Does morality exist?

[Betterave]

Ender: Bravo, Ender, bravo. You are really hitting it out of the park, here.

Yes, let’s hear the reason that murder is immoral. So far, we’ve heard the rather unconvincing argument, “It just is.”

This is too silly. If you’re not interested in reading, at least trying to understand, and responding honestly to what others have to say, don’t bother responding at all.

Ender wrote:

“If you cannot show that murder is immoral then you clearly cannot claim that morality exists.”

…But this was after stipulating that, by definition, murder (as such) is not immoral (it is only unlawful). If, by definition, murder is not immoral, then it is absurd to propose that someone show that murder is immoral.

 

[AntiTheist]

Ender is saying that by definition murder is illegal. We’re not talking about the legality of it. We’re talking about what makes it immoral in your view. You can’t just say, “I define it to be immoral” because then you’re just declaring that you’re right. That would be the exact equivalent of saying, “It just is.”

See that? I’m paying very careful attention to your argument, which is why you can’t pull a fast one on me.

What is the basis on which you make the claim that something is “immoral”? What is it about murder that makes it “immoral”?

 

[Ender]

Don’t you think that the unlawfulness of murder is grounded in its being wrong?

Whether it is grounded in the fact that it is wrong or on the perception that it is wrong is yet to be determined.

Anyway, *if *murder is merely ‘unlawful’ killing, then murder is *not *inherently immoral (*unless *the laws it contravenes are *moral *laws); therefore, your bolded claim above is incoherent.

I said nothing about it being “merely” unlawful; I said that the definition pertains only to its legality, not its morality. It could be illegal and amoral as well as illegal and immoral; there is nothing incoherent about it. The definition makes no statement one way or the other about the morality of murder.

Ender

 

[Betterave]

Ender is saying that by definition murder is illegal. We’re not talking about the legality of it. We’re talking about what makes it immoral in your view. You can’t just say, “I define it to be immoral” because then you’re just declaring that you’re right. That would be the exact equivalent of saying, “It just is.”

See that? I’m paying very careful attention to your argument, which is why you can’t pull a fast one on me.

What is the basis on which you make the claim that something is “immoral”? What is it about murder that makes it “immoral”?

Okay, thanks Anti, I can see you genuinely tried this time. Now try to slow down and actually understand the conceptual structure of what is going on here (Ender missed it too). Reread my argument where I claimed that murder is defined as immoral killing. Now see what happens when we say murder is defined as unlawful killing (it makes no difference):

“Murder is unlawful killing” - that’s true by definition.
“Some killings (including some ‘murders’ now) are morally justified” - true.
“This particular killing was justified” - we might not be able to say.

Now the point of the argument was made in the comparison:

Pneumonia is a lung infection. (True by definition)
Some cases of pneumonia are fatal, some are not. (True)
It was pneumonia that was responsible for Bill’s death. (We might not be able to say.)

The point was that if we don’t know the truth value of certain moral propositions, it does not follow that morality is not objective/real or that moral propositions are not subject to cognitive appraisal (any more than those claims would follow in the case of pneumonia). Got it?

 

[Ender]

The thought of asking someone to prove that murder is immoral actually occurred to me in another context. We have all been asked to prove why something we condemn is immoral; homosexuality is a good example of this type of question. Such demands cannot be satisfied without an agