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reggieM
Guest
We could exclude the term concept and the logic is the same.
There is a difference between finite worlds and infinite worlds.
That which caused the difference between the two exists in all possible worlds.
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There is a difference between finite worlds and infinite worlds.
That which caused the difference between the two exists in all possible worlds.
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Darryl_B
Guest
My friend, you must truly be the first person ever to quote Francis Bacon to me. It is a very thought provoking reasoning, though I do wonder how much he had contact with the atheist who did not have the inclination to destroy the thought of God.
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Vera_Ljuba
Guest
Infinite in what respect?
I gave you a mathematical proof that a “necessary” being does not exist.
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Perplexity
Guest
The Gods do not exist “in” possible worlds, but rather cause them to be. Their necessity is thus not captured by contemporary modal semantics – which concern beings, and not those who are beyond being. To illustrate, consider that something could exist in every possible world, but only because it is caused to do so. The “existence” of the Gods is better captured by something like “aseity” than “necessity.”
Be that as it may, I’ve got a number of a priori arguments for the Gods. Here’s one I used to play around with, probably more relevant than others because most of the folks here are Catholic:
D1. Epistemic potentiality =df. the potentiality of something, as far as we know.
D2. Epistemic actuality =df. the actuality of something, as far as we know.
D3. Epistemic possibility =df. the possibility of something, as far as we know.
Now, full disclosure, I think the Scholastics got thangs awfully wrong, and so I wouldn’t talk about the Gods in terms of “actuality” in a more formal setting. But, getting an atheist to admit there’s a pure actuality is significant enough that I’d play along in order to move on to the real stuff.
Be that as it may, I’ve got a number of a priori arguments for the Gods. Here’s one I used to play around with, probably more relevant than others because most of the folks here are Catholic:
D1. Epistemic potentiality =df. the potentiality of something, as far as we know.
D2. Epistemic actuality =df. the actuality of something, as far as we know.
D3. Epistemic possibility =df. the possibility of something, as far as we know.
- Whatever is epistemically possible is either epistemically potential, or epistemically actual.
- The existence of a pure actuality is epistemically possible.
- Therefore, the existence of a pure actuality is either epistemically potential, or epistemically actual. (1, 2 M.P.)
- But, the existence of a pure actuality is not epistemically potential.
- Therefore, the existence of a pure actuality is epistemically actual. (3, 4 Disj)
Now, full disclosure, I think the Scholastics got thangs awfully wrong, and so I wouldn’t talk about the Gods in terms of “actuality” in a more formal setting. But, getting an atheist to admit there’s a pure actuality is significant enough that I’d play along in order to move on to the real stuff.
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ferdgoodfellow
Guest
Then I must confess I don know nuttin bout possible worlds.
My naive understanding of PW’s is to begin imagining a world truth table with brazillions upon brazillions of statements describing the actual world. E.g. Donald Trump is president of the US is true. Hillary is president is false. There are penguins is true. There are unicorns is false. Melania’s inaugural outfit is powder blue is true, and so on. A possible world involves taking any one or more of the brazillions upon brazillions of statements and changing the truth value. The result will be deemed a “possible world” as long as the world truth table contains only statements which are logically possible. A truth table which assigns T to “There are round squares” cannot be a possible world. So the cardinal rule for constructing a possible world is “Don’t put into your World Truth Table any statements that are nonsense.”
Now if we posit the possibility of necessary existence, we are asking, in possible worlds lingo, whether it is possible for there to be an X such that “There is an X” is true in every possible world. Not knowing anything about X, we quite naturally think that we can assign a truth value of false to that particular statement in our World Truth Table. For all we know, it could be T or F. If there is nothing nonsensical about assigning F to this statement, we’ve got a possible world.
But what if we were to know more about X. What if X is defined as TWNGCBT? Assuming there is nothing contradictory in the idea of TWNGCBT, and following a chain of reasoning which would make it illogical to assign a truth value of F to “TWNGCBT exists,” wouldn’t we have to say this statement has to be true in every possible world? If we say “TWNGCBT” is false, we are violating our cardinal rule and this World Truth Table could not be a possible world.
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Vera_Ljuba
Guest
You overcomplicate it.
There is no need for truth tables and such. As you said, we start with our current existing world. And then change it in some respect. As long as there is no logically incoherent or contradictory in the changes, the result is still a possible world. The change does not HAVE to be physically possible.
