Comments

  • A few metaphysical replies
    By "substantive truth", do you mean an alleged objective, fundamental, concrete "existence" for our physical world and its things and its stuff?
    Now we are getting somewhere. Idealists and anti-realists more generally can (and have) made the distinction between substantive truth and logical truth, so no, one does not need to be a materialist in order for the distinction to make sense. You seem to be a fan of online philosophy encyclopedias - look up "logical truth" and see how complex a notion it is and how various philosophers have tried to distinguish it from substantive truth. As far as I can tell, every example of if-then fact that you introduce is an example of a logical truth, but substantive truths are the ones that concern the empirical world (whether that world be independent of our coming to know it or not). Since we, as sentient beings, are in the empirical world, it is substantive truth that will have a bearing on whether or not we can be reincarnated, not logical truth.

    Now, if you want to argue that there is no genuine distinction between logical truth and substantive truth, that might be an interesting discussion to have. Take a look at Quine's "Two Dogmas of Empiricism" for example.
  • A few metaphysical replies

    In answer to your question, the system of axioms that I'm using is the one that is usually used, stated and cited.
    Well, I don't want to turn this into a thread about mathematical logic, but Peano arithmetic is one of the standard ways of defining the natural numbers, so I'd have to challenge you to provide a more "usually used, stated or cited" system of axioms for doing that.
    In any case, you cannot define "1" this way (as you do):
    Let "1" mean the multiplicative identity.
    without already having defined multiplication (recursively) over the natural numbers, which means that the natural numbers need already to have been defined within your system, which is what the Peano axioms do. Perhaps you have some non-standard set of axioms to capture what a natural number is supposed to be? But in any case, you will not be able to infer 2+2=4 without all those axioms. MetaphysicsNow is right about that and you are wrong.
  • A few metaphysical replies

    Three question marks - does that indicate that you are not aware of the proof for 1+1=2 within Peano arithmetic? Sorry. Here's a straightforward presentation which will give some context to the remark I made about the definition of the symbol "2".
    http://mathforum.org/library/drmath/view/51551.html
  • A few metaphysical replies
    The proofs that I've seen of 1+1=2 do require all the axioms of the number system being used, since the axioms together define what a natural number is and then certain of the axioms are reused in the recursive definition of addition. (You also need to make some symbolic definitional equivalences of course so that, for instance, "2" is defined as "1' " and so on). If that is true for 1+1=2, then its true for 2+2=4 as well. I don't see what mistake you believe MetaphysicsNow is making when he says you need all the axioms to prove 2+2=4. What system of axioms are you using, and what is the proof of 2+2=4 in that system?
  • A few metaphysical replies


    Now then, do you disagree with one or both of my premises?
    I think the point is that nobody can really tell what your premises are. I suppose one of them must be
    "There are if-then facts"
    But when you give examples of what these if-then facts are supposed to be, you just give tautologies, and then refuse to engage in a discussion about the distinction between logical truth and substantive truth that risks being conflated when identifying tautologies as a kind of fact.
  • A few metaphysical replies
    No. Janus asked me to state, in regards to my argument for my metaphysics, a premise, conclusion, and to tell how the premise implies the conclusion.
    No, I asked you for premises and a sound argument (and all sound arguments are logically valid ones by the way), and you said you would provide at least the premises of the argument:
    Presumably the idea is that there is a sound argument with metaphysical premises (i.e. premises which concern existence) which are acceptable to all and that has as for its conclusion that reincarnation happens. — jkg20


    Yes, well said. That's what I mean.

    So, Michael Ossipoff, over to you to lay out the premises one by one so we can subject them to scrutiny.


    Will do.

