Saturday, July 17, 2010

Fine-Tuned for Pantheism?

In his book, Immortality Defended, John Leslie argues (in his Chapter 5) that the characteristics of our world can serve as evidence for his model of pantheism. Recall that Leslie thinks our world is one of many called forth from possibility into actuality by the creative power of the Good. These worlds can also be characterized as those worthy of being thought about by a divine mind.

This position can be thought of as intermediate between a non-theistic concrete modal realism (David Lewis’ model), where all metaphysically possible worlds exist, and classical theistic models where a personal deity creates our world alone (although some modern thinkers allow for a personal God to create many worlds, too.)

Causal Orderliness

Leslie argues against Lewis that if all worlds exist, then many more chaotic and disorderly worlds exist than orderly ones. And he says there would be many which may be orderly for a time but where people living in them “suddenly turned into blackberry jam.” At every instant, innumerable things can go wrong. If all these worlds exist, then chances are we would inhabit one of them. So our expectation of a continued orderly existence implies accepting that these disorderly worlds don’t exist. The pantheistic idea would be that the world’s causal orderliness makes it worth contemplating for the divine mind inside which it has its being.

Cosmic Fine-Tuning

The argument that the parameters of physical law are fine-tuned for life has become a familiar one, and Leslie thinks it has some force. The idea that there are many universes, however, dilutes the force of the argument: if there are innumerable universes of all sorts, then we shouldn’t be surprised to find ourselves in a universe conducive to life, since otherwise we wouldn’t be here to observe it (observational selection rather than divine selection).
But Leslie sees things about the universe which remain mysterious even considering the observational selection effect. First, he finds it mysterious that force strengths and particle masses are tuned for many different needed purposes at the same time. His example is the electro-magnetic force, which is tuned to provide for many seemingly distinct phenomena that all must manifest themselves for life to result. This suggests that the multiverse has to be one where all possible laws of physics needed to be tried out (not just parameters on the forces we know). Maybe there are regions of reality with no recognizable laws? Leslie thinks this makes the multiverse idea too foreign and strange to be reasonable. He also says he thinks it strange to contemplate that something as fundamental as relativity theory might only exist in a local region of reality. So, he thinks the observational selection effect can explain why we see our world among others which may have somewhat different parameters, but it has a harder time accounting for the existence of laws themselves.

Pantheism vs. Theism

Leslie thinks fine-tuning provides some support for the existence of God, but on the other hand he also thinks there certainly can be many worlds with different characteristics, including many lifeless worlds. He thinks traditional theism is inconsistent with the creation of these other worlds – why would God bother when his focus is supposedly on we humans? To pantheists, in contrast, he says these many orderly, if lifeless, universes may very well be seen as worthy of contemplation by the divine mind.

Now, putting aside the question of other worlds, many are skeptical that the deity of classical theism would create our world at all, given its flaws. In the same vein, one might ask a pantheist to address why the creative power of the Good would call forth our often miserable world? Leslie thinks that while there may indeed be innumerable worlds better than ours, there’s enough good about it that it could be worthy of creation as well.

Comments

I’ve not been impressed in the past with fine-tuning arguments, and I have thought the simplest explanation for the existence of our radically contingent world was that all metaphysical possibilities do exist. Still, as I discussed in this prior post, I am disturbed by the vision of so many worse-than-our-world scenarios granted concrete being in this modal realist model.
And I’m reminded that even in this model, its normal to accept some limits on what exists: logical necessities and perhaps mathematical ones. Why not some further restrictions? And if one is a realist about value, perhaps there are necessities about value which govern or shape what is concrete? It’s worth thinking about.

21 comments:

Allen said...

As to the blackberry jam point, didn't David Lewis address a similar issue in his book, "On the Plurality of Worlds", pg. 119 in the version that Google Books has online.