For example to remove the middle entity from the “grandfather - father - child” state of affairs, does not make it impossible. It is just a different world, with different physical characteristics. You can add, subtract or change anything - except “4 sided triangles” or “married bachelors”, or “two sided Mobius strips”.
Specifically, as I gave the constructive method in one of the posts above, you can arrive at the two worlds, one with a single electron and the other one with a single neutron. Since they have nothing in common, that takes care of the “necessary being”.
There is one basic problem with your analysis. Propositions do not exist in every possible world. Propositions ABOUT the possible worlds exist in THIS world, because we make those propositions. And, of course you made another error in your analysis when you said: “What if X is defined as TWNGCBT?” You cannot define something INTO existence.
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ferdgoodfellow
Guest
Good morning Vera, and happy 4th of July, wherever in the actual world you exist! I live and move and have my being in North Dakota where it is too dry for fireworks. But no matter, I don’t have to go to work today!
Up to this point I haven’t defined anything into existence.*
Most likely. Along with Winnie the Pooh, I am a Bear of Very Little Brain (BOVLB).
OK.
But I get hung up here, and I am not sure if I can explain why. Granted, in our possible world constructing we are just dealing with logical possibilities. That means that we can spin all kinds scenarios, as long as we don’t produce anything nonsensical. Even though your single electron world and single neutron world are logically possible, I don’t think you can then add that they have nothing in common. That probably is nonsensical. At the very least they are both hypothetical beings in a possible world. There has to be some abstract residuum they have in common.
Regarding the charge of defining something into existence, I plead not guilty. I can come up with any definition of an entity I want. So I can define God, as Anselm and Hartshorne do, as that than which nothing greater can be thought (TTWNGBT). Assuming there aren’t contradictions lurking in the concept, God, thusly defined, is possible. *
Up to this point I haven’t defined anything into existence.*
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ferdgoodfellow
Guest
Although I can offer nothing really clinching yet, I severely doubt that necessary existence is impossible. I don’t think your disproof of necessary existence works because it is impossible to construct two possible worlds with nothing in common.
Coming at it from another direction, I think we agree, along with Parmenides, that something or other has to exist. It is certainly possible that a candidate for necessary existence is a single entity.
So, given the first premise that TTWNGCBT (perfection) is possible, and given the second premise that that which cannot fail to exist (necessary existence) is possible, the argument proceeds inexorably to its conclusion.
Coming at it from another direction, I think we agree, along with Parmenides, that something or other has to exist. It is certainly possible that a candidate for necessary existence is a single entity.
So, given the first premise that TTWNGCBT (perfection) is possible, and given the second premise that that which cannot fail to exist (necessary existence) is possible, the argument proceeds inexorably to its conclusion.
- Perfection is possible
- Necessary existence is possible.
- It is greater to exist necessarily than contingently.
- Assume that Perfection exists contingently.
- But this creates a contradiction, because contingent existence is an imperfection.
- Therefore Perfection exists necessarily.
- Therefore Perfection exists.
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Vera_Ljuba
Guest
And a Happy 4th to you, too. It does not matter, where we live, it is the 4th of July.
(Unless it is on the other side of the international date-line) Happy birthday to all the Yankee-doodle babies!I did not “invent” the concept of “possible worlds”, it is a common principle in philosophy. I will return to your phrase “nonsensical” at the end of this post.
You could easily say (and truthfully, too) that they are both “something”. That is in every possible world there is “something”, and therefore “something” is a “necessary being”. You could say (equally correctly) that they are both composed of matter, therefore “matter” is the “necessary being”. If you could demonstrate the existence of a “non-matter based but ontological entity”, like an angel or a demon, then we could postulate a possible world consisting of exactly one angel, and another one consisting of exactly one demon.
But that is not what we mean. Any being (necessary being) is some actual entity, which exists ontologically. Ideas, concepts are not ontological entities, they are abstractions. And abstractions only exist in some world where there are sufficiently advanced entities that are able to conceptualize.
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Vera_Ljuba
Guest
How can you deny the constructive proof I presented?
This is just a long-winded version of Anselm’s idea that “actual existence” is grater than “possible existence”. And you “sprinkled” it with the word: “perfection”. But “perfection” is JUST ANOTHER concept - and meaningless at that in an abstract form.
In other words you try to treat “existence” as just another attribute, which may or may not be present, and assert (without any arguments) that existence is greater than non-existence.
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Perplexity
Guest
I think this exchange is suffering from some ambiguities concerning modal logic:
The difference between metaphysical and logical possibility has to do with not violating different kinds of laws. To keep things simple, look at propositions instead of objects, events, states of affairs or whatever: a proposition p is logically possible just in case p’s truth does not imply or entail a violation of any law of logic; p is metaphysically possible just in case p’s truth does not imply or entail a violation of any law of metaphysics.