    Michael Ossipoff
    — michael ossipoff

    You still haven't done that.
  • A few metaphysical replies
    And no, at least in Merriam Webster, "Wheen" isn't listed as meaning "Wean" in any language. Merriam-Webster lists it with an adjective meaning and a noun meaning.
    Calm down, I didn't say that "wheen" meant what "wean" means. There is a word used in Scotland "wheen" which means "small amount of something" - I think, I stand to be corrected on its meaning, but its existence as a word I'm sure of. I thought maybe MN's being acquainted with that word accounted for his mispelling. Anyway, MetaphysicsNow's own explanation for the spelling mistake makes more sense - he meant wean but wrote "wheen" because he cannot get an author out of his head.
  • Math and Motive
    @StreetlightX
    Not at all. The other option is simply to reject that irrationals are numbers tout court. And for the longest time this is just what happened. For a good history of this, see Daniel Heller-Roazen's The Fifth Hammer.
    When it comes to how the Greeks dealt with the notion of an irrational number the term "history" is a little bit misleading I think - lack of reliable sources. There's evidence that once we get to Socrates (or at least Plato - I'm thinking of early passages in the Theatetus here) that there's no question whether they are numbers or not, just how to handle them as numbers. I've not read the work you refer to - what sources does Heller-Roazen have for indicating that the Greeks refused to regard the irrationals as numbers at all?
  • Math and Motive
    But again, do you want to claim that the connection is arbitrary? Do you have reason to believe that nature plays by different structural rules despite the evidence to the contrary?
    To the first question, what connection are you asking me about being arbitrary? The connection between physical models and an independently existing nature? Well, I'd have to be a realist even to accept the terms of that question. Or the connection between physical models and the purported reality they claim to represent? This is not an arbitrary connection in the sense that the models are there precisely to model what the modellers take the models to be models of. The issue that got this whole post running is when models come up against a problem, what is to be done and are we free to choose arbitrarily what is to be done? The SM comes up against the issue that it doesn't account for gravity, and yet gravity is something that manifests in the physical world that SM purports to model. In come "gravitons" as a proposal to extend the SM to take into account gravity. The arbitrariness of choice might make more sense concerning a question about whether we persist with the SM + graviton approach or if we look for different proposals. I'm not involved in the world of theoretical physics so I don't know if there are genuine alternatives being actively pursued or not, but I don't see why there couldn't be. In any case, the importance of symmetry to modelling nature seems to be something about which we do not have a choice - symmetry is at work in the General Theory - so there at least I agree with you.
  • Math and Motive
    Group theory itself not arbitrary: given the Group axioms and classical laws of inference, all sorts of theorems follow of logical necessity - I used to be able to prove a few of them myself at one time. So no, Group theory is not arbitrary. As for the axioms of the theory and the status of the rules of inference - that might be a different issue.
    How do we account for the usefulness of pure mathematics in describing and predicting reality? That's a different question, but I'm certainly not convinced that the answer to it requires either mathematical realism or physical realism.
  • Math and Motive
    It would depend what you mean. The standard model has its problems and its alternatives/adaptations, and the existence of "gravitons" is contentious (some even think it is a conceptual confusion to model gravity as a force at all). So if you mean by "convinced" "convinced that the Standard Model describes reality as it is in itself independently of our means of modelling it", then no I am not convinced. What would convince me of that? Well, something that had already convinced me that metaphysical realism is true would be a pre-requisite. But perhaps you think there is a way in which one can be convinced of the Standard Model without having to be a metaphysical realist? In which case, let me know and I might have a different answer to your question.
  • A few metaphysical replies
    Really? You are reduced to counting spelling mistakes? Metaphysicsnow has revealed his Scottish roots.:wink:
    I've been away a while and just skim read through the various posts. Aren't we still waiting for your explicit statement of premises, one by one, giving us a valid argument that takes us from those premises to the conclusion that reincarnation happens? I asked you for that right at the beginning of this thread and you've waffled on quite a lot it seems, but logically valid arguments seem impossible to dig out of your words.
  • Math and Motive
    So maths and physics are talking about the same universal mechanism.
    Maths deals with symmetries in Group theory, and those mathematical tools are used by physicists and other scientists to model reality and this or that part of reality. Does that tell us anything about reality, or does it just tell us about the way we currently model that reality?
  • Math and Motive
    Not to mention the fact that it allows Derrida and Russell to be considered as part of the same subject.
    Depends who you ask - I know the Cambridge faculty of philosophy (at least at one time) would have rejected any claim to the effect that Derrida was a philosopher. Russell, of course, was truly venerated as one. But then, that's probably grist to your mill :wink:
  • Germany receives Marx statue from China. Why?
    I have already said the labor theory of value is "fictitious."
    I think LD Sanders was responding to the wrong person, and had me in mind when he threw the "theory of value is false" in your face. Having said that, I'd rather pick this up with you than LD Sanders, as I stand a good chance of getting a meaningful discussion of the idea.
    I'm willing to admit that the labour theory of value cannot be proven in an a priori way, and that Marx shouldn't have wasted his time trying to do this - and let's be honest he spends hardly any time at all trying to prove it - a paragraph or so at the beginning of Capital. However, it seems pivotal to his economic theory, particularly since it underpins his explanation for the law of the tendential fall in the rate of profit, which is the bell that tolls the ultimate demise of capitalism. These days, Marxists economists who still hold to the labour theory of value regard it as an empirical theory that commodities exchange at prices which are determined by the role of labour in the production process, and there are some statistical studies that support this. So, whilst Marx might make sense without a metaphysically loaded labour theory of value (where exchange value is regarded as some mystical stuff) can it make sense without a labour theory of value of the kind that regards prices as determined by the function of labour in the production process? I believe some Marxists have tried to push this kind of line, but it never really made sense to me.
  • The Principle of Sufficient Reason.

