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Switch to Forum Live View Hatcher's Proof of the Existence of God
3 years ago  ::  Oct 02, 2011 - 3:04AM #31
Jiwe
Posts: 492

Oct 1, 2011 -- 6:35AM, Lilwabbit wrote:


Hi there James,


Thanks for your valuable comment.


Oct 1, 2011 -- 5:31AM, Jiwe wrote:


It seems pretty risky of Hatcher to treat causality in terms of the material conditional. That's making a lot of assumptions. The conditional is an extensional connective, for one. But it's not obvious that causality is. For instance while "A --> A" is a tautology it's not clear that "A causes itself" is.


James




Logician Chris Taylor from the University of Sussex offers an in-depth analysis on the various types of causality, as well as the different types of causality inherent in formal logic itself (in other words causalities between propositions).


www.informatics.sussex.ac.uk/users/chris...

Taylor discusses, among other things, the notion of "nomic dependence" according to which material implication represents in fact one class of causalities between propositions where a causal dependency exists.


Material implication is a causal relation between two atomic propositions in which the truth-value of one atomic proposition depends (note: causality) on the truth-value of the other proposition or alternatively on a third proposition (depending on its three different true valuations 1-1, 0-0 and 0-1).


Since material implication is true with the valuation 1-1, it can be aptly applied to describe causality between phenomena, just as Hatcher does. This is the case simply because in an ontological scheme (like Hatcher's), both cause and effect, are real/true. Material implication is particularly apt for describing total causality (as Hatcher does) where a phenomenon A is either a sufficient reason for its own existence (A → A) or then some other phenomenon B is a sufficient reason for its existence (B → A). The applicability is precise and perfect since the material implication with valuation 1-1 corresponds accurately with an ontological state-of-play where the condition/reason for "the existence of a certain phenomenon" (in logical terms, the material condition of a "true proposition") is "the existence of a certain phenomenon", whether the same or another phenomenon (in logical terms "another true proposition"). Hence the causality implied by the principle of sufficient reason is quite accurately represented by the operator "material implication" or "→".


With kind regards,


LilWabbit





Thanks for the link - and the summary. The dissertation looks really interesting. This is a comment to what you said though. Material implication is also true with the valuation 0-0 but I doubt anyone would be tempted to say that the moon being made of green cheese is the cause of Lincoln killing Kennedy. And if you restrict it to both antecedent and consequent being true you still get the problem of contraposition (the absence of the effect causing the absence of the cause).


James

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3 years ago  ::  Oct 02, 2011 - 4:28AM #32
Lilwabbit
Posts: 2,905

G'day James,


Oct 2, 2011 -- 3:04AM, Jiwe wrote:


Thanks for the link - and the summary. The dissertation looks really interesting. This is a comment to what you said though. Material implication is also true with the valuation 0-0 but I doubt anyone would be tempted to say that the moon being made of green cheese is the cause of Lincoln killing Kennedy. And if you restrict it to both antecedent and consequent being true you still get the problem of contraposition (the absence of the effect causing the absence of the cause).


James




Thanks for the comment. In Hatcher's schematic, the contraposition would indeed be true as well. However, in the contrapositive you offered the terms "cause" and "effect" are somewhat vague and thereby misleading. For the purposes of the present proof, we must employ Hatcher's definition of total causality: a sufficient reason for a phenomenon to exist (which is actually a reformulation of Leibniz's definition). The precise formulation of the contrapositive would then go as follows: The absence of the consequent is a sufficient reason for the absence of the antecedent (or ~A → ~B when the positive is B → A). I would say Hatcher's contraposition is pretty neat and sensible and therefore holds its ground.


Here is a more formalistic formulation of Hatcher's principle of sufficient reason:


(∀x) [(x → x) v (y → x)]


where x is any real entity or collection of real entities, y is any real entity other than x, and  → is a sufficient reason for an entity to exist.


By the way, it is an enjoyment to engage in a rational exchange with you.


With kind regards,


LilWabbit

"All things have I willed for you, and you too, for your own sake."
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3 years ago  ::  Oct 02, 2011 - 5:50AM #33
JCarlin
Posts: 6,818

I have noticed here and elsewhere on the board that theists seem to be somehow ashamed of faith as a basis for God and since they have no scientific basis, they resort to logic to prove or justify their God.  Amusing but unnecessary as the faith is intrinsic to the logic.  As with Pascal's wager, why not go straight to faith and skip the logical middle person.  

J'Carlin
If the shoe doesn't fit, don't cram your foot in it and complain.
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3 years ago  ::  Oct 02, 2011 - 6:07AM #34
Lilwabbit
Posts: 2,905

Howdy Jcarlin,


Oct 2, 2011 -- 5:50AM, JCarlin wrote:


Amusing but unnecessary as the faith is intrinsic to the logic.