I won't type the passage in, but here is a summary of it that I found. As one would expect, his solution relies on infinities:

"Forrest argues that there is a sense in which worlds at which the inductive reasoning of observers fails predominate across the possible worlds, even though the cardinality of the infinitely many deceptive worlds is the same as the cardinality of infinitely many non-deceptive worlds. More particularly, the deceptive worlds might be ones at which Occam's Razor fails such that they include all manner of epi-phenomenal rubbish that does not interact with observers or things observed. As the ways in which otherwise qualitatively identical worlds can include such epi-phenomenal rubbish infinitely outnumber the one way that an otherwise qualitatively identical world might lack any such rubbish, and it is the same for every equivalent class of worlds qualitatively identical save for the inclusion of epi-phenomenal rubbish or its absence, it appears that it is infinitely probable that Occam's Razor fails at the actual world. Lewis responds to this argument from his modal realism to the failure of an important theoretical heuristic with the stance that, if the cardinality of the rubbishy and clean worlds is the same then you can partition equivalence classes any way you want them. They could even be partitioned so that it comes out that the clean worlds predominate and it appears infinitely probable that Occam's Razor correctly predicts the sparseness of existing things at the actual world."

Steve said...

That's right, thanks. I don't like his response - it always seems too easy to invoke these infinities, but I need to work on this issue.

Allen said...

What's wrong with easy?

Is that your only discomfort with the idea? Too easy?

I think most of the puzzles and conundrums of philosophy are largely a result of refusing to accept the obvious answer.

Epistemologically, conscious experience is fundamental.

Why would it not also be fundamental ontologically?

So what we know are our conscious observations. And we try to build foundations under those observations to adequately support them.

But just placing something beneath them does not a foundation make.

In fact, I think it’s rather clear that conscious experience is the foundation that everything else builds on.

We’re not at the top of a explanatory stack looking down at what supports and causes our experiences. Instead, we’re at the bottom, looking up at all the things built on top of our conscious experience.

Things which aren't independent of our experience, but rather are aspects of it.

I think nearly everything else falls into place if you can just make it past that first step.

Any critism you can level at it, I'm pretty sure I can show how physicalism or panpsychism or theism or whatever suffers from the same issues, but introduce extra complexity in an attempt to paper over them.

Steve said...

Well, my mind just finds arguments which utilize infinities difficult to evaluate, I guess.

For the rest of your comment; as you know I also think conscious experience is fundamental, although I adopt the panexperientialist version of this.

I ask you: if your conscious observations are fundamental and are not composed of anything else, why does brain damage affect them?

Steve said...

Thinking again about this issue of disorderly/deceptive worlds, I wonder if the problem is an artifact of an incorrect conception of possible worlds.

I think Lewis' idea of worlds was wrong. His were static spatio-temporally connected entities which were wholly isolated from each other.

As we learn more about our cosmos, we realize this isn't a good model of our universe, so it is likewise not a good model for other possible worlds.

I believe modal realism works at the level of events (possible and actual). The actual "world" is just the regional, locally accessible, network of causally related events. This region is orderly (in the indeterministic, quantum mechanical sense that prior and adjacent events constrain, but do not completely determine a new event).

Our region seems to have undergone a phase transition (think of the "crystallizing block universe" model), and we are surrounded by this orderly region. Perhaps there are other "pocket worlds" like ours, and perhaps there are vast parts of reality which remain unactualized and hence unordered possibilities.

Thinking about this alternative model of the multiverse or megaverse, it seems less likely to me that humans could exist at some border where order would be in danger of failing imminently. It took many years of order to reach the current state of the world, and order is unlikely to suddenly vanish -- the application of the copernican principle should make it more likely we are near the middle of the zone of stability.

Crude said...

He thinks traditional theism is inconsistent with the creation of these other worlds – why would God bother when his focus is supposedly on we humans?

That doesn't seem to be strictly true with traditional theism. I take it you mean Abrahamic faiths here, as opposed to something like classical theism that was more broad?

But even with the Abrahamic faiths, that doesn't seem right. God has a focus on humans, but THE focus to the exclusion of all else? Right in Genesis you have God creating, and regarding each created thing as 'good'. That alone is pretty striking.

Steve said...

That's a fair point. We don't know that a personal god wouldn't consider it good to create different sorts of worlds, including lifeless ones.

Neil B said...

The meta-crew here has wrangled over this before at each of our blogs! Again, I note where Alexander Pruss brought up the usual claim that we can't do probability on infinite sets. OK, but I provided some of what IMHO (of course ...) are decent rebuttals. My point is basically that if we can imagine the logic of probability applied locally or discretely, then it should extend to more of the same (ie, the boundary conditons can't make it all moot.)

I really think there has to be some "expectation" based on circumstances, would modal realists really want to say there aren't? There would just be a vanishingly small chance of not being in a rubbishy sloppy world, since you'd have to be "lucky" enough to stay in a perfect groove. You can say whatever about infinities, we just wouldn't "likely" end up there. And to me, like to John Leslie, that means "God" in some sense.

