What is the justification for "axioms"?

[Oreoracle]

1. morals are objective.

Any comments or objections?

Not really, but I have a few questions. I would like to know how you determine that morals (should-statements) are objective. Surely this is not assumed? I don’t consider it axiomatic that my chair exists. Rather, I have come to the conclusion that the chair does in fact exist because I am sitting on it, detecting it with my senses. Have you ever observed a moral? Have you detected one with your senses? Can you give me an example of a moral, just so I know that we’re on the same page?

 

[Prodigal_Son]

Not really, but I have a few questions. I would like to know how you determine that morals (should-statements) are objective. Surely this is not assumed? I don’t consider it axiomatic that my chair exists. Rather, I have come to the conclusion that the chair does in fact exist because I am sitting on it, detecting it with my senses. Have you ever observed a moral? Have you detected one with your senses? Can you give me an example of a moral, just so I know that we’re on the same page?

You’re evaluating the statement as if it were not an axiom.

Consider: Have you ever observed modus ponens? Have you detected it with your senses?

 

[tdgesq]

Not really, but I have a few questions. I would like to know how you determine that morals (should-statements) are objective.

I’m not determining that. I’m just assuming it like other axioms that are assumed.

Surely this is not assumed? I don’t consider it axiomatic that my chair exists.

But you do consider it axiomatic that your senses give you accurate data so that you can conclude the chair exists.

Have you ever observed a moral? Have you detected one with your senses?

No, but I have observed instances of morals. I would argue that you have never observed “chair,” but have simply observed instances of “chair.” You have never observed the concept of a chair. Similarly, you have never observed a law of thought as Prodigal Son points out above.

Can you give me an example of a moral, just so I know that we’re on the same page?

Sure. People ought not to murder one another.

 

[Oreoracle]

You’re evaluating the statement as if it were not an axiom.

Consider: Have you ever observed modus ponens? Have you detected it with your senses?

I think you’re using a false analogy. As we know, there is quite a difference between logical laws and stating that the existence of an object is axiomatic. What must we use to determine that an object exists? We must use our senses. The existence of an object is not axiomatic because it is not irreducible; it falls back on an even more fundamental principle. This principle is our axiomatic assumption that our senses accurately perceive what exists. Logical laws have nothing to fall back on, and so they are axiomatic, but in order to identify an entity as an object, you must place axiomatic trust in your senses, and so this knowledge of existing objects is not irreducible and thus is not axiomatic.

In short, if you’re identifying something as an object, you’re already making an assumption, and so the existence of that object cannot also be considered an assumption. Axioms don’t support axioms. If one axiom precedes another, then the latter is not an axiom.

 

[Oreoracle]

I’m not determining that. I’m just assuming it like other axioms that are assumed.

Which do you assume: a) your computer exists, or b) the physical senses you’re using to detect the presence of your computer are reliable? I cannot sympathize with the former, and if it’s the latter, then the existence of the object (your computer) isn’t axiomatic, but instead the trust you place in your senses is axiomatic. The existence of objects, in our conception, is derived from our trust in our senses, which is the axiom. Thus, the existence of objects is not the most fundamental assumption we make (indeed, it isn’t an assumption in itself), so it cannot be considered irreducible or axiomatic.

No, but I have observed instances of morals. I would argue that you have never observed “chair,” but have simply observed instances of “chair.”

Could you elaborate on both of these ideas?

 

[Prodigal_Son]

I think you’re using a false analogy. As we know, there is quite a difference between logical laws and stating that the existence of an object is axiomatic. What must we use to determine that an object exists? We must use our senses. The existence of an object is not axiomatic because it is not irreducible; it falls back on an even more fundamental principle. This principle is our axiomatic assumption that our senses accurately perceive what exists.

I quite agree with you. I wasn’t comparing the object (goal) of morals to physical objects. Our direct knowledge of things through sense precedes all of our other sorts of knowledge.

In short, if you’re identifying something as an object, you’re already making an assumption, and so the existence of that object cannot also be considered an assumption. Axioms don’t support axioms. If one axiom precedes another, then the latter is not an axiom.

I’m not sure about that. Doesn’t any rule of inference depend upon non-contradiction? And yet, we cannot prove the rules of inference with non-contradiction.

At any rate, all I’m saying is that mathematical/logical truth seems to be truth that is not perceived by the senses. Your argument against moral objectivity involves the question “why can’t I touch or see moral realities?” But this question is irrelevant.

Consider: ***Couldn’t moral truths exist in some possible world? *** If they did, wouldn’t they be invisible? Invisibility is not an argument for nonexistence.

