Templeton prizewinner Alvin Plantinga


Now you see that I was not joking. But I think it is useful to clarify the definition. The definition of a “possible world” is a “state of affairs, which is different from our existing world is some aspect”. That is IT. There is nothing else. If you have a problem with it, there is no reason to continue. But I hope not. It is a very simple concept.

I don’t, because it is irrelevant. We are NOT concerned with cosmology or cosmogony. The thought experiment starts with our existing world - which is physically possible, since it exists. We can postulate a different world, for example, where there is an oak tree, instead of a pine tree at a certain place. Or another world where Hitler was a stillborn, and as such there would be no Holocaust. How could that happen, is none of my concern. It is just another “possible” world. Not just logically, but physically possible. And whatever is physically possible, it is also metaphysically possible - adding again - whatever that might be.

Causal antecedents are only applicable for events within a world, but inapplicable for the “world” itself. That would assume that the world “needs” an outside creator, and that is what you might wish to establish. It is a logical fallacy to include your “wished for” result into the argument itself, it is called “begging the question”.

The proof I presented starts with the existing world. We apply certain transformations, being mindful that the transformations should not “introduce” a logical impossibility. Eliminating parts of the existing world cannot introduce logical contradictions. Removing all the galaxies, except the Milky Way would make a “simpler world”, but still possible. Then eliminating all the solar systems, except ours, would make the world even simpler. This kind of gradual elimination process always yields in another, simpler “state of affairs”. Finally, when we are at a very simple world, we eliminate everything except an “up” quark - in one case, and eliminate everything except a “down” quark in the other case, hereby creating two possible worlds, without any overlap. And that takes care of the “necessary being”.

This process does not care about “God”. It simply gets rid of the concept of necessary being. You are welcome to worship the God of the Bible. I read some time ago: “Everyone believed in God, until some philosophers tried to prove his existence”. You cannot. Be happy with your faith, and leave reason alone. As Luther was fond of saying: “Reason must be trampled underfoot” and “Reason must be made the handmaiden of faith” - and he said that when he was a well-respected Catholic theologian.


Not everything has a maximum. There may be great beings, greater beings, but how do you know that there is a maximally great being?
Take for example, the set of positive integers. Given a number, say 1000, you can find a greater one, say 1001, but there is no maximally greatest integer.


I have no problem with you starting with the physical world and GIVEN that world as an assumption propose small changes to it. The reason this kind of scenario is both physically and metaphysically possible is because it assumes the real world with its physics and metaphysics intact.

Here you begin to go off track. Given the physics and metaphysics of the real world, any “possible” world, relying upon those physics and metaphysics to hold, would simply assume them. What you want to do, is simply abandon everything about the real world – all of the physical and metaphysical laws that apply, in order to propose whatever you imagine as “physically possible.” A world with a solitary ‘up’ quark has NO physics or metaphysics to order it and undergird it. As such it isn’t a possible WORLD at all.

It “takes care” of absolutely nothing. You may as well propose a “possible” world where the logical law of non-contradiction is inapplicable to “take care” of and disprove the necessity of the law of non-contradiction in this universe and in all others. That is pure quarky nonsense.



“This process” not only “does not care about God,” it also does not care about logic and reality. And it uses that flagrant lack of concern to cross the line between reason and irrationality to become pure sophism and nonsense.

If you can use “possible worlds” which have no basis in reality to disprove what could very well be necessary about reality, then you have thrown reason and the rules of logic out the window. If I can imagine a world where a single necessary wombat exists a se without need for any food or water and functions essentially as the necessary creator deity of that world, I haven’t thereby proved wombats can be God or necessary existents in this world or any other. Yet that is essentially your argument. You can imagine a single ‘up’ quark in a world with no physical or metaphysical laws and THAT is submitted by you to prove that no world nor this real universe requires a necessary Creator?