BTW I'm into Captcha synchronicity and mine is "trump." Hmmm.

Steve said...

Right. Regardless of the issues involved with applying probabilities, we might still be justified in asking whether the order which exists locally (including the remarkable usefulness of mathematics in describing it) implies something about reality. [I think.]

Allen said...

Back from vacation! Sorry about the delay!

"I ask you: if your conscious observations are fundamental and are not composed of anything else, why does brain damage affect them?"


Brain damage doesn't affect conscious observation. The experiences that you base that inference on are, effectively, dreams.

===

Physicalism:

According to physicalism, why does brain damage affect one's conscious experiences?

Why do some arrangements of matter and energy give rise to pleasure, while others give rise to pain? What decides that one arrangement "represents" pain while a second arrangement represents pleasure, rather than vice versa?

Representations require interpretation, don't they? Things must be "re-presented" to someone in order to acquire meaning?

Further, why does disrupting these arrangements disrupt the associated experiences? What is the nature of the causal link between the arrangments and the experiences that accompany them? What determines the direction of the causal link? And what causes the cause?

===

Panpsychism:

Assuming panpsychism, why would certain combinations of experiential subcomponents lead to the formation of a unified consciousness whose experience is not of being an aggregate, but instead of being an individual?

Okay, knocking the experiential subcomponents out of alignment leads to a change of consciousness, but why one kind of change instead of another? What rule-set governs this relationship? And why do we operate under that rule-set instead of some other rule set?

AND, why did the offending knock on the head occur instead of not occur? What past events brought our poor brain-damaged subject to his sorry state? Why that set of past events instead of some other past?

What does asserting the existence of experiential subcomponents plus the associated rule-set really accomplish?

Fine - instead of saying that conscious experience exists fundamentally and uncaused, we have: The experiential subcomponents and associated governing rule-set exists fundamentally and uncaused.

Why is that an improvement?

===

Hume:

Besides, how do you *know* that brain damage actually does affect conscious observation? I pose this question on two levels.

First, you infer from your observations that brain damage affects consciousness, but why should you trust this inference? I've had dreams where I inferred from experience that flapping my arms would "cause" me to fly. But not only was flapping my arms not the cause of my flight, I wasn't even really flying - I was dreaming.

And secondly, but still related: I think Hume's discussion of casual connections is relevent:

"When we look about us towards external objects, and consider the operation of causes, we are never able, in a single instance, to discover any power or necessary connexion; any quality, which binds the effect to the cause, and renders the one an infallible consequence of the other. There is required a medium, which may enable the mind to draw such an inference, if indeed it be drawn by reasoning and argument. What that medium is, I must confess, passes my comprehension; and it is incumbent on those to produce it, who assert that it really exists, and is the origin of all our conclusions concerning matter of fact."

So, you observe brain damage. Then you observe altered behavior. And you infer a causal connection. But I'll follow Hume on caual connections: "it is incumbent on those to produce it, who assert that it really exists".

===

AND finally, I refer you to my link on the Irrationality of Physicalism, where I think my argument applies not just to physicalism, but to any system that has consciousness "caused" by an underlying causal system.

Allen said...

Steve,

"I believe modal realism works at the level of events (possible and actual). The actual 'world' is just the regional, locally accessible, network of causally related events. This region is orderly (in the indeterministic, quantum mechanical sense that prior and adjacent events constrain, but do not completely determine a new event)."

So what is an "event"?

So five things exist:

1) Actual events

2) Possible events

3) Causal relations between events

4) The background "state space" that allows events to differ

5) A dimension of "time" that allows for change

And this all just exists? Uncaused and fundamental?

"It took many years of order to reach the current state of the world, and order is unlikely to suddenly vanish"

Why not? What enforces the symmetry between order’s appearance and it’s dissipation?

Again...I still don’t see what all this inferred metaphysical machinery really buys you.

Allen said...

Neil:

“OK, but I provided some of what IMHO (of course ...) are decent rebuttals.”

I think that all your rebuttal showed is what I stated in *my* comment on Pruss’s post.

Which is that if you can construct a finite description of a process that would generate your infinite set, then you can talk reasonably about what to expect from the described generating process.

But that isn’t necessarily the same as talking about the actual infinite set.