    I agree to some extent, the PSR, whatever it is, is not a fact of the garden variety scientific or non-scientific kind. However, if the following two statements are true
    1) Any true proposition could constitute an explanandum.
    2) All explananda have explanans
    and if 2) is an acceptable formulation of the PSR, we either invite an infinite explanatory regress, invite a regress that can be terminated only by fiat and thus in violation of the PSR, or we need to come up with some explanatory circle that leads us satisfactorily back to the PSR. Since (2) is pretty much a matter of definition, it means we need to reject (1) to escape the regress/circularity and insist that somehow or other the PSR is not the kind of true proposition that could constitute an explanandum. This is presumably the approach of those who would look on it as an axiom.
  • A few metaphysical replies
    I have to agree with @MetaphysicsNow - looks to me like you are confounding a few things (such as facts and propositions) that should be kept apart - at least to begin with. Let's take a look at this claim for instance:

    Among that infinity of complex systems of inter-referring if-then facts, there’s inevitably one that’s about events and relations that are those of your experience.

    There’s no reason to believe that your experience is other than that.

    Now the only sensible way to interpret "if-then fact" on the basis of what you have said in your introduction is that an "if-then fact" is just an unfortunately chosen name for a conditional proposition. That being so, the complex systems of inter-referring if-then facts you talk about here are just "bundles" of propositions with logical connections between each other. My experience is certainlyother than that because my experience is not a proposition at all, either simple or compound. There are true propositions about my experience, and there are also true conditional propositions in which propositions concerning my experience feature as antecedents and as consequents. My experience, whatever else it is, is something that is capable of making such propositions true.
  • A few metaphysical replies
    Presumably the idea is that there is a sound argument with metaphysical premises (i.e. premises which concern existence) which are acceptable to all and that has as for its conclusion that reincarnation happens.
    So, @Michael Ossipoff, over to you to lay out the premises one by one so we can subject them to scrutiny.
  • Numerus “Numerans-Numeratus”
    If I had said...

    "is nothing"

    therefore

    "is zero"

    yes then it would have been a non sequitur....
    — Conway

    Wrong yet again. A non-sequitur is a proposition/statement that purports to, but in fact does not, follow from previously given propositions/statements. By extension the term also refers to an entire argument in which the concusion is a non-sequitur. "is nothing" and "is zero" are neither of them propositions or statements, so neither of them, nor the combination of them, can be a non-sequitur. For examples of real non-sequiturs I refer you to a number of your previous posts in this thread.
  • Numerus “Numerans-Numeratus”
    I may have two cups before me, both empty...but of varying size. Therefore varying amounts of zero. — Conway

    I can't believe MetaphysicsNow let this one go - he is being too gentle with you. This is another non-sequitur - you are clearly really fond of them. If I have two empty cups of different sizes I don't have two cups containing varying amounts of zero, I simply have two cups with different capacities for containing actual stuff. In actual fact, those cups are of course filled with different volumes of air, but go on, I'll let you put them into a perfect vacuum, I still just have two empty cups with different capactities for holding liquids, not different capacities actually containing amounts of zero.