 

[Neil_Anthony]

I know what justifies axioms:

The success of the logical system that depends on the axioms justifies the axioms.

A logical system is successful if it 1) doesn’t contradict itself, 2) seems to make sense 3) is useful.

 

[hatsoff]

Not to ignore intervening posts, but let me propose two axioms:

1. God exists as the ultimate cause of being; and
2. morals are objective.

Any comments or objections?

For what system are you declaring these axioms?

 

[tdgesq]

Which do you assume: a) your computer exists, or b) the physical senses you’re using to detect the presence of your computer are reliable? I cannot sympathize with the former, and if it’s the latter, then the existence of the object (your computer) isn’t axiomatic, but instead the trust you place in your senses is axiomatic. The existence of objects, in our conception, is derived from our trust in our senses, which is the axiom. Thus, the existence of objects is not the most fundamental assumption we make (indeed, it isn’t an assumption in itself), so it cannot be considered irreducible or axiomatic.

The assumption that your senses are reliable depends upon yet another axiom: that you exist. You just need to declare what makes an axiom. If it’s irreducibility, then not even the reliability of the senses meets your test. And really, there is nothing that tells me irreducibility makes an axiom.

Could you elaborate on both of these ideas?

I could, but I decline. Please answer the question in the OP.

For what system are you declaring these axioms?

I’m not sure what you mean. Do axioms require that there first be a “system” in place before they can be declared? Besides, I didn’t declare any axioms. I proposed two. If you want to place them in a “system,” I suppose the first would be in ontology/metaphysics and the second would be in ethics.

 

[Oreoracle]

The assumption that your senses are reliable depends upon yet another axiom: that you exist. You just need to declare what makes an axiom. If it’s irreducibility, then not even the reliability of the senses meets your test.

True, but I think you’re missing the point. Would you say that it’s reasonable to assume that an object exists before you’ve sensed it or induced/deduced that it exists based on what you’ve already sensed? Through the use of no intuition of your own, senses or otherwise, you’ve concluded that an object (morality) must exist. I know you haven’t assumed this. I know that no one would assume this. So how does one go about coming to this conclusion?

And really, there is nothing that tells me irreducibility makes an axiom.

Uh, yeah. The definition does.

…To clarify, an axiom is not irreducibility, it just possesses the quality of being irreducible.

I could, but I decline. Please answer the question in the OP.

I already did. The utility of the system constructed by the axioms justifies the axioms. The axioms of mathematics and those of the scientific method are justified because both systems have served us well. Your original question was not asking what an axiom was but what justifies one.

 

[Oreoracle]

I’m not sure about that. Doesn’t any rule of inference depend upon non-contradiction? And yet, we cannot prove the rules of inference with non-contradiction.

True. But I still think it stands that it’s unreasonable to assume that an object exists without any sort of indicator that it exists. What sense, induction, or deduction have we used to determine that morality exists?

Consider: ***Couldn’t moral truths exist in some possible world? ***

I don’t think so. A statement that expresses truth is a fact, correct? What do all facts look like? Well, they might look something like, “There are more than seventy Playstation 2 games in my room.” This is a fact, because a) we can test its truth value since “my room” and “Playstation 2 games” can be proven to exist or not, and b) the statement passes the test. As I’m sure you know, everything mentioned in the fact (or, before it is tested, a proposition) must correspond to reality in some way or it won’t have a truth value.

Now, when we say that murder is wrong, “wrong” is usually meant in the sense that the object, murder, should not exist. If we look at morality as objective, then this is to say it is obligated, by the laws of nature, to cease existing. How can an object or process possess the objective quality of being obligated not to exist, this obligation being caused by the very laws that made the event possible and, indeed, necessary (minus the willpower involved, perhaps)? Preposterous! Laws do not combat one another. Obligation is, in fact, a human concept pertaining to the ideal world of each of our dreams. How did we get this idea of an ideal world (that can differ from individual to individual)? You can believe what you wish, but it seems pretty emotional to me.

And even if you disagree with the above, no one has provided a logical argument that concludes with an ought statement using only is-statements as premises (the is-statements being devoid of words such as “good,” “should,” etc.). You’re welcome to try.

Let me give an example:

1. Murder is the intentional, premeditated killing of a human, motivated only by malice and commited by a human.
2. Bob has murdered a person.
3. ???

C. Bob should not have murdered.

Please fill in the blank, using an is-statement, to make the argument valid. Or you can use more premises, if you need to. But if you can’t make this argument valid, I won’t be convinced that morality is objective.

 

[Prodigal_Son]

True. But I still think it stands that it’s unreasonable to assume that an object exists without any sort of indicator that it exists. What sense, induction, or deduction have we used to determine that morality exists?

