What is Metaphysics & Why Is It A Valid Means Of Describing Reality?

[Just_Lurking]

That doesn’t seem to be the case in metaphysics? The terms used have no precise definition and the axioms used seem comoletely arbitrary?

On what basis do you say this? I have not studied Ontology, but from the little I’ve been able to understand about the science of “being” … there is a definition of terms according to Socratic philosophical definition … if you speak that language, then I would have to conclude there is a body of understanding to hold a person’s feet to … as a basis of definition and communication of terms …

now if you are a person who does not agree to Socratic philosophical definition of terms … then you speak in another language without any ability to understand metaphysics … because it is in a language you simply don’t understand or speak. You would be like a Mexican trying to understand someone who is speaking Chinese without you having any understanding of Chinese … utterly futile …

Take one example - infinity. In mathematics, I know the definition of infinite cardinal numbers, infinite ordinal numbers, infinite surreal numbers, countably infinite, uncountably infinite, and the list goes on. Each one of these has a precise mathematical definition.

Metaphysics seems to have potential infinities and actual infinities and some axiom that actual infinities cannot exist. So where do I go to find the precise definition of these?

 

[Just_Lurking]

How about the metaphysical argument that the mind is more powerful than the body? Isn’t that a conclusion that can be independently examined and analyzed?

What do “mind” and “body” mean? Is the brain part of the body? If so, the body contains the organ responsible for the mind, so wouldn’t that negate the argument?

In mathematics, proofs are so precise that they can be checked by computer, for example, the Mizar system (see here). What about metaphysical arguments?

As a consequence, mathematicians are in agreement about what has been proven. For example, mathematicians agree that Fermat’s little theorem is true. Do all metaphysicians agree about which metaphysical arguments are considered proven, or is it just a big free-for-all where the loudest person wins?

 

[Prodigal_Son]

How do you tell if a metaphysical chain of reasoning is valid?

For mathematics, if a proof obeys the rules of logic, then you can rely on its conclusion. That doesn’t seem to be the case in metaphysics. The terms used have no precise definition and the axioms used seem completely arbitrary.

Well, the difference between mathematics and metaphysics is obvious: it is a matter of the subject’s relation to the world. Mathematical proofs often have no direct bearing on the experience, beliefs, or decisions of the people who accept the proof. They are (usually) intensive.

Metaphysical proofs are extensive. They explain what the world is, and how we can know what the world is. They are dynamic, and they rely on a dynamic set of definitions. But the definitions **do **matter, and they are made clear – or as clear as possible.

Consider: a man wants to build a house, but all he has is a tape measure. The tape measure is more accurate than any other tool he will use, but a house cannot be made with it. Just so, mathematics is more accurate than metaphysics, but mathematics cannot capture such a broad range of important questions as metaphysics can.

 

[Just_Lurking]

So how do you determine if a metaphysical argument is valid? Does each person decide for themselves if they like the argument or not? I have not seen any metaphysical argument that did not strike me as complete nonsense. Is that an acceptable metaphysical response?

For example, if someone says they don’t like the proof of Fermat’s little theorem, then that means they aren’t real mathematicians.

 

[Prodigal_Son]

So how do you determine if a metaphysical argument is valid? Does each person decide for themselves if they like the argument or not? I have not seen any metaphysical argument that did not strike me as complete nonsense. Is that an acceptable metaphysical response?

For example, if someone says they don’t like the proof of Fermat’s little theorem, then that means they aren’t real mathematicians.

In my understanding, mathematics is about pure logic – a priori understanding. Its terms, as such, have no reference outside of their own system; they are relational terms. Metaphysics is all about correspondence to reality, which means that the terminology must have reference to the real world. And this is where all the disputation comes in, because we don’t even know what we’re referring to when we refer to the “real world”. Are properties real? Which properties? Etc.

That said, most metaphysical arguments must follow the rules of logic – some of which are fixed, others of which are contentious. If their assumptions are true, their conclusions must be true. But very few of their assumptions are verifiably true.