    Emmenthal is a cheese with holes in it - but I cannot eat the cheese and leave the holes behind for someone else to enjoy later.
  • How and why does one go about believing unfalsifiable claims?
    One might, on the basis of this fact, conclude something similar to what the logical positivists did and claim that all unfalsifiable claims are at best meaningless. The trouble with this position is that it appears self-refuting. The claim that all unfalsifiable claims are meaningless cannot itself be falsified. Thus, all the logical positivist has done is demonstrated the incoherence of his own position.
    Read the last sentence, looks to me like you are making a claim about the logical positivists being self-refuting on the basis that they equate falsifiability with meaningfulness.
    1) Logical positivists were verificationists, not falsificationalists.
    2) Sophisticated logical positivists made room in their theories for non-verifiable claims to play a role in discourse, and hence have meaning.
    3) Karl Popper introduced the "falsifiability" vocabularly, but not to demarcate meangingfulness from non-meaningfulness, but to demarcate the scientific from the non-scientific.
  • How and why does one go about believing unfalsifiable claims?
    What kind of idealism are you talking about and who falsified it? Your example begs the question against at least one form of idealism that I'm aware of (the empirical idealism of Berkeley) rather than prove that it is false.
  • Mental illness, physical illness, self-control
    Now you've lost me completely, since many of your own posts use modal terms like "possibile" "possibly" "might have" etc - in a way that would suggest you had some conception of what possibility is in some cases, which would mean that at least for you at least possibility is intelligible. Two examples:
    But physical illness is not necessarily neurological though. That is the problem, there are many possibly factors, diet, hormones, etc.
    There are many instances where John might decide to vote "Yes", but actually vote "No". He might change his mind, as you mentioned, he might forget, as we already talked about, or he might just make a mistake in marking the ballot. Notice that even a mistaken action is a very real possibility and must be accounted for.

    But if you think that possibility is completely unintelligible, then given that what is unintelligible cannot be meaningfully talked about, you seem to be commiting yourself to have been talking nonsense whenever you discuss modality.

    I'll have to leave you and MetaphysicsNow to fight it out, I'm afraid, and find a more classically coherent thread to follow.
  • How and why does one go about believing unfalsifiable claims?
    As a third option, one might wish to pull the rug out from under the original claim that only non-scientific claims are unfalsifiable. The fact that a scientific hypothesis can be confirmed through experiment need not entail that the hypothesis is true. On the other hand, perhaps this isn't required for assent to the alleged truth of the hypothesis, which would be merely provisional. Unfalsifiable claims might similarly be accepted provisionally, in the absence of their being shown to be fallacious.

    I'm not clear what this third option is. If by "pulling the rug out from under" you mean something like "negate", the negation of the claim "Only non-scientific claims are unfalsifiable" would be "there exists at least one scientific claim that is unfalsifiable". But what would a scientific claim that is unfalsifiable look like? An example might help me understand. A scientific hypothesis that has been confirmed is not an unfalsifiable claim, since it remains possible that some future experiment will disconfirm it. Perhaps "pull the rug out from under" means something different?

    The logical positivists, by the way, had a more sophisticated notion of meaning than just simply "if it's not falsifiable it's not meaningful" - I'm not a logical positivist by any means, but it seems a little unfair to condemn a whole philosophical movement on the basis of a strawman.
  • Numerus “Numerans-Numeratus”
    Let "F" stand for "is nothing".
    Let "G" stand for "is zero"
    Then statement 1 becomes, in first order predicate logic:
    1) -Ǝx(Fx)
    Statement 2 becomes
    2) Ǝx(Gx & -Fx)

    MetaphysicsNow is 100% correct in his claim against you that in this argument 2) is a non-sequitur. There are no logical rules of inference that allow you to infer 2) merely from 1), hence by definition it is a non-sequitur. If you want your claims about the philosophical implications/entailments of your mathematical symbolism to be taken seriously, you should really try to avoid basic errors in formal logic of this kind.

    To help you out here, if you want to render the formal argument logically consistent (so that 2) is NOT a non-sequitur) you have to introduce the premise:
    1a) Ǝx(Gx)
    1), 1a) therefor 2) is a logically consistent argument, now let's consider its soundness a little

    In the interpretation we are giving to the symbols, 1a) states that there is something which is zero. Now the issues about semantic interpretation of the symbolism come into play (and we thus move beyond merely formal logic and mathematical symbols and into the realm of metaphysics). The claim that there is something which is zero sounds perilously close to saying "there is something which is nothing" and I think MetaphysicsNow is homing in on the intuition that this is paradoxical. You might want to say that mathematics needs to quantify over an object to which it assigns all the properties that zero has, but even in saying that you are venturing outside of mere mathematics and into metaphysics, since the question arises "what properties does zero have?". You might then say that it is the additive identity, but then one reply is that this is to define zero in terms of the positive integers and their relations to one another, and one does not need to metaphysically "reify" an object to perform that role, we need only to reify the positive integers and their relations to one another. Furthermore, even if MetaphysicsNow could be forced into a corner and admit that one has to reify one object to which the term "zero" or "0" refers, that's where the metaphysical commitments concerning the use of the term "zero" stop. Your mathematical symbolism might end up being consistent - I cannot comment on that - and it might quantify over several different types of zero, but then I guess MetaphysicsNow will just say, "too bad for your symbolism, it multiplies entities beyond necessity".
  • Help with logic exam:
    Incidently, I'd be interested to know what your prof told you regarding that last exercise we were struggling with - I only gave it a few moments of thought, admittedly, but even on the technique I suggested (negating the sequent as an assumption and aiming to find a contradiction) it looked like being a very long and tortuous proof. Did your prof have anything to say about finding an easier proof?
  • Mental illness, physical illness, self-control
    Possibility is something which is infinite, and an infinite thing is unintelligible.

    There seems to be some element of talking past each other here between you and MetaphysicsNow. Perhaps you are right that because there are infinite possibilities we (as finite beings) cannot survey all of them at once. However, I think MetaphysicsNow is suggesting that this is to some extent irrelevant because it does not impact our abilities to entertain any specific possibility. "Possibility" is ambiguous between your two usages. For you it appears to be the sum of all possibilities. For MetaphysicsNow it appears to be just that which defines something as being a member of that group of infinite things. MetaphysicsNow is perfectly correct that possibility is intelligible if he means by "possibility" what I believe he means. You might be right that possibility is unintelligible if you mean by that that we cannot survey all possibilities at the same time. Metaphysicsnow is using the term "possibility" in one of its perhaps more usual senses, but that doesn't mean that you cannot use the term in your sense. However, in order to avoid misunderstanding, I suggest that where it is important to make the distinction between your two meanings, that you use distinct terms. So that neither one of you calls "foul" I suggest that MetaphysicsNow use the phrase "the notion of possibility" instead of "possibility" and that you use "the sum of all possibilities" instead of "possibility". You can both still use the word "possibility" to say things like "it is a possibility that I will win the lottery tomorrow, since I bought a ticket" or "there are possibilities no one has thought about yet" without risk of ambiguity, but where the claims start becoming metaphysically significant, it would help clarify both positions and all your arguments if you use the terminology I suggest. Would you both agree with that?
  • Help with logic exam:
    Congratulations, that's great news - the work you put in paid off. Now you can get on with enjoying some real philosophy ;-)
  • Help with logic exam:
    Good luck with the exam, by the way.
  • Help with logic exam:
    Hi
    If you mean that from 1) above you first use the universal elimination rule to derive
    3) Ey(Tya->Az~(Taz))
    and then use it again on 3) to get
    Ey(Tya ->~(Taa))
    Then that is fine, you have just used the universal elimination rule twice.
    Generally speaking all you have to remember when applying universal elimination is that all of the occurrences of the variable bound by the quantifier must be replaced by the same name - in universal elimination you are free to choose the name you use to replace the bound variable, and that means you are free to choose a name you have already used. So if you have AxAyAz(......) you can replace all the x's with a all the y's with b and all the z's with a if it helps you prove what you are aiming to prove.
  • Help with logic exam:
    The negation in 2) above has widest scope of all the logical operators, so
    -(a≠b & (Fa & Fb)) is not equivalent to
    a=b & (Fa & Fb)
    but to
    (a=b V -(Fa & Fb))

    a=b & (Fa & Fb) would be inferrable from (-(a≠b) &(Fa & Fb)) where the negation has scope only over the statement a≠b.

    As for the technique to follow for the exercise, it is basically saying that given the two premises, the sequent follows. In this kind of circumstance it is often a good technique to make the assumption that the sequent is false and then aim to draw out a contradiction. So, I would try beginning your proof with
    1) Ex(Fx) Premise
    2) -(Ex)(Ey)(x≠y & (Fx & Fy)) Premise
    3) -(Ex)(Ay)(x=y <->Fy) Assumption

    and seeing how you can progress from there to get a contradiction which will allow you to discharge assumption (3) by negation and thus infer by double negation the sequent (Ex)(Ay)(x=y <->Fy). Bear in mind that the negation in 2) and 3) has widest scope and covers the entire statement in both cases, not just the identity statements.

    Concerning your general remarks about proving biconditionals, certainly the way to do that is to prove both the conditionals, but in this case I'm not sure that would be the simplest way to go about the proof.

    Remember, though, that in this case you are aiming to prove syntactic entailment, so you can only use the rules you've been given, so (unless you've been given them as a rule to use) you cannot just help yourself to my "short cuts" concerning conversion of negated quantifiers. Those short cuts are useful when one is dealing with proofs of semantic entailment (double turnstiles "|=", not single turnstiles "|-") where one is allowed to argue less formally in terms of interpretations.
  • Help with logic exam:
    First of all you don't ever substitute quantifiers like " -(Ex)", you substitute only the variables bound by quantifiers (in this case "x"), so you don't ever substitute negations as such - you cannot negate an object, you can only negate sentences concerning objects.

    Secondly, if you have a quantified sentence in first order predicate logic which is negated, you should transform the statement into an appropriately non-negative quantified sentence where the negation covers the statements over which the quantifiers have scope. As per my previous post, these are the basic rules to remember for transferring negated quantifications over statements into quantifications over negated statements:
    -Ex(Fx) = Ax-(Fx)
    -Ax(Fx) = Ex-(Fx)

    So when you have :
    -(Ex)(Ey)(x≠y & (Fx & Fy))
    the negation at the beginning covers the entire sentence, and so is equivalent to
    AxAy-(x≠y & (Fx & Fy))
    If you now substitute x with a you get
    Ay-(a≠y & (Fa & Fy))
    Notice that the negation stays where it is, covering the entire compound statement over which the quantifiers have scope, and does not attach itself individually to the substitutions that are made.