As for Steve’s comment:

“the order which exists locally (including the remarkable usefulness of mathematics in describing it) implies something about reality.”

Mathematics is just precise expression and inference to avoid contradiction. It’s no more surprising that I can use mathematics to describe reality than it is that I can write prose to describe it.

The magic isn’t in mathematics, it’s in mathematicians.

Steve said...

Welcome back Allen.

A running theme in your thinking seems to be that if an explanation isn't final and complete, then it's not worth anything. How do you feel about partial explanations?

There are two senses of this, perhaps. One kind of partial explanation is where it is useful, even though we know it's not final. A mechanic can tell me (hopefully) what's wrong with my car, even if he can't provide a final metaphysical account of it.

The second kind is one where we know there is a propensity for something to happen, but we don't know (and can't know in principle) why it manifested itself at a particular time or location.

Critics of the principle of sufficient reason say that if we had a complete explanation of every detail of reality, then it would be like saying everything exists necessarily, which is, in turn, not much different then saying it exists brutely.

So, Timothy O'Connor used the term "not-fully contrastive explanation" to discuss the way a necessary being might create a particular world. He thinks a personal agent god with certain characteristics would provide such an explanation. I'm inclined to disagree and look to a necessary megaverse-entity which encompasses all metaphysically possible event, but creates these in a choatic, spontaneous, probablistic fashion. Sometimes these actualized events order themselves in a way which allows for more interesting event-complexes -- such as us. Then we call this sequencing "causal".

Steve said...

With regard to your comments on mathematics. First, mathematics is more than just first order logic. Second, mathematicians feel that they are discovering mathematical truths, not inventing them. I tend to give some weight to the intuition there.

Allen said...

"A running theme in your thinking seems to be that if an explanation isn't final and complete, then it's not worth anything. How do you feel about partial explanations?"

The problem isn't that some particular explanation is incomplete, but rather that even if it *was* complete, there would still be the question of what explains the explanation, and what explains what explains the explanation, and so on. Infinite regress.

Either there is a cut-off point where you say, "it just is that way", or you are committed to an infinite hierarchy of explanations. Because, how can an explanation explain itself as well as reality?

Even if we had a scientific Theory of Everything that addressed all observable phenomena and was perfectly predictive - there would still be the question of why the universe is that way instead of some other way, and indeed why a universe exists at all.

Further, given that all we know is our observations, how can we ever justify the belief that our observations reveal something true about the way reality "really is"? I keep coming back to Moravec's point about life in a computer simulation. Science there would only reveal the rules of the simulation. Science would never reveal anything about the programming language the simulation was written in or anything about the underlying hardware that ran the program.

Indeed, even discovering something true about the rules of the simulation would require that this discovery be implicit the simulation logic and the initial data the logic started with.

In other words: You could only discover the rules if that discovery was written into the rules.

Which is just as true of a non-simulated universe.

There is no reason to believe that our observations carry information about anything except the observations themselves. There is no reason to believe that our observations carry information about any underlying reality.

To me this seems very clear and incontrovertible.

What do you think I'm missing?

===

"One kind of partial explanation is where it is useful, even though we know it's not final."

That you find something "useful" is purely an aspect of your subjective experience. What is the significance of usefulness in a world with no free will? Or in a world where everything reduces to fundamental laws (like electromagnetism) acting on fundamental entities (like quarks)? Or in a static 4-D block universe such as that implied by Relativity?

Usefulness. Pah.

===

"it would be like saying everything exists necessarily, which is, in turn, not much different then saying it exists brutely."

All metaphysical theories ultimately rest on the brute existence of something, don't they?

Given that this is the case, why not just say our conscious experience exist brutely and save the extravagance of all the additional (but ultimately pointless) metaphysical machinery involved in physicalism, theism, panpsychism, etc.?

===

"I'm inclined to disagree and look to a necessary megaverse-entity which encompasses all metaphysically possible event, but creates these in a choatic, spontaneous, probablistic fashion."

But here you've basically given up everything *except* the idea that there is something that underlies and generates our conscious experiences.

Your "events" are so chaotic that the only purpose they serve is to provide a backstop for consciousness. But what backstops the events?

The events are supposed to explain consciousness, but what explains the events?

What is it that stops you from taking the final step and just accepting that there is nothing beneath conscious experience?