The most appealing metaphysical assumption, perhaps, is the doctrine of the empiricists: that all that we know comes through our senses. But this doctrine cannot explain the knowledge of mathematics, which puts us right back where we started.

 

[Newbot]

So how do you determine if a metaphysical argument is valid? Does each person decide for themselves if they like the argument or not?

I imagine it would be as one judges any line of reasoning: if the premises are true and the logic rigorous, the argument is valid and the conclusion sound. Any imperfection or outright failure if premises or logic will diminish our certitude as to the conclusion. But perhaps what you said earlier would make this clearer…

How do you tell if a metaphysical chain of reasoning is valid?

For mathematics, if a proof obeys the rules of logic, then you can rely on its conclusion. That doesn’t seem to be the case in metaphysics. The terms used have no precise definition and the axioms used seem completely arbitrary. So a metaphysical argument doesn’t seem to really establish anything, nor is the conclusion something that can be independently examined and analyzed.

It is probably worth distinguishing the rigor (if I may call it that) of a chain of reasoning from its validity. Any proof which obeys the rules of logic (i.e. in which the conclusion and premises are or can be arranged according to proper syllogistic form without equivocation) may be called rigorous, in the sense that the conclusion necessarily follows from the premises, but that does not mean it is valid. If the premises are not also true, the conclusion may be false and should not be relied on.

For instance: Every even number is divisible by two. Every prime number is even. Therefore every prime number is divisible by two. The logic is flawless, it is just that one of the premises is false, so in this case the conclusion is false too.

I don’t see why, in theory, metaphysics can’t have formal rigor in its proofs. If you are saying that, in practice, metaphysicians generally aren’t very rigorous, that is one thing, and probably true often enough. But if you are saying that metaphysics, because it is metaphysics (i.e. the study of what is most universal – and by most universal I mean most common or abstract, like ‘being’), cannot make use of rigorous logic, then I fear I fail to see why .

Concerning the validity of the premises, you raise the difficulty that, in metaphysics, the terms have no precise meaning. It is true that unlike mathematics, there are terms in metaphysics which cannot be defined according to what they are, using a “genus and species-making difference”. For instance, if I recall correctly, St. Thomas defines “essence” as “that which the account [or definition] signifies” – which, while it distinguishes “essence” from every other concept, does not tell us what essence is itself except through a sign. In addition, mathematical terms are sometimes fairly concrete and particular (though of course not always, e.g. ‘tensor’), whereas metaphysical terms are highly abstract (e.g. ‘being’ or ‘actuality’), and one might argue that ‘abstract’ is simply a fancy way of saying ‘vague’.

Still, I don’t see how either of these difficulties are, in theory, problematic for metaphysics (though of course in practice they mean that one is likely to slip up). The fact that we cannot define metaphysical terms according to genus and species does not make the definition any less precise and determinate. We can still clearly delimit our meaning such that we include all we intend and nothing we do not intend.

And again, in metaphysics as in math, the abstraction of the terms does not negate the precise use of those terms as abstract. E.g. if I wish to write an abstract proof of the fundamental theorem of calculus which applies to both geometrical curves and algebraic functions, I cannot use any properties, axioms or theorems peculiar to the curves without first proving the algebraic analogue (e.g. the intermediate-value theorem, the geometrical equivalent of which is fairly obvious, if not axiomatic). Again, if I want to write a geometrical proof in the style of Euclid by which a perpendicular line can be dropped to an n-dimensional volume from a point not contained by the volume, I must avoid any assumptions only applicable to 3- or 4-dimensional space. Presumably there is nothing wrong if metaphysics, too, deals with abstract concepts precisely.

Let me know if I said anything false. I’m also a little unsure if what I said actually addresses your points, so let me know .

 

[Newbot]

Whoops, Prodigal, you must have posted while I was writing my post. Sorry .

Just a quick question: could you expand a little on the distinction between ‘fixed’ rules of logic and ‘contentious’ ones?

 

[Just_Lurking]

So is infinity a concept in metaphysics? In mathematics, an infinite cardinal set is one that is equinumerous with a proper subset of itself. What does infinity mean in metaphysics?