I don’t think so. A statement that expresses truth is a fact, correct? What do all facts look like? Well, they might look something like, “There are more than seventy Playstation 2 games in my room.” This is a fact, because a) we can test its truth value since “my room” and “Playstation 2 games” can be proven to exist or not, and b) the statement passes the test. As I’m sure you know, everything mentioned in the fact (or, before it is tested, a proposition) must correspond to reality in some way or it won’t have a truth value.

But the reference of these truth values need not be physical!

2+2=3

The above statement is false. It is not false because two sticks piled on two sticks makes four sticks. It would be false even if there was only one object in existence. Its truth or falsity is not contingent upon any physical object.

Consider two propositions: “My hat is on” and “Two plus three is five”. The word “is” in these two sentences is used in completely different ways, is it not? The first sentence means that, in the world of physical objects, the object “my hat” occupies a place on my head. The second sentence means what? What does it refer to? Does it refer to the “world of mental objects”? Or, at least, to some type of truth that cannot be seen? If not, how is it true?

A set of sentences:

1. Reality contains mathematical truth.
2. If reality contains mathematical truth, then there may be other kinds of truth that reality contains.
3. We have access to mathematical truth because of the intuitions of our rational minds.
4. If we did not have these intuitions, we would not know mathematics.
5. We also have intuitions about morality, intuitions which are phenomenally similar across generations and cultures.
6. Moral truth may be one other kind of truth that reality contains.
7. If moral truth is one other kind of truth that reality contains, then we only know it because of the intuitions of our rational minds.

Now, when we say that murder is wrong, “wrong” is usually meant in the sense that the object, murder, should not exist. If we look at morality as objective, then this is to say it is obligated, by the laws of nature, to cease existing.

That’s not what I mean by wrong. I mean that a rational person is obligated not to murder. I make no existential claims.

How can an object or process possess the objective quality of being obligated not to exist, this obligation being caused by the very laws that made the event possible and, indeed, necessary (minus the willpower involved, perhaps)? Preposterous!

“Murder” has no obligations, nor any properties. It does not exist, except as an affective relationship of a person toward his intentions.

Let me give an example:

1. Murder is the intentional, premeditated killing of a human, motivated only by malice and commited by a human.
2. Bob has murdered a person. * (I ignore this premise).*
3. Bob is a person.
4. All persons are internally compelled to follow moral laws, although they may resist this compulsion.
5. Bob is internally compelled to follow moral laws, although he may resist this compulsion.
6. There exists a moral law against murder, which Bob has access to (through his intuitions).

C. Bob is internally compelled not to murder, although he may resist this compulsion.

I took out the word “should” in the conclusion, because I think it is unnecessarily vague. Here is the key: insofar as he is a person (what the Church would call “fully human”), Bob will not murder.

Prove to me that such a moral law being true is less likely than the laws of logic being binding. You can break moral laws, just like you can break laws of logic. Either trespass can lead to very bad results, although these results have nothing to do with the validity of the laws. If someone breaks a law of logic, they are in error. If someone breaks a moral law, they are in sin.

(Please note: people’s intuitions about morality are not always right, but they are obligated – read: internally compelled – to follow their intuitions even as they educate their intuitions).

 

[tdgesq]

True, but I think you’re missing the point.

I’m pretty sure I haven’t missed the point. You proposed that irreducibility is a test of what justifies an axiom. I simply pointed out that the proposition “my senses are reliable” presupposes that you exist. I would add that it also presupposes that propositions contain logical content. So I’m having a difficult time understanding how reliability of the human senses is “irreducible.” Irreducible in what way? Certainly not in the sense that it doesn’t depend upon other axioms – other presuppositions.

Would you say that it’s reasonable to assume that an object exists before you’ve sensed it or induced/deduced that it exists based on what you’ve already sensed? Through the use of no intuition of your own, senses or otherwise, you’ve concluded that an object (morality) must exist. I know you haven’t assumed this. I know that no one would assume this. So how does one go about coming to this conclusion?

There are a number of serious problems with your assertions here. First, laws of morality are not physical objects, just like laws of logic are not physical objects. Second, it is quite reasonable for most of us to assume that physical objects exist before we’ve sensed them. There are many objects I haven’t sensed that I still assume exist. Subatomic particles come to mind. Maybe you meant that our knowledge of these things still come about through the senses. Finally, you’ve subtly and perhaps unknowingly shifted the standard of justification from “irreducibility” to “reasonableness.” It’s perfectly fine to do that. You can require both. It’s just that now we need to determine what “reasonableness” consists of.