Another empty claim. Please demonstrate how Hatcher's faith is intrinsic to the logic? Otherwise let James speak on behalf of the atheists here as he actually seems to understand what Hatcher is saying.


With kind regards,


LilWabbit

"All things have I willed for you, and you too, for your own sake."
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3 years ago  ::  Oct 02, 2011 - 6:33AM #35
Jiwe
Posts: 492

Oct 2, 2011 -- 4:28AM, Lilwabbit wrote:


G'day James,


Oct 2, 2011 -- 3:04AM, Jiwe wrote:


Thanks for the link - and the summary. The dissertation looks really interesting. This is a comment to what you said though. Material implication is also true with the valuation 0-0 but I doubt anyone would be tempted to say that the moon being made of green cheese is the cause of Lincoln killing Kennedy. And if you restrict it to both antecedent and consequent being true you still get the problem of contraposition (the absence of the effect causing the absence of the cause).


James




Thanks for the comment. In Hatcher's schematic, the contraposition would indeed be true as well. However, in the contrapositive you offered the terms "cause" and "effect" are somewhat vague and thereby misleading. For the purposes of the present proof, we must employ Hatcher's definition of total causality: a sufficient reason for a phenomenon to exist (which is actually a reformulation of Leibniz's definition). The precise formulation of the contrapositive would then go as follows: The absence of the consequent is a sufficient reason for the absence of the antecedent (or ~A → ~B when the positive is B → A). I would say Hatcher's contraposition is pretty neat and sensible and therefore holds its ground.


Here is a more formalistic formulation of Hatcher's principle of sufficient reason:


(∀x) [(x → x) v (y → x)]


where x is any real entity or collection of real entities, y is any real entity other than x, and  → is a sufficient reason for an entity to exist.


By the way, it is an enjoyment to engage in a rational exchange with you.


With kind regards,


LilWabbit





Thanks for that reply LW! I agree with you that Hatcher is committed to the contrapositive holding as well, and my "objection" is as you point out based on intuition and therefore necessarily vague. But I want to turn that around and say that it's leading rather than misleading. What I mean by that is that just like a theory of probability should be based on some natural/intuitive desiderata for scientific and plausible reasoning, so should a theory of causation. And one desideratum I see is that causal and logical connections be held apart. If they are lumped together our intuitions about plausible reasoning soon become implausible. While a causal connection implies that there exists a logical one, the converse isn't (or shouldn't!) be true. For instance, I take it (as a Bayesian!) that knowledge of later events can affect the probability of earlier ones, but that this doesn't extend to causation.


 


I never liked that whole thing about interpreting an antecedent of a material conditional as a sufficient reason/condition for the consequent and in turn the consequent as a necessary reason/condition for the antecedent. One reason is given by my cheese/Kennedy example above. It just strikes me as weird. The connection in the material conditional seems too "thin" or too formal or something to do that kind of substantial work. There just doesn't seem to be any kind of conceptual connection between material implication and causation at all, and an attempt to mold them together seems very contrived. And formally it seems like any falsehood is a sufficient reason for any truth at all! It seems to me that you need some non-classical logic to do the work here. Things become more intuitive when you take into account the meanings as well as the truth-values of the antecedent and consequent, but then you're doing intensional logic.


 


James

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3 years ago  ::  Oct 02, 2011 - 7:34AM #36
Eudaimonist
Posts: 2,036

"Hatcher's Proof" doesn't work for me in part because I view causality in a different way.


In my view, any entity A at time t (aside from any cosmic egg at t=0, which may be an uncaused source of causes, though not IMV a deity), is not only explained by the causal influence of external entities B, C, and D (etc) at time t-1, but also by A at time t-1A at t-1 is of course not identical with A at t, but in many cases it seems absurd to consider it something external to A at t.


For instance, I might not be identical to myself at the time just before I started writing this post, but I think it absurd to think that this past entity is external to myself causally.  It seems to me that this entity is very intimately related to my current existence, certainly more than anything external to that entity, and it may also be that I am still self-caused in the sense that nothing need explain the continued existence of matter/energy in my body except for the existence of my body, even if the form of that body has changed.


The "Proof" also gets wonky at the end with the "refinement principle".  I find that completely unintuitive and uncompelling.


Thanks for posting the proof, in any case.  It was good to read something new to my experience.


 


eudaimonia,


Mark

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3 years ago  ::  Oct 02, 2011 - 7:50AM #37
Lilwabbit
Posts: 2,905

Hi there James and Mark,


I'm gonna hit the nearby woods with my son now to play big bear and small bear. Albeit having a busy remainder of the Sunday and a somewhat hectic week ahead, I will come back to your points shortly, insha'allah. It's nice to have you guys around...