All the mathematical versions of infinity have very counter-intuitive properties, which are only discovered via rigorous proofs of unexpected theorems. How does metaphysics determine the properties of metaphysical infinity?

 

[Newbot]

As used in metaphysics, I believe that “infinite” means “without bounds”, or more precisely, “without limit”. “Limit” has a number of senses, of which several are (following Aristotle):

1. The last part of each thing, or the first part outside of which no part can be found, or the first part inside of which all parts exist.
2. The form of a magnitude or of that which has magnitude.

As to the first sense of limit, Aristotle defines “a part” as “that into which a quantity can be in any way divided.” I am not sure how one would define “quantity”. I also do not know how one would define “division”: presumably “making to be divided”, where a “thing divided” is, insofar as it is divided, many. But I’m just guessing. As to the second sense of limit, I think one might define a “magnitude” as a “continuous quantity”, and understand the “form” as the figure or shape (though form is itself a technical term).

In brief, then, the infinite would be:

1. That which lacks a last part, or a first part outside of which no part can be found, or a first part inside of which all parts exist.
2. A continuous quantity lacking a form (or figure).

I think the second is the more precise definition generally used of quantitative infinities in metaphysics.

I hesitate to give an example of a metaphysical argument concerning infinites, because to understand it rigorously it would first be necessary to lay out the definition of a number of other technical terms like “matter”, “form”, and “actuality” (which are hard to grasp because they are so abstract), and then defend a number of premises used in the argument (e.g. that nothing is in act except through its form). But the general method is clear enough: from premises self-evident or true by definition, or propositions proved from such, one would proceed syllogistically to the conclusion. An example of such a conclusion would be what you mentioned earlier, that an actual quantitative infinity is impossible.

Hope I’m not over-posting – I just find this subject really interesting.

 

[warpspeedpetey]

What is Metaphysics & Why Is It A Valid Means Of Describing Reality?

I have never seen a thread devoted entirely to Metaphysics. I am going to take a back seat on this, as i want to see a debate rather then get involved at the moment. But i realize that there are allot of people who seem to think that Metaphysics is hocus pocus; and thats people who are both theist and atheist.

Is there anybody who cares to defend Metaphysics?

yes, i can define metphysics.

its the club i use to beat the ignorance out of …well you know.

 

[Just_Lurking]

An example of such a conclusion would be what you mentioned earlier, that an actual quantitative infinity is impossible.

Okay, one of the problems in physics is what is the value of the cosmological constant, which is the coefficient of one of the terms in the equation for the law of gravity in general relativity. Some values of the cosmological constant are consistent with a finite universe, while others are consistent with an infinite universe.

Does the metaphysical conclusion about the impossibility of actual quantitative infinity mean that physicists should just rule out those values of the cosmological constant which result in an infinite universe, without having to perform any actual experiments, as physicists are prone to do?

 

[Newbot]

Okay, one of the problems in physics is what is the value of the cosmological constant, which is the coefficient of one of the terms in the equation for the law of gravity in general relativity. Some values of the cosmological constant are consistent with a finite universe, while others are consistent with an infinite universe.

Does the metaphysical conclusion about the impossibility of actual quantitative infinity mean that physicists should just rule out those values of the cosmological constant which result in an infinite universe, without having to perform any actual experiments, as physicists are prone to do?

Nice .

In general terms, the question seems to be: if physics and metaphysics can make conclusions about the same subject, how should their conclusions be reconciled? Should one invalidate the other? Or should one science’s investigation exclude the other’s?

I think in general one would say of physics and metaphysics what one would say of any other two sciences: if the reasoning is sound, they will agree. If something can be proved by one science, there is no reason not to investigate it in another science. If there is disagreement, one has to look over the reasoning of both and see which one went wrong and where. Hence there is, apparently, disagreement between the predictions of general relativity on the basis of Hubble’s observations, and the predictions of quantum field theories, as to the value of the cosmological constant. Each science needs to reexamine its evidence and its line of reasoning to see where the contradiction came from and how it might be resolved.