While the laws of logic are relatively uncontroversial (outside the dusty corners of logician’s offices), one might wonder what laws of metaphysics are supposed to be. Here are some examples for illustration: nothing comes from nothing, nothing causes itself to exist, every cause precedes its effect, etc. Logical possibility concerns what is consistent with the laws of logic, metaphysical possibility concerns what could be ‘real’ – and not just ‘physically’.
A few more problems I’m seeing:
The difference between metaphysical and logical possibility has to do with not violating different kinds of laws. To keep things simple, look at propositions instead of objects, events, states of affairs or whatever: a proposition p is logically possible just in case p’s truth does not imply or entail a violation of any law of logic; p is metaphysically possible just in case p’s truth does not imply or entail a violation of any law of metaphysics.
While the laws of logic are relatively uncontroversial (outside the dusty corners of logician’s offices), one might wonder what laws of metaphysics are supposed to be. Here are some examples for illustration: nothing comes from nothing, nothing causes itself to exist, every cause precedes its effect, etc. Logical possibility concerns what is consistent with the laws of logic, metaphysical possibility concerns what could be ‘real’ – and not just ‘physically’.
A few more problems I’m seeing:
- It’s a fallacy to infer metaphysical possibility from logical possibility, and I’ve never seen anyone argue without begging the question that there is a metaphysically empty world, or two or more metaphysically possible worlds with nothing in common.
- There is a difference between existing “in” a possible world, and being true “at” a possible world. The problem with saying that a God exists “in” a possible world is that it strips that God of ultimacy and makes her a constituent of something more fundamental. Classically minded theists can’t acquiesce to that. But, they can say it is true “at” a possible world that their God exists.
- One only needs to examine every possible world in order to know if any one thing is true at all of them if the modal axiom S5 is not true. But, why think that? Moreover, theists don’t even need to wade through the technicalities of S5 debates because, shelving talk of necessary existence, they can appeal to the Barcan formula.
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Vera_Ljuba
Guest
I am not sure I understand what you say. A “proposition is simply a sentence (or several ones)”. Every proposition is “physically possible”, even the one “this proposition is false” or “the crunchy color of the middle-c is loud” or “tomorrow it will rain at this physical location”. They may not resolve to a “true” or “false” value, but they exist. They may be self-contradictory, undecidable or downright nonsensical, but they are still propositions.
The examples you presented are simply assumptions. They are not “laws”. Very plausible assumptions, of course, but still nothing more than assumptions. And that is what “metaphysics” happen to be. Speculations and assumptions about the reality.
What is physically possible can be found out by studying the reality - science - not by speculations.
Now, in the thought experiment I presented by systematically shrinking the existing (therefore physically possible) world until we arrive at some kind of “minimal world” (one elementary particle). Since this process can arrive (at least) at two different worlds, without intersection, it is proven that “necessary” existence is an empty proposition.
By the way, what Plantinga attempted to do with “if it is possible that it is possibly necessarily true that X, then X is necessarily true” is simply incorrect. (Let’s substitute X with “there are purple-pink polka dotted elephants”) Nothing can be “necessarily” true by declaration. It can only be correct if one examines ALL the possible worlds (which is impossible). However, the inverse is simple. All one has to do is find one counter example, which I provided in the thought experiment.
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Perplexity
Guest
Well, a proposition is what sentences express: it’s their content. With this distinction in hand, it can be seen that the sentences “this proposition is false” and “the crunchy color of the middle-c is loud” do not express propositions: there’s nothing about the former to be false – it’s contentless – and the latter is incoherent. But, it’s true, we can say that propositions qua objects are possible. However, the possibility of their existence bears no interesting consequences for their possible truth – which is what we’re after here.
“Assumption” is not contrary to “law” as the two belong to different categories – the former to epistemology and the latter to ontology. But, I think you’re of the mind that the reasons for believing in metaphysical laws are not particularly impressive, or at least the ones that I mentioned. I guess I just disagree: the arguments on their behalf strike me as conclusive, often taking the logical form of reductio ad absurdum.
I don’t think science is, strictly speaking, the only or even the best means of finding out about physical possibility; but, I wholeheartedly agree that mere speculation is not up to the task.