Well, let me think on that for a nanosecond… :thinking:

It is still nonsense. You may as well use the ‘up’ quark world to “PROVE” that the laws of physics and rules of logic need not apply in the real world either, on the grounds that you can imagine your ‘up’ quark world without them.

And you suppose you have proven Plantinga incorrect by this flight of fancy into a world of illogic?

I can imagine, even picture, this little ‘up’ holder…

That does not mean it is possible.


And what would be the definition of “small” changes? That sounds suspiciously like accepting “micro evolution”, but denying “macro evolution” - as if there would be any difference. How many “small” steps make up one “giant” leap? Precisely, if you would? And, of course the distinction of “micro” vs. “macro” evolution is just a dumb attempt to deny reality by some creationists.

It does not have to be intact. We can start with the existing physics, and make modifications to it. Right now the Avogadro number is 6.0221409e+23. It could be changed to something else, and the world would still be possible. The law of non-contradiction does NOT hold in the world of subatomic particles. The “double slit diffraction” experiment proves that one electron can pass through two slits at the same time and create a diffraction pattern with itself. We can start to replace every elementary particle with its symmetrical “anti” part, and the world still stays possible.

You mean the physics would be different. Just like the physics of the singularity is different. So what? And you still did not come clean about that pesky “metaphysical” thingy. You really should learn that “metaphysics” is simply navel-gazing.

Thought experiments are like that. As long as there is no logically impossible assumption in them, they are a valid foundation to explore the “what if”-s. Einstein and others loved the thought experiments. Read some here: http://www.businessinsider.com/5-of-albert-einsteins-thought-experiments-that-revolutionized-science-2016-7 . The only requirement for a “possible world” is that it cannot contain logical contradictions, nothing else.

Yes, indeed. I love Escher’s beautiful pictures, too. It is not a possible world, because it contains a logically impossible state of affairs. :slight_smile:


Actually, the argument from gradation that Aquinas gives (fourth way) is not that there is a “maximum” necessarily, but the standard for the quality of “greatness” must exist and that standard would be the “source” or derivative origin from which qualitatively great things would obtain the quality of their greatness with regard to that quality.

Ergo, for something to be more or less hot, you need the quality of “hotness” or heat. For something to be more or less true, the truth must exist somehow. To have more or less courageous individuals, the quality of courage must exist. So what is courage and where is it to be sought?

Lesser or greater goodness requires the standard of goodness. Lesser or greater wisdom requires the standard of wisdom. Likewise, to have lesser or greater numbers, you obviously need numbers.

So to have lesser or greater beings, you require, first of all, beings or being. And to have lesser or greater greatness would require a standard of greatness by which “greatness” would be gauged or measured. So what, precisely, would that standard of greatness be?

This is where greatness and being meld together into maximally great being – where does the idea of greatness comes from and how does greatness conjoin with the actuality of existing or being?

Plantinga’s argument is far more subtle than its critics admit. There is far more involved in it than the superficial critiques of it take into consideration.


So let’s see…

…you want your cake:

…and eat it, too:

The law of non-contradiction “does NOT hold in the world of subatomic particles,” such as your solitary ‘up’ quark one but yet SHOULD hold in possible worlds because possible worlds should NOT contain “a logically impossible state of affairs.”

What is the standard for “logically impossible” if not the law of non-contradiction? Think: married bachelors, square circles, possibly necessary, logically impossible possible worlds, etc., etc.

Let’s remind ourselves what the law of non-contradiction holds: Something cannot be both true and not true at the same time with respect to the same context.

So, within the context of a possible world, your solitary ‘up’ quark does not need to abide by the law of non-contradiction, and yet Escher’s picture is not a logical possibility within the context of any possible world because it contains a logically impossible state of affairs – i.e., because it contravenes the law of non-contradiction.

So the law of non-contradiction, itself, can be both true and untrue at the same time with respect to the same context, possible worlds?

Possible worlds CAN, then, BOTH contain logical contradictions (when single ‘up’ quarks are involved) but MUST NOT contain them (when Escher drawings are involved) depending upon your druthers.

