the other hand, if we restrict our notion of a prediction to a known statistical correlate of an outcome then we have eliminated scepticism concerning induction, since there is no longer a conceptual gap separating our notions of induction and prediction for justification to fill. We have also eliminated the cultural relativism of convention, since mere guesses are no longer considered to constitute predictions. Yet the resulting conception of objective truth is now trivial, for our predictions are now definitionally equivalent to inductive bias that speaks nothing of the future.

Cases 1, 2 and 3 demonstrate that the public meaning of a noun is structural. The so-called "realness" of a lemur refers to an non-quantifiable set of empirical associations between an open set of stimuli and an open set of responses to said stimuli, as ambiguously and implicitly laid-out by public conventions that dictate the appropriate use of the word. In contrast, one's private meaning of "Lemur!" when shouted in response to whatever one is experiencing, would constitute a behavioural expression which could either be said to be necessarily correct, or to be said to not be truth apt.

As an ex-rationalist I can sympathise with those who mistake habits of thought for a priori truths. But thought experiments are composed of memories and are ultimately a form of empirical simulation. Einstein was only able to perform successful thought experiments in lieu of observing actual experiments.

If science consisted of a universal method of induction, then it's method could be automated using machines, by translating it into a universally applicable learning algorithm that on average would outperform every other conceivable learning algorithm across every possible data-set. But that isn't the case, as Wolpert's No Free Lunch Theorem demonstrates. In order for a learning algorithm to have superior predictive performance with respect to one group of data is for it to have inferior predictive performance with respect to another group of data. Hence science has no "method" of induction. What methods of induction really consists of is simulating some process (the 'simulated') using another process (the 'simulator') , and measuring the similarity of the simulated process to the simulation by using some arbitrary criterion of similarity. If the simulator is a machine learning algorithm, then this similarity measurement is fed back into the simulator so that it automatically adapts so as to make the simulation more closely resemble the simulated. What is considered to be a simulation of one thing by another thing is in the eye of the beholder and whether the simulation is satisfactory depends on his practical purposes.

Consider the boardgame Cleudo. Cluedo's concept of murder is finite and fully decidable; Cluedo's rules of 'proof' always lead to a single and unambiguous conclusion as to "who killed" Dr black that is "true by convention" and obeys the classical logic law of excluded middle. In other words, to have a proof that a certain murder hypothesis cannot be eliminated is to 'know' that the hypothesis is correct. Before the game ends, all murder hypotheses that aren't yet eliminated are equally likely. So it wouldn't make sense for a player to say that they "believe" any particular hypothesis, rather their only substantial beliefs refer to sets of hypotheses. For example, they might believe the culprit was male if there were more male suspect cards still in play. Hence beliefs in Cluedo reduce to sets of observations. Now compare this game to the historical investigation as to who was Jack the Ripper. Here our concept of murder is neither finite nor decidable. For we do not have a finite and closed list of suspects and no matter how much we learn about the past we can never have a controversy-free constructive proof of who-did it. At most we can say that a state-of-the-art simulation of history that we determined through our current and fallible state of knowledge suggests a particular person. At this point, some people will take this simulation to be the very definition of who did it, whereby their concept of truth regarding jack the ripper becomes truth-by-convention as in the game of Cluedo. Others will abstain from accepting this convention and remain open minded. Also, consider a computer game implementation of Cluedo that is played against AI opponents. The computer could either generate the truth of the murder before the game is played, analogous to a realist's conception of history that is factually precise but unknowable. Or the computer might merely generate the cards held by each player, as and when each player requires them, analogous to the anti-realists conception of history as factually imprecise but knowable and determined through current activity.

From a behavioural perspective, all that a person means when saying " There is Donald Trump" are the potential stimuli that can provoke him to say it. If a person's stimulus-responses were completely understood they would never be interpreted as saying anything controversial, even if they asserted that an impersonator was "Donald Trump". Consider how an engineer might react if their version of Amazon Alexa insisted that "Donald Trump isn't the US President". They wouldn't think it was useful to accuse Alexa for being "factually wrong" for they would believe that they had technical insight into the causes of her wayward linguistic behaviour. Rather, they would think there is a database hitch, or that the programmers were playing a joke, etc.

I think you've just given a reasonable description of "absolute truth", namely in terms of facts that are considered to be unchangeable (at least if we are restricting ourselves to physical truth and ignoring metaphysical possibility). But there is a problem here, namely it isn't clear what the object of a belief is or how it should be decided. For example, it is physically true that a Flat Earther has asserted the sentence "The Earth is flat". Furthermore there are physical causes of their assertion. Therefore if the object of the Flat Earther's belief is taken to refer to the causes of his belief then his assertion must be necessarily correct, regardless of the opinions of his community. This implies that the notion of truth is vacuous; any substantial notions called "truth" refer only to matters of linguistic convention. Likewise, if I believe that I know Saturday's lottery numbers but today is only Wednesday, then my prediction has no object unless it is taken to refer to its physical causes. In which case my prediction is again, necessarily correct. After the results of Saturday's lottery are announced I can at least console myself by saying that my earlier prediction is only wrong post-hoc by linguistic convention.