A classical understanding of a God precludes any deity from existing “in” a possible world because it holds her to be the cause of all things other than herself, and existing in a possible world would make her a constituent of something more fundamental, and thus not the cause of everything other than herself. So, even if you could systematically shrink the existing world until you arrived at two worlds without intersection, it would imply nothing about the existence of a God on a classical understanding. But, even if the classical understanding is incorrect, you’re only able to shrink the existing world to two worlds without intersection because you do not count a necessary being as a constituent of the existing world. Your argument takes atheism for granted, and thus provides theists with no reason to change their mind.
I think Plantinga would say it’s true that if it’s possible that it’s possibly necessarily true that there are purple-pink polka dotted elephants, then it is necessarily true that there are such elephants. That’s just a hypothetical statement. Problem is, it’s not possible that such a thing is possibly necessarily true. Why? Because it’s not part of what it means to be such an elephant that it exists – even possibly. One of the things atheist philosophers such as Graham Oppy have staunchly pointed out is that conceivability =/= possibility.
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Vera_Ljuba
Guest
We try to communicate. To do that we can only use language. Languages are composed of sentences. A simple sentence like “ouch!”, when you stab your toe, is not a proposition. But “ouch, this was painful” is a proposition. A sentence can resolve to “true”, “false”, “undecidable”, “self-refuting” or “incoherent”. There is no reason to declare that some of these are not propositions.
The “laws” of metaphysics you mentioned are “assumptions”. Of all the different parts of philosophy, the “highest” one is epistemology. If there is no way to find out if a proposition is true or not, there is no reason to present that proposition.
Hold it. There is not one word about God (classical or otherwise) as of now. All we do is examine the concept of “possible world” and “necessary existence”. A possible world is simply a state of affairs, which may or may not contain someone called a God. (This God could be the “source” of everything else in that possible world.) Necessary existence means that there is an ontological entity, which is present in all the possible worlds. The “world” is not limited to any specific state of affairs. The physical world is obviously “possible” since we experience it.
Every attempt to try to prove God’s existence MUST start with a fully atheistic point. It would be a fallacy to include the “hoped for” final result (therefore God exists or therefore there is a “necessary being”) into the premises of the argument. Necessary existence must be proved, not assumed.
The phrase “possibly necessary” is sheer nonsense. Something is either possible or not. Something is either necessary or not. If something would be “necessary”, it would also be “possible”. Not everything is possible if it can be conceived. I can conceive of a 4-sided triangle, but it cannot exist. I can also conceive of a triangle, where the sum of the internal angles does not equal 180 degrees - and such a triangle is possible.
Only logically contradictory states of affairs are impossible.
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Perplexity
Guest
You’ll be hard pressed to find philosophers of language who think the relevant sentences express propositions. “Incoherence”, in particular, is not a property propositions can have, since they are by definition truth-apt, and there’s nothing about meaningless sentences to be true or false.
I understand you feel that way, but you’ll have to do some fancy foot work to convince those of us who have dedicated hundreds upon hundreds of hours to considering metaphysical issues that they just rest on “assumptions.”
Your argument against necessary beings is circular because it has to presuppose that there is no necessary being in order to shrink the world into two non-overlapping worlds. But, it’s also irrelevant to this thread unless it is directed against a non-classical understanding of a God.
There is a difference between not assuming that a God exists and assuming that a God does not exist. The former is what is required of a sound argument for a God, but it is not atheistic.
Here again I find you arguing against well established philosophical principles. Your debate is not with the theists here, but with the logicians who forged systems of modal logic: “possibly necessary” is widely recognized. All it means is that from the perspective of some possible world, W1, there is some entity x that is necessary.
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ferdgoodfellow
Guest
Vera and Perplexity,
Back from my pyrotechnically-deprived celebration of the 4th. It was actually quite nice.
I am afraid you have both left me in the dust. I will try and catch up.
I am still trying to articulate why I don’t find Vera’s constructive disproof of necessary existence compelling. Vera, of course, is in good company. Kant, Russell and many others have held that no existential propositions are necessarily true. They are always, always contingent.
Perplexity, maybe you are onto something when you said:
Back from my pyrotechnically-deprived celebration of the 4th. It was actually quite nice.
I am afraid you have both left me in the dust. I will try and catch up.
I am still trying to articulate why I don’t find Vera’s constructive disproof of necessary existence compelling. Vera, of course, is in good company. Kant, Russell and many others have held that no existential propositions are necessarily true. They are always, always contingent.
Perplexity, maybe you are onto something when you said:
That seems right. Necessary existence is ruled out from the get-go in Vera’s PW analysis. It is therefore quite easy to construct two worlds without interesection.