As to the particular question (which is where the real difficulty is): I’m not sure. I don’t think I’m enough of an expert to decide. Of course physicists should continue to perform experiments – nothing wrong with proving the same thing from many angles – but I suppose your point is: should physicists, in light of a metaphysical proof for the finitude of quantity, expect or assume one result and not another (as, for instance, was the case with the Michelson/Morley experiment)? To be sure, I’d have to know:

1. Is the metaphysical argument actually valid? Or does it have some fallacy?
2. Strictly speaking, the conclusion of the argument is “a mathematical body cannot be infinite in act.” Which leads to two questions:
   2a. Concerning “body”: Perhaps we have, not one infinite body, but an infinity of finite bodies? In which case we would have to discuss whether an actually infinite number of bodies is possible.
   2b. Concerning “mathematical”: Is it conceivable that while a mathematical body cannot be infinite, a physical body can? Unlikely, but we’d need to reason the matter out explicitly.
3. On the subject of which, does the infinitude of the universe on the basis of the cosmological constant necessitate either an infinite body or an infinite number of bodies? In other words, there are regions that, as far as we can tell, are ‘empty’: are they really empty, or are they filled with some body, or is there some field there, or is some other answer the right one? The answer would affect whether we can apply this metaphysical conclusion to the size of the universe.

I’m not even sure if questions like these are the right ones. Still, it is certainly true that metaphysics, back when it was studied seriously, was studied only after natural science, and made use of the conclusions of natural science (e.g. that immaterial beings were possible, which was considered a conclusion of natural science then – rightly or wrongly, doesn’t matter here). It does not seem troublesome to me that physics or natural science should force metaphysics to reexamine itself and make new distinctions, or that metaphysics should do the same for physics.

 

[tonyrey]

What do “mind” and “body” mean? Is the brain part of the body? If so, the body contains the organ responsible for the mind, so wouldn’t that negate the argument?

The key word is “if”. This is where metaphysics come in. The answers to your questions are not all equally satisfactory. Their value depends on how adequate they are. If the brain is “responsible” for the mind then the mind is not responsible for what it does. In fact nothing is responsible for anything because everything is a cog in the machine of nature.

In mathematics, proofs are so precise that they can be checked by computer, for example, the Mizar system (see here). What about metaphysical arguments?

Metaphysical arguments can use mathematical proofs but mathematical proofs cannot use metaphysical arguments. Mathematical proofs by themselves are just intellectual exercises whereas metaphysical arguments are necessary to clarify and justify our interpretation of reality. They can achieve a high level of precision by defining the meaning of the terms they use and examining to what extent they correspond to our experience and expectations.

As a consequence, mathematicians are in agreement about what has been proven. For example, mathematicians agree that Fermat’s little theorem is true. Do all metaphysicians agree about which metaphysical arguments are considered proven, or is it just a big free-for-all where the loudest person wins?

I haven’t come across anyone who is a nihilist, a solipsist or a total sceptic…

 

[JDaniel]

How do you tell if a metaphysical chain of reasoning is valid?

For mathematics, if a proof obeys the rules of logic, then you can rely on its conclusion. That doesn’t seem to be the case in metaphysics. The terms used have no precise definition and the axioms used seem completely arbitrary. So a metaphysical argument doesn’t seem to really establish anything, nor is the conclusion something that can be independently examined and analyzed.

In these regards, metaphysics seems a lot like string theory!

Actually, it is pretty much the same for metaphysics as for mathematics. You say that, “The terms used have no precise definition and the axioms used seem completely arbitrary.” Please give an example or two.

jd

 

[JDaniel]

Take one example - infinity. In mathematics, I know the definition of infinite cardinal numbers, infinite ordinal numbers, infinite surreal numbers, countably infinite, uncountably infinite, and the list goes on. Each one of these has a precise mathematical definition.

In each place that you have the word, “infinity”, above, replace that word with the word, “gargoyle”. Do you see any difference?

Metaphysics seems to have potential infinities and actual infinities and some axiom that actual infinities cannot exist. So where do I go to find the precise definition of these?