Even if (by some miracle) there is something, it is forever hidden from us...not just in practice, but in principle - as Kant realized with his noumenal and phenomenal worlds.

Steve said...

Either there is a cut-off point where you say, "it just is that way", or you are committed to an infinite hierarchy of explanations. Because, how can an explanation explain itself as well as reality?

Only a necessarily existing entity can explain itself as well as other things. I think an entity which is the sum of all metaphysical possibilities is a candidate for this.

Further, given that all we know is our observations, how can we ever justify the belief that our observations reveal something true about the way reality "really
is"?

There is no reason to believe that our observations carry information about any underlying reality.


This (and the reference to Kant) doesn’t bother me. All of our observations are participatory interactions. These events are the concrete reality. Our knowledge about reality is relational rather than absolute, but so be it.

Given that this is the case, why not just say our conscious experience exist brutely and save the extravagance of all the additional (but ultimately pointless) metaphysical machinery involved in physicalism, theism, panpsychism, etc.?

Otherwise I think you’re just throwing the science baby out with the philosophical bathwater. Neuroscience, chemistry, physics shows we are composite creatures – so our consciousness, despite its unified nature, is built from other stuff.
It was maybe OK for Bishop Berkeley to be an idealist in the 18th century. I don’t believe it’s tenable now.

Allen said...

Ack, the size limit on comments is cramping my style!

Part 1:

"Only a necessarily existing entity can explain itself as well as other things. I think an entity which is the sum of all metaphysical possibilities is a candidate for this."

What would be an example of a metaphysical *impossibility*?

So, in a similar vein, given that my experiences exist it seems plausible to me that all *experiences* exist.

However, I don't even know what it would mean to say that something exists outside of experience. I have no experience with things outside my experience.


"All of our observations are participatory interactions."

Participation of what with what? Interacting according to what rules or laws?


These events are the concrete reality.

If events are experiences, then I guess we are in agreement. But I don't think that's what you mean. Or at least it's not all that you mean. You seem to imply that there is something in addition to these events - for instance, the rules that govern their interactions or relationships.


Otherwise I think you're just throwing the science baby out with the philosophical bathwater.

If you're positing that all metaphysical possibilities exist, then you've also thrown the science baby out with the bathwater, haven't you? Science in that case just describe our local branch of the overall structure, which would surely contain vastly different branches...some of which contain conscious entities who are vastly deluded about the nature of existence.

But we can just as well say that science describes our experiences, without taking the further leap of faith that the equations used actually describe anything "real".


Neuroscience, chemistry, physics shows we are composite creatures – so our consciousness, despite its unified nature, is built from other stuff.

You're a physicalist now?

I would say that correlation does not equal causation. The fact that we are conscious of things that *seem* to be correlated with changes to our conscious experience does not in fact mean that these things we are conscious of *actually* caused the changes in our conscious experience.

And, indeed, a little thought quickly uncovers problems. The bottom line on neuroscience is that particular arrangements of atoms *causes* our conscious experience. By stacking a collection of atoms one way, you can cause the experience of pleasure, but by stacking them another way you can cause the experience of pain.

But, there's nothing in my conception of atoms or arrangements that would have caused me to predict, beforehand, that this would be the case.

And, in fact, I don't believe it to be the case.

Surely if you are right about all metaphysical possibilities existing, one of those possibilities is a being with my experiences whose experiences are in fact *not* caused by neural activity, chemistry, or physics?

In fact, is it not metaphysically possible that free-floating conscious experiences exist? If not, why not?

Allen said...

Part 2:

It was maybe OK for Bishop Berkeley to be an idealist in the 18th century. I don't believe it's tenable now.

I think you underestimate the sophistication of Berkeley, Leibniz, Hume, and Kant.

"L'Homme machine" by Julien Offray de La Mettrie, was published in 1748 and claimed that man was just a very complicated machine.

Even before that, Leibniz had considered the idea in his book Monadology, in 1714, but rejected it.

"17. Moreover, it must be confessed that perception and that which depends upon it are inexplicable on mechanical grounds, that is to say, by means of figures and motions. And supposing there were a machine, so constructed as to think, feel, and have perception, it might be conceived as increased in size, while keeping the same proportions, so that one might go into it as into a mill. That being so, we should, on examining its interior, find only parts which work one upon another, and never anything by which to explain a perception. Thus it is in a simple substance, and not in a compound or in a machine, that perception must be sought for. "

Also, Kant was the first to propose that the solar system formed from a collapsing cloud of dust.