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Vera_Ljuba
Guest
Not “ruled out”. It is treated as a hypothesis, which needs to be examined.
Just remember the famous thought experiment about faster-than-light motion. It is explicitly assumed that faster-than-light travel is possible, but the thought experiment shows that faster-than-light travel is impossible.
(The thought experiment is this: a spaceship has a light source at the back wall of the ship, and a mirror on the front wall. We have two observers, one inside the ship, and one outside. If the spaceship moves faster than light, then for the outside observer the light from the lamp will never reach the mirror, since the ship moves faster than the light. For the inside observer the ship is stationary (special relativity), so the light will be reflected from the mirror.)
I did the same. I assume that some necessary being exists (by the way why does it have to be only one?), then conducted the thought experiment of “shrinking” the existing world and arrived at the conclusion that there cannot be a necessary being.
Your objections are frighteningly similar to one of the “defenses” of God’s benevolence. Some believers assert that the “seemingly evil actions” that God performs or allows are actually beneficial. When they are asked, how can benevolence be reconciled with these events, the answer is: “but you already ruled out God’s benevolence, so it is easy to show that these events are not benevolent. You are guilty of circular reasoning”. That is what Perplexity did.
Come on. Get serious. The circular reasoning is exactly the reverse. You cannot assume God’s benevolence and then declare reality “a misunderstanding”, since it is contradicted by the hypothesis. For every hypothesis the process is the same. We create a “null-hypothesis”, stipulating that the hypothesis is correct. Then we conduct experiments, and every successful experiment lends credence to the null-hypothesis. However, just one negative outcome refutes the null-hypothesis. It is the ultimate “no-no” to discard the negative outcome on the ground that it is contradicted by the null-hypothesis. The hypothesis cannot be used as a tool to discard an “unpleasant” result, and keep only the supporting results.
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Vera_Ljuba
Guest
Now that is what I call “fancy footwork”.
That is not a correct representation. The assumed “necessary existence” means that “X” (and possibly “Y”, also “Z”) exists in all possible worlds.
As for the “widely recognized”, I recall the emperor’s new clothes, which was “widely” recognized and admired… until that street urchin came along.
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Perplexity
Guest
It’s pretty straightforwardNow that is what I call “fancy footwork”.
I do not assume that aliens exist, but I do not therefore assume that they don’t.But, in possible worlds semantics we can only speak from the perspective of one possible world or another. This has to do with “accessibility relations”, or which worlds are accessible from another. Logicians and philosophers have discovered different relations that hold between worlds: reflexive, symmetric, transitive etc. If you think that to be necessary in any world is to be necessary in every world (such that the accessibility relation is Euclidean), then you unwittingly subscribe to the S5 system of normal modal logic, and the debate is over.
You say that you assumed
But, this is clearly not the case. Had you assumed that a necessary being exists, you would have shrunk a world with a necessary being in it and so could not have arrived at two non-overlapping worlds. Sorry man, maybe you have a good argument against necessary beings elsewhere, but this one is sunk.
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Vera_Ljuba
Guest
The error here is that you try to use your hypothesis as part of the proving process. The assumed existence of the “necessarily existing object” is supposed to be the end result of the proving process, not part of it.
There are two proving methods: the “direct proof” and the “indirect proof”. The “direct proof” would examine all the possible worlds, and find that object “X” is actually present in each and every one of them. That you cannot do.
Are you familiar with the concept of “indirect proof”? Here is an example:
Theorem: there exist two positive integers “p” and “q” the ratio of which is exactly square root of two and they do not have a common divisor. Formally
p/q = sqrt(2)
From here we deduce that
p^2 / q^2 = 2
From that it follows that
p^2 = 2* q^2
which means that “p^2” is an even number, and therefore “p” is an even number.
p = 2 * x and as such
p^2 = 4 * x^2
so 4 * x^2 = 2 * q^2
so q^2 = 2* x^2
as such q^2 is an even number, and therefore q is an even number.
As such p is an even number, and q is also an even number, and therefore they have a common divisor, and therefore it is false that there are two positive integers, the ratio of which is exactly 2. So the theorem is false.
Exactly the same process was applied to your necessary existence. The “reduction of the world” process is the equivalent of the reduction process of “divisible by two”.
For anyone, who understands this basic mathematics, nothing else needs to be said. For the rest…
why should I care?But, just for the fun of it: “WHAT (exactly) is that ‘necessary’ being that cannot be removed during the reduction process”???
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