For the most logical and real reasons - which we’ll get to soon.

jd

 

[JDaniel]

What do “mind” and “body” mean? Is the brain part of the body? If so, the body contains the organ responsible for the mind, so wouldn’t that negate the argument?

In mathematics, proofs are so precise that they can be checked by computer, for example, the Mizar system (see here). What about metaphysical arguments?

As a consequence, mathematicians are in agreement about what has been proven. For example, mathematicians agree that Fermat’s little theorem is true. Do all metaphysicians agree about which metaphysical arguments are considered proven, or is it just a big free-for-all where the loudest person wins?

OK. With all of the precision about mathematics that you have explained, mathematics should be able to tell us - with absolute precision, beyond any shadow of a doubt - whether infinity, the number that is, is odd or even.

jd

 

[JDaniel]

So how do you determine if a metaphysical argument is valid? Does each person decide for themselves if they like the argument or not? I have not seen any metaphysical argument that did not strike me as complete nonsense. Is that an acceptable metaphysical response?

For example, if someone says they don’t like the proof of Fermat’s little theorem, then that means they aren’t real mathematicians.

Very similarly. St. Thomas Aquinas didn’t like St. Anselm’s so-called ontological argument and argued against it.

But, as a real Catholic, you should know this.

jd

 

[JDaniel]

One of the main problems, that I have seen, is that many people seem to want to legitimatize metaphysics, for their own reasons. They usually do this by bringing in stuff from outside of metaphysics and trying to force it into the waters of metaphysics. Thus, there appears things that are senseless precisely because they have no relation to or with that which is really metaphysical.

Some of the questions that belong to metaphysics are: what is substance, cause, relation, act, and being. All of these are questions that are asked by people, in general, looking for answers to some of the mysteries of existence in much the same way as certain questions are asked by science. You must admit that they are questions that are not satisfactorily answered - or even answerable - by science (or math). Yet, they are questions you, yourself have asked at one time or another in your life.

If they seem imprecise that is because the average person does not immerse himself into the science of metaphysics as he might for mathematics. The reason why is that ultimately, the questions of metaphysics leads to the cause of its object (being) which is, of course, God. Many scientists will stop at an arbitrary point before God where it seems to them that reality stops. That is unfortunate. It is understandable that the Atheist would do this. But, why would the theist scientist do it? (Of course, some do not.)

jd

 

[Leela]

How do you tell if a metaphysical chain of reasoning is valid?

The problem with metaphysics is not whether the various philosophers and theologians have developed good reasoning in their various systems. In general they have. If you talk to a materialist, she can give you a good account of reality based on her materialist assumptions of a reality based on substance. Same thing if you talk to an idealist who bases reality on the subjective self, or if you talk to Robert M. Pirsig of Zen and the Art of Motorcycle Maintenance fame who based his metaphysics on Quality, or Heidegger on Being, etc. You could have the same sorts of conversations with Taoists or Buddhists or Christians and others who all have very different fundamental assumptions about the nature of reality. You will find that all these systems demonstrate valid chains of reasoning within the frameworks that they have set up. The truth is that self-consistent rationally sound metaphysical systems are a dime a dozen, so we shouldn’t be too impressed that the fact that they are self-consistent and rationally sound. Aquinas’s dictum “when you reach a contradiction, make a distinction” tells us exactly how easy it is to ensure that your system is self-consistent.

In short, whether a metaphysical chain of reasoning is valid is the wrong question. What we would need to adopt any of these systems and what no one has ever invented is a method that stands outside of metaphysics that tells us how to choose between such systems. Pragmatists like myself say that even this is not an issue because we are in no way forced to choose among these systems or create a new one.

The project of metaphysics, which is to get past appearances to reality as it really is, is one that we don’t need to engage in. We don’t have to think of inquiry as trying to find the one true account of reality but rather we can use whatever descriptions are useful for whatever purposes they are useful for.

Best,
Leela

 

[Leela]

The only thing that “REALLY IS” … is God … because only God by nature must exist … and cannot NOT exist. It is God’s nature to exist.

All else that has been brought into being by God only “really is” by God’s sheer will to continue it’s existence in being.

So you say, but saying so doesn’t make it true.