Uh, yeah. The definition does.

…To clarify, an axiom is not irreducibility, it just possesses the quality of being irreducible.

I stated in the OP that I already know what the definition of an axiom is and that what I’m interested in is the justification for axioms. So when I ask things like “what makes an axiom” or “when do we decide that a proposition qualifies as an axiom” I’m obviously asking about justification, not the definition.

I already did. The utility of the system constructed by the axioms justifies the axioms. The axioms of mathematics and those of the scientific method are justified because both systems have served us well. Your original question was not asking what an axiom was but what justifies one.

I thought “irreducibility” and “reasonableness” or some combination of both were the justification for axioms? If you want to add “utility” to the mix, that’s fine. Notice that if utility is the only standard then the axiom doesn’t actually need to be true so long as it serves us well. It appears to me that objective morality could provide enormous utility.

 

[Oreoracle]

But the reference of these truth values need not be physical!

2+2=3

The above statement is false. It is not false because two sticks piled on two sticks makes four sticks. It would be false even if there was only one object in existence. Its truth or falsity is not contingent upon any physical object.

True, but numbers aren’t objects, they are concepts. This doesn’t counter my argument, because we’re talking about two entirely different things.

[qute]Consider two propositions: “My hat is on” and “Two plus three is five”. The word “is” in these two sentences is used in completely different ways, is it not?

I agree…

The first sentence means that, in the world of physical objects, the object “my hat” occupies a place on my head. The second sentence means what? What does it refer to? Does it refer to the “world of mental objects”? Or, at least, to some type of truth that cannot be seen? If not, how is it true?

For the sake of convenience, let’s call mental objects “concepts” from now on. I think this will prevent confusion.

Anyway, “is,” in this case, is used as a means of inference: we are saying that, given the arbitrary values we’ve assigned the labels “two” and “three” to, their relationship–that is, their being added–will make them equal to another arbitrary, conceptual value: “five.”

Personally, I wouldn’t say that “two plus two equals five” is true, but rather valid. Truth deals with objects, validity deals with concepts.

“Murder” has no obligations, nor any properties. It does not exist, except as an affective relationship of a person toward his intentions.

Of course. I mean that murder produces something you consider to be evil.

1. All persons are internally compelled to follow moral laws, although they may resist this compulsion.

And here’s the problem. Upon trying to prove the existence of a moral law, you assume that moral laws exist.

1. Bob is internally compelled to follow moral laws, although he may resist this compulsion.

1. There exists a moral law against murder, which Bob has access to (through his intuitions).

A separate argument has to be made to support the existence of these moral laws that you’ve assumed. Still, you may be right that we feel that murder should not occur, but it does not follow from this that murder is objectively wrong. Again, “should” is a word we use as a transition from the world that is to the world of our desires. “Murder,”–an object of this world–“should not occur.”–would not be present if the world would be as I want it to be.

(Please note: people’s intuitions about morality are not always right, but they are obligated – read: internally compelled – to follow their intuitions even as they educate their intuitions).

Why are we obligated to do what we feel we are obligated to do? Doesn’t that strike you as being circular?

 

[Oreoracle]

Personally, I wouldn’t say that “two plus two equals five” is true, but rather valid. Truth deals with objects, validity deals with concepts.

LOL. I knew it would happen one day. I said that two plus two equals five because I had to rush when making this post. Please disregard that and other silly errors.

 

[Prodigal_Son]

True, but numbers aren’t objects, they are concepts. This doesn’t counter my argument, because we’re talking about two entirely different things.

How can a concept be true?

What is 5+4? There is a fact of the matter, is there not? This fact is objective; it is not merely true because of how I define the terms. Likewise, when I say modus ponens is a valid form of reasoning, I am speaking to something that is objectively true.

It could be the case that there is no objective truth to moral statements. But it could also be the case that there is an objective truth to moral statements, analogous to the objective truth of logical claims.

A completely different (and seemingly irrelevant) question: If I look out my window and see a flash of light in the sky, am I justified in thinking it is an alien spaceship?

Anyway, “is,” in this case, is used as a means of inference: we are saying that, given the arbitrary values we’ve assigned the labels “two” and “three” to, their relationship–that is, their being added–will make them equal to another arbitrary, conceptual value: “five.”

A comment on the word “arbitrary”. The word used to refer to a number is arbitrary. There is nothing arbitrary about the number itself.

Personally, I wouldn’t say that “two plus two equals five” is true, but rather valid. Truth deals with objects, validity deals with concepts.

By your own admission, then, the above two statements cannot be true.

(There is, of course, the problem of reference. We can never “deal with” objects, in words. Words (except names) are perfect universals, which seems to make truth – in the sense you gave above – entirely inaccessible to us?)