One remarkable tendency of metaphysical realists with respect to a given domain of inquiry is their passion for studying that domain, which they might not have if they didn't believe that there existed an absolute truth to search for. For example, consider a realist and an anti-realist whose attentions are drawn to a dimly illuminated flower whose colour they agree is ambiguous and purple-looking. The realist says "is that really a purple flower? let's turn up the light". The anti-realist replies "Our description is already satisfactory; we agree that the colour is ambiguous and purple-looking. Turning up the light to remove the ambiguity cannot change our current opinion because we would no longer be comparing like for like"

Any description of science as providing a picture of reality sounds realist to my ears, even if all that is meant by 'picture' is a coarse and fallible sketch of reality. The problem with the picture-sketch metaphor, to anti-realist ears, is that it still sounds like it is appealing to a subjective-objective distinction , even when pragmatic users of the metaphor insist that their "picture of reality isn't supposed to be objective." Here, the picture metaphor still suggests that scientists are passive observers of nature, whose investigative practices are irrelevant and non-contributory to the existence of the entities referred to in their empirically tested theories. For example, a realist physicist would understand the concept of the Higgs-Boson very narrowly and atomically as designating only the particular sub-atomic entity 'confirmed' by experimentation. Consequently the realist interprets successful particle accelerator experiments as proving the objective, i.e. investigation-independent existence , of the Higgs boson. In contrast, an anti-realist physicist would understand the concept of the Higgs-Boson very broadly and holistically in a way that is both culturally relative and inextricably connected to the performance of certain experiments and activities. They might say " 'The Higgs Boson exists' means that IF you do This THEN you see That, assuming that you act in conformance with our culture so as to automatically satisfy certain implicit auxiliary assumptions that are unstated in our scientific framework. "

To accept the evidence-proof distinction is equivalent to believing in truth-by-correspondence with respect to a secure foundation of knowledge. Science does not rest upon a such a foundation, and it has no need of one - at least for those of us who are happy to accept the holistic and vaguer notion of truth-by-coherence. For such a Coherentist a proof simply refers to a chain of evidence-based conjecture that a person is willing to swallow.

Quantum Mechanics isn't relevant to the problem, because the free-will debate is purely ontological and concerns only the conceptual relationship between one's notion of personal identity and one's notion of physics and is therefore not a scientific question. The question of free-will is independent of the empirical implications of any particular physics theory. It is only dependent upon one's ontological and psychological interpretation of a physics theory which has no testable empirical implications. Generally, if a body is conceived as being a separate entity to it's surroundings and as possessing its own independent existence, and furthermore if only the motions of the body are considered and not the motions of it's surroundings, then the body is naturally describable as being causally controlled by it's surroundings, and give rise to the impression that its surroundings constitute some sort of externally imposed causal agency. For example, the Earth considered "in and of itself" might be described as being controlled by the gravitational effect of the Sun. On the other hand, suppose the motions of the Earth and the Sun are considered together and simultaneously. Which controls which now? For all we have is a system of gravitation equations describing and relating the simultaneous motion of two objects in some frame of reference. Perhaps we might want to say that the Earth and the Sun don't control each other when they are considered as a joint-system, but are together controlled by an independent gravitational field. But then the notion of causal agency once again disappears if the motions of the Earth, Sun and Gravitational Field are modelled together. Also consider that if an event A that occurs on the earth cannot interact with an event B occurring on the sun due to it requiring faster-than-light travel, then A and B do not have a well-defined temporal ordering according to special relativity. People commonly seem to think that determinism in the sense of a fully predictable universe constitutes an opposing thesis to freewill, which as a consequence produces the illusion that the question of free-will is scientific and scientifically testable. But this is a mistake in my opinion, partly because of the empirical impossibility of distinguishing so-called 'true' randomness from the pseudo-randomness generated by an algorithm, and partly because the psychology of the "free will" question has little to do with predictability and everything to do with the divided self.

To my mind there are two entirely different ways of interpreting the under-determination of theory by evidence depending on one's interpretation of causality. -The standard skeptical and epistemological interpretation is that there exists a hidden matter-of-fact concerning how the universe operates beyond our perception, which our understanding based on evidence can approach but never fully determine: Note that if we are living in a quantum universe, then according to this interpretation it is trivial to claim that we are indeed living in a 'Classical Physics' simulation on a simulator whose hidden operations are actually quantum mechanical. Of course one might argue that our quantum mechanical laws might be simulated by a classical Turing machine on an even lower level of simulation that we have not, and perhaps could never determine. So in a nutshell this skeptical interpretation assumes that the nature of the universe is forever hidden from us and unknowable to us due to it's operations being under-determined by any finite amount of observational evidence we have of them. We as it were, only know what the software has shown us up until now, yet we assume that the software must be the result of hidden hardware operations lurking behind the scenes which we can never determine precisely. -By contrast, ,a nonstandard and non-skeptical interpretation of theory under-determination, is there does not exist a hidden matter-of-fact concerning how the universe operates. The universe being as it were, a superficial movie rather than a piece of virtual reality software. According to this interpretation there exists nothing apart from our observations. Any laws of causation and hidden variables that we propose in response to our observations are merely convenient ways of re-describing our observations and our behavioral reactions to them, such that laws of causation have no culturally independent existence or prescriptive value. Here under-determination is interpreted non-epistemologically to refer to the under-determination of our cultural policies that we find ourselves proposing *in response to* our observations, rather than as referring to the under-determination of a "thing in itself" that is considered to be responsible for our observations.