    I hope that clarifies things a little.
  • Help with logic exam:
    It's basically to do with the negation of quantifiers. If I say everything is red , Ax(Rx), then the negation of that claim is equivalent to saying that there is at least one thing which is not red, i.e. Ex-(Rx). If I say that at least one thing is red, Ex(Rx), the negation of that claim is equivalent to saying that everything is not red, i.e. Ax-(Rx). So, negating the whole of a quantified statement is essentially the same as switching the quantifier type and negating the proposition governed by the quantifier (this can be proved in first order predicate logic, but I won't bore you with that). The same principle works when quantifiers are compounded, so that the negation of AxAy(Rxy) becomes ExEy-(Rxy), the negation of ExEy(Rxy) becomes AxAy-(Rxy), the negation of ExAy(Rxy) becomes AyEx-(Rxy) and the negation of AxEy(Rxy) becomes ExAy-(Rxy). Suppose for instance that R is the relation 'is uglier than'. AxAy(Rxy) says that everyone is uglier than everyone else, and its negation is simply that there are at least two people such that one of them is not uglier than the other. ExAy(Rxy) states that there is at least one person that is uglier than everyone else - i.e. there is at least one contender for the title "ugliest person of the year". The negation states there is no such person, which is equivalent to saying that everyone is such that we can find someone who is uglier than they are - basically, no matter who you choose, they are better looking than at least someone else. Formalised, then, -(ExAy(Rxy)) is equivalent to AxEy-(Rxy). Now, it doesn't matter whether we replace Rxy by some more complicated compound sentence (although it becomes more difficult to find "real world" examples). So, if we replace Rxy by ((Rxy & -Ryx) -> (Rxx<->Ryy)), we will still be able to infer from -(ExAy((Rxy & -Ryx) -> (Rxx<->Ryy))) to AyEx-((Rxy & -Ryx) -> (Rxx<->Ryy)). You know already from basic first order calculus that -(A->B) is logically equivalent to A & -B. So, replacing A with (Rxy & -Ryx) and B with (Rxx<->Ryy), we end up with the conclusion that -(ExAy((Rxy & -Ryx) -> (Rxx<->Ryy))) is logically equivalent to AyEx((Rxy & -Ryx) & -(Rxx<->Ryy)). Now the claim |≠(Ex)(Ay)((Rxy & ~Ryx) --> (Rxx <-> Ryy) is essentially saying that there is at least one interpretation in which (Ex)(Ay)((Rxy & ~Ryx) --> (Rxx <-> Ryy)) comes out false, i.e. where -((Ex)(Ay)((Rxy & ~Ryx) --> (Rxx <-> Ryy))) is true for at least one interpretation, which, by the foregoing reasoning is equivalent to saying that there is an interpretation in which AyEx((Rxy & -Ryx) & -(Rxx<->Ryy)) is true. The challenge is to find the simplest interpretation which does the job (and apparently it is an interpretation with four objects).
    Hope that helps.
  • Help with logic exam:
    Happy to (try to) help:smile:
  • Mental illness, physical illness, self-control
    2) Giving explanations of type (4) has as a consequence the removal of all agency from all human behaviour. — MetaphysicsNow


    This is the main premise I disagree with in your argument.

    Sorry to interrupt here, but MetaphysicsNow gave an argument for that premise in terms of consistency of reasoning:
    If opening and closing a door 10 times, qua bodily motion, has its ultimate explanation in terms of (4) when the rationalization in (3) is initially given, why not also in cases (1) and (2)? After all, in all three cases precisely the same bodily motions are occuring, and if those bodily motions have their ultimate explanation in terms of neural/muscular occurences for case (3), then the same neural/muscular occurences will also be available for explaining the bodily motions in (2) and (1).
    I suppose you disagree with that argument, but it's not clear to me on what grounds you do not believe it to be sound.
  • Does QM, definitively affirm the concept of a 'free will'?
    (We are veering a bit off-topic...)
    Agreed. I will reread the paper and perhaps start a new thread. Whilst the author certain says that his position should be distinguished from what he refers to as "crude operationalism" (which may be a straw man in any case) just saying that his position should be so distinguished doesn't make it distinguishable.
  • Does QM, definitively affirm the concept of a 'free will'?
    Point taken. I was just wondering whether you thought that these latest approaches to QM actually had metaphysical consequences that took instrumentalism off the table.
  • Does QM, definitively affirm the concept of a 'free will'?
    Quantum Mechanics Unscrambled.
    Just read it. Overly complicated - one suspects that at some points he is just showing off that he's technically proficient with QM formalism and complex analysis - and it is almost entirely devoid of any metaphysics, so I wouldn't bother wasting your time, unless you are interested in the technical idea that QM theory can be reshaped as a new kind of probability theory. At a couple of points he touches on the idea that what these "novel" approaches are proposing is just some kind of instrumentalism/operationalism, but he does nothing to actually argue that they should not be taken in precisely that kind of way.
  • Does QM, definitively affirm the concept of a 'free will'?
    @apokrisis
    Some say it is going back to CI. But for me, that is ontic in that it puts the observer - or at least, points of view - in the spotlight as the critical factor.
    So for you the "shut up and calculate" approach of some of those who support CI is no longer an option under these new "Bayseian" interpretations?