And here’s the problem. Upon trying to prove the existence of a moral law, you assume that moral laws exist.

Hence tdgesq’s claim that “moral laws exist objectively” is an axiom.

I wasn’t trying to *prove *that moral laws exist. Such a thing can neither be proven nor disproven. You asked how we can get an ought from an is – I was showing you one interpretation that will get you there. And yes, it uses an axiom along the way.

Again, “should” is a word we use as a transition from the world that is to the world of our desires.

Whereupon the Christian would claim that the world of our desires exists – hence the insistence that we live as if we were there.

Why are we obligated to do what we feel we are obligated to do? Doesn’t that strike you as being circular?

My point in that afterthought was simply this: the human conscience is capable of being misled. This changes the “should”, until such time as the conscience is restored. A man who honestly doesn’t think stealing MP3s is wrong is not sinning, despite the fact that stealing MP3s is wrong.

 

[Prodigal_Son]

LOL. I knew it would happen one day. I said that two plus two equals five because I had to rush when making this post. Please disregard that and other silly errors.

Didn’t even notice. It becomes even more silly, considering my reply!

 

[Oreoracle]

How can a concept be true?

A concept can only be true if all of its elements correspond with reality. Numbers only represent some factors of reality (such as non-contradiction and the existence of multiple objects that react to one another), and do not necessarily correspond with it. There’s nothing in reality that we can label “five.” We can use “five” to describe a group of objects, but we can’t say, “What you are observing is five.” We instead say, “What you are observing are five [insert name of objects here].”

What is 5+4? There is a fact of the matter, is there not? This fact is objective; it is not merely true because of how I define the terms.

I’m not so certain. If five is not an arbitrarily set value–that is, a concept that we create for the purpose of devising a useful representative system–then where is the concept derived from? As I said above, it’s certainly not something we’ve observed.

Likewise, when I say modus ponens is a valid form of reasoning, I am speaking to something that is objectively true.

I’m having a problem with your usage of “true.” “There is a computer in my house” is true, because it is a statement whose elements correspond with the tangible world. But this is a separate kind of truth from what you’re using. I’m not necessarily addressing modus ponens here, but if we’re talking about the “truth” of logical laws, then the truth value of such laws is solely determined by their consistency with the system they constitute. “2+2=4” is true, in this sense, because it is a statement that is consistent with the accepted axioms, postulates, and theorems of mathematics. In this case, we are not extrapolating, attaching the elements of the equation to objects of reality, or reaching outside the system of mathematics in any way. Thus, true mathematical equations are very unlike everyday factual statements, such as “there is a computer in my house.”

So we have logical truths and objective truths. Do you agree with this dichotomy? If so, can we say that logically true statements are simply “logically valid” to prevent confusion?

It could be the case that there is no objective truth to moral statements. But it could also be the case that there is an objective truth to moral statements, analogous to the objective truth of logical claims.

I’m having trouble catching your meaning here. While I think that ethics in themselves are meaningless in that they don’t correspond with reality, objectivity is certainly involved in ethical deliberation. We must take in information to come to ethical conclusions, right? You’ve seen what death does to society, and how it can easily result when malice is involved. You’ve realized from a young age that when someone has passed away, they won’t be around to comfort or provide for you anymore. This information that you’ve gathered is very unsettling to you, I’m sure. It might even surprise you and others that people would be capable of feeling any other way. Could these feelings contribute to the claim that murder is wrong? When I say that ethics are subjective, this is, in fact, all that I mean. In itself, “murder is wrong” is meaningless, but if we look at the context in which the claim is made, it makes perfect sense.

I’m sorry, I’ve got to run again. Dad needs me to help with some errands. Later.

 

[geometer]

Could these feelings contribute to the claim that murder is wrong? When I say that ethics are subjective, this is, in fact, all that I mean. In itself, “murder is wrong” is meaningless, but if we look at the context in which the claim is made, it makes perfect sense.

I’m sorry, I’ve got to run again. Dad needs me to help with some errands. Later.

Everyone one earth is a subject, this is what life is about, being a subject. That which is subjective is all meaning. There is nothing that is subjective that is not meaningful.

Objectivity, simply means subjects toss around ideas about demonstratable properties of objects.

Subjective has nothing to do with meaninglessness. We can quantify all of the observable properties of objects. Since it all becomes reduced to pure mathematical abstracts. It can be played with by the logical toys of your choice.

Philosophers have an immature facination with the machinery of logic. Somewhat like the autisic child who is endlessly entertained by spinning a jar lid on the kitchen floor…