We are still very much in the same basic conceptual framework laid down by Galileo, Descartes, and Newton - though obviously with adjustments and refinements.

What conceptual insights have occurred that renders Berkeley's position obviously wrong and untenable? I'm not aware of any.

Steve said...

First, let me try to clarify my panexperientialist position vs. physicalism and idealism:

Reality is full of events/happenings: some we are party to (we participate in), others we don’t. We are conscious of the ones we participate in. Science is a methodology for making reliable inferences about events we don’t participate in. The events we don’t participate in we call “physical”. Our knowledge of these is indirect and of limited scope, but still counts as knowledge (yes it is knowledge of our particular region of reality – where there is order and regularities -- things may be very different elsewhere). Now, there is no reason to be an ontological dualist: all events have a common, experiential, character. There is no essential difference between mental events and physical events other than the fact that we participate in the former and infer the existence of the latter (the only dualism is the dualism of first person and third person points of view). Physicalism goes wrong (absurdly wrong), by taking the descriptions of the inferred events as real at the expense of conscious experience. It’s absurd because all knowledge starts with experience.

But science has gained us something – we know something of the character of what’s around us. There’s no reason to be too skeptical about the world beyond direct experience.

My criticism of old-fashioned idealism is that, while it is a cousin of panexperientialism, it seems to assume the only things that exist are full-blown human or divine minds. The other parts of reality we have learned about through science have some experiential character, but sticks and stars do not have the right organization/composition to be full blown minds. Your position reminded me of idealism because you seem to sometimes think that full blown (healthy) human conscious experience is the only unit of reality.

You're a physicalist now?

I would say that correlation does not equal causation. The fact that we are conscious of things that *seem* to be correlated with changes to our conscious experience does not in fact mean that these things we are conscious of *actually* caused the changes in our conscious experience.

And, indeed, a little thought quickly uncovers problems. The bottom line on neuroscience is that particular arrangements of atoms *causes* our conscious experience. By stacking a collection of atoms one way, you can cause the experience of pleasure, but by stacking them another way you can cause the experience of pain.

But, there's nothing in my conception of atoms or arrangements that would have caused me to predict, beforehand, that this would be the case.

And, in fact, I don't believe it to be the case.


Now, you can see that I’m not a physicalist, but the difference is a little subtle: the physicalist would say the arrangement of atoms caused the experience; I would say the atoms are physical descriptions of micro-experiential events which composed our experience. But they do go together every time.

Steve said...

In fact, is it not metaphysically possible that free-floating conscious experiences exist?

If not, why not?


And you earlier asked:

What would be an example of a metaphysical *impossibility*?

So, in a similar vein, given that my experiences exist it seems plausible to me that all *experiences* exist.

However, I don't even know what it would mean to say that something exists outside of experience. I have no experience with things outside my experience.


This returns to the earlier problem in our thread of what exists in total, including what’s beyond our region. I think metaphysical impossibilities would include logical contradictions and probably things which contradict mathematics. Might it be restricted beyond this? John Leslie thinks all regions have order. We have a certain kind of order in our region, but I seem to be able to imagine other regions which lack order, or do it differently. Maybe almost everything goes, and it is just due to chance and the observational selection effect that we’re in an ordered region. This is what I’ve been thinking a lot about lately.

Allen said...

Meeker's thoughts on mathematics, with which I agree:

"Numbers are defined by order and successor - neither of which are present or implicit in a mere collection of atoms or anything else.

A proposition like 'Every number has a successor' or '2+2=4' don't say tell us anything about whether numbers exist. Truth values in logic are just arbitrary assignments of T to some propositions (axioms) and F to others (contradictions). The are not evidence of existence.

Truth is property of sentences. In mathematics it's just a token T you attach to some sentences (the axioms) and then applying some rules of inference that are assumed to preserve T you see which other sentences get T. It is nonsense, in the sense that pure mathematics is not about anything. It is useful for creating models of things because it guarantees that the model will not be inconsistent, i.e. lead to the inference of every statement. Mathematics attains certainty by giving up meaning.

If you speak according to the rules of English you will utter English sentences. It doesn't make English a fact of nature."

"In mathematics we never know what we are talking about or whether what we say is true or false."
--- Bertrand Russell