You see no problem here?

To put the frosting on the cake, you want to use a world which contravenes the law of non-contradiction (your ‘up’ quark one) as your “proof” that Plantinga is incorrect in his logic. :thinking:


The physics (I mean the REAL physics not some "meta-physics) is different for some systems. But from that it does not follow that the single-particle world is somehow logically impossible. You accepted that the starting point, our actual world is “possible”. We apply the transformation of successive removals of this world. None of the removals lead to a logically impossible state of affairs. Yet, you declare - without any justification - that the final step (the single particle world) all of a sudden became impossible. Somewhere within this procedure there is a step, where W(n) is till possible, but W(n+1) is impossible. Where is this magic number of “n”?

Where is the logical contradiction in the single quark world? Actually the Escher drawing only depict an optical illusion, and no one argues that optical illusions are real… well, I take it back. Escher’s illusions can be built with LEGO blocks, and from ONE specific angle they “look like” real. It is really hilarious that you use optical illusions as examples against reality.


A single quark does not a world make.


I suppose it stopped being “a world” when the laws of physics that require dependencies of particles on other particles suddenly got dropped from your “possible” world. It isn’t clear within any laws of physics that a single “up” quark is sustainable as a self-existing entity.

Besides, you aren’t doing actual physics, you are into theoretical and quantum physics which are notoriously abstracted from any real world requirements and where not even the law of non-contradiction appears to hold. That, in itself, should be telling.


How many is needed? Two, three? One million? How many?

You “suppose”? That is not particularly convincing. But relax. The existence of each particle is not contingent upon the existence of others. There is no “law” which would assume that an electron (for example) requires the existence of a proton, or a neutron, or vice versa.

Well, well… running out of arguments, I see. Theoretical and quantum physics are part of this world. :slight_smile: So I will give you another solution. Let’s take our existing world, and replace every particle with a corresponding “anti”-particle. Electrons with positrons, protons with anti-protons, neutrons with anti-neutrons and so on. There is no intersection at all, and the existence of the world is not contingent on the electric charge of the particles. The world is symmetrical in this respect. Chew on that one. I am wondering what kind of nonsense will you come up now. Better realize, this particular “proof” for God does not work. Get back to your faith, and leave reason alone. You are not well equipped to use it.


How does that prove that the law of non-contradiction does not hold? the path integral formulation of the problem shows that the interference pattern is produced by the differences in the relative phases along the different paths and there is no contradiction.


The laws of physics are all about relationships. Even basic quantum physics require other particles. Take one of the central principles of quantum physics, quantum entanglement: multiple particles are linked in such a way that the measurement of any one particle’s quantum state is what determines the possible quantum state or wave function of other particles.

And here’s the kicker…

Though this interpretation does mean that the quantum state of every particle in the universe affects the wavefunction of every other particle, it does so in a way that is only mathematical. There is really no sort of experiment which could ever — even in principle — discover the effect in one place showing up in another location.
Source: https://www.thoughtco.com/what-is-quantum-entanglement-2699355

Meaning, the “interpretation” is purely mathematical and theoretical. There is NO WAY – “even in principle” – to show this in the real world.


Not that “hilarious” actually, because it is an illusion of a structure, a structure that could not be built because it is only an optical illusion. Kind of like your argument from “up” quarks possible world is a logical illusion (sophistry) that cannot stand in the real world.


Right. Ok, so this argument works in the modal system called S5, which is fairly commonly accepted among modern philosophers, at least within the analytic tradition (which is the most common one in the u.s./england).

The idea of a “possible world” really should be construed as widely as you can. Anything that doesn’t entail a logical contradiction is a possible world. “Possibly X” means X exists in at least one possible world. “Necessarily X” means X exists in all possible worlds. “Possibly necessarily X” and “necessarily possibly X” are not equivalent. “Possibly necessarily X” means that X is necessary in at least one possible world. Under most modal systems, anything that is necessary in one possible world is necessary in all of them, so X is necessary. “Necessarily possibly X” means in all worlds, there is one world where X is possible, so X is possible. This works under S5’s accessibility relation, which includes reflexivity and transitivity and symmetry. There are other versions of modal logic where world a is possible relative to world b, and world c is possible according to world b, but world c is not possible relative to world a. Those aren’t commonly accepted for modal logic however.

There are also impossible worlds with things that we can conceive of but that aren’t actually possible. I don’t think anyone’s written a logic of these that’s coherent and accepted.

The most common counter is to question the first premise - whether there is in fact a maximally great being and that existence is a necessary attribute of a maximally great being.

Also, modal logic is a real pain to do anything complex in natural language. This would be much easier with a diagram or something. Trying to do it in words is kind of like trying to do geometric proofs while only using words.


It is difficult to grasp how something (X) could be necessary in only one or some possible worlds since any contingencies within that world that would make X only necessary there would be contingencies that would themselves be necessary only in those worlds. Yet how could contingencies be necessary only in some possible worlds without a dependency upon some other necessary condition, which would then itself only be necessary in those worlds?

Ergo, “Under most modal systems, anything that is necessary in one possible world is necessary in all of them.”


That utterance is a nonsensical proposition. An entity cannot be “necessary” in one “possible world”. What Plantinga was doing here is playing fast and loose with the ambiguity concerning “necessary” and “possible”. Necessary in one possible world is an invalid construct. :slight_smile:

And you are right: the concept of “greatness” is also undefined, and undefinable. The author (originally Anselm) simple chose a few “good sounding” attributes, and declared that THOSE are the ones he would like to use when defining “greatness”. Unfortunately there are not enough “street urchins” among the philosophers, who would stand up and declare “the emperor has no clothes”!!


They’re perfectly sensible propositions, although the technical language produces phrases that are odd in english. It’s kind of like, if you do math, you can get an answer that is negative negative one, which we all know is equivalent to (positive) one. So, similarly, necessary in one possible world reduces down to necessary, period. In plainer language, it would reduce down to something like “God is either necessary or impossible. If he is possible, then he is necessary.
So, since God is possible, God is necessary.” Remember that in philosophy, all necessary things are possible things, although not all possible things are necessary things. It doesn’t have the same implication that natural language often has that if something is possible to be it’s also possible not to be.

Trust me, there are plenty of philosophers who would argue against that if it were incoherent. Philosophers are rarely shy about calling things illogical or incoherent, and the majority of analytic philosophers are atheists.


Plantinga mixed the everyday English with the philosophical usage. Something is “necessary” in the philosophical jargon if it exists in ALL possible worlds. It is nonsensical to say that an entity is “necessary” in ONE possible world - as long as one uses the philosophical meaning. It could be meaningful in the everyday usage, by stipulating that there are some circumstances which make the nonexistence of this entity logically impossible. But if an entity is logically necessary in one particular world, it does not follow that it is also logically necessary in another possible world, much less in ALL of them.

I know that many philosophers disagree on the meaning of many words. That makes their personal opinion irrelevant. After all philosophy (and religion) is nothing more than a collection of opinions - which cannot be tested against the reality. If they could be tested, they would become science.

Maybe you remember the old saying:

  1. Those who know it, do it.
  2. Those who cannot do it, teach it.
  3. Those cannot even teach it, manage it.
  4. Those who are unable to manage it, regulate it.
  5. And finally, those who are unable to regulate it, philosophize about it.


Keep in mind that this is an english translation of a formal argument. So in this setting (the one where possibility and necessity are referring to the S5 modal system, although B is actually the minimal one needed), there’s pretty strict definitions. Specifically, under the S5 system, all possible worlds are reflexive, transitive, and symmetrical. “Necessity” here also refers strictly to ontological necessity, as opposed to other sorts of necessity (e.g. necessity under the laws of nature). In plain english the problem is that necessity refers to a bunch of different philosophical concepts.

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