With kind regards,


LilWabbit

"All things have I willed for you, and you too, for your own sake."
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3 years ago  ::  Oct 02, 2011 - 10:20AM #38
Lilwabbit
Posts: 2,905

Hi Mark and good evening from Helsinki,


I agree that all the remainder (last five paragraphs) of my citation of Hatcher (concerning the "refinement principle") is on a tad shakier ground. Neither is it technically a part of Hatcher's intended proof. The refinement reasoning is no longer based on a closed system of clearly defined premises and logical principles as the more formalistic logical proofs are expected to be.


Oct 2, 2011 -- 7:34AM, Eudaimonist wrote:


"Hatcher's Proof" doesn't work for me in part because I view causality in a different way.



The question rather is whether you can demonstrate anything seriously flawed about Hatcher's use of causality. One of the beautiful things about first-order logic is that it is rarely a matter of personal predilection ("what works for me doesn't work for you", etc.)


Oct 2, 2011 -- 7:34AM, Eudaimonist wrote:

In my view, any entity A at time t (aside from any cosmic egg at t=0, which may be an uncaused source of causes, though not IMV a deity), is not only explained by the causal influence of external entities B, C, and D (etc) at time t-1, but also by A at time t-1A at t-1 is of course not identical with A at t, but in many cases it seems absurd to consider it something external to A at t.


For instance, I might not be identical to myself at the time just before I started writing this post, but I think it absurd to think that this past entity is external to myself causally.  It seems to me that this entity is very intimately related to my current existence, certainly more than anything external to that entity, and it may also be that I am still self-caused in the sense that nothing need explain the continued existence of matter/energy in my body except for the existence of my body, even if the form of that body has changed.



Mark, I fail to see the connection of the foregoing (otherwise fine) reasoning to Hatcher's proof. At least it does not invalidate it in any way (which it appears was not your intention either). However, it appears as if you have mistaken Hatcher's causality to imply "externality" when he employs the term "otherness". This, however, is not the case if you read carefully. For instance, in Hatcher's schematic, for V (the collection of all existing entities) to be "other-caused" simply means that V contains an entity G that is the cause of itself as well as the rest of V. Since G ≠ V, G is therefore "other" than V.


Moreover, you are presenting far more vague terms than Hatcher for a proper logical examination. You also seem to be constraining your terms of causality a priori by an additional predicate of time, rendering your approach far more vulnerable to various kinds of additional criticism. One of the strengths of Hatcher's proof is that it need not appeal to time, space, laws of physics, physical constants, metaphysical postulations, or any other "ontological" variables except for the simple assumption that "something exists." The property of time may well be one of many existing phenomena within V without any imperative to formally include the predicate in the proof of God itself.


With kind regards,


LilWabbit

"All things have I willed for you, and you too, for your own sake."
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3 years ago  ::  Oct 02, 2011 - 10:34AM #39
JCarlin
Posts: 6,818

Oct 2, 2011 -- 6:07AM, Lilwabbit wrote:

Otherwise let James speak on behalf of the atheists here as he actually seems to understand what Hatcher is saying.


With kind regards,


LilWabbit


Happy to do so.  Convoluted arguments to get from I to believe hold no interest for me. 

J'Carlin
If the shoe doesn't fit, don't cram your foot in it and complain.
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3 years ago  ::  Oct 02, 2011 - 11:03AM #40
Lilwabbit
Posts: 2,905

Oct 2, 2011 -- 6:33AM, Jiwe wrote:


Thanks for that reply LW! I agree with you that Hatcher is committed to the contrapositive holding as well, and my "objection" is as you point out based on intuition and therefore necessarily vague. But I want to turn that around and say that it's leading rather than misleading. What I mean by that is that just like a theory of probability should be based on some natural/intuitive desiderata for scientific and plausible reasoning, so should a theory of causation. And one desideratum I see is that causal and logical connections be held apart.



I agree that generally a logical connection cannot directly translate into an ontological one. However, I would remind that logical causality is a logical connection. In fact, in his definitions Hatcher does not explicitly identify the causality relation with the material implication. I have made the association which, in fact, may or may not be feasible. If Hatcher indeed is applying the material implication, he is employing the material implication in its strictest possible sense. In this slideshow presentation for a university audience, Hatcher explains how logical causality is empirically well-grounded (starting from page 35):


Generically, causality is a logical relation, but this relation has an empirical counterpart in the physical world: If A → B holds, then it can never occur that A holds without B holding. "Never A without B" is thus a necessary (but not sufficient) condition for A → B to hold. This is like semidecidability. If ever we observe an instance of A without B, then we know certainly that A does not cause B. But in the absence of such a clear counterexample, we can draw no conclusion either way. However, the empirical requirement that "never A without B" is clearly enough to ground empirically the causality relationship. The point is that causal links are inferred (logically), and not observed, as Hume already indicated. Causality is thus a legitimate principle of minimalist metaphysics. We now proceed with certain definitions related to the causality relationship...


With kind regards,


LilWabbit

"All things have I willed for you, and you too, for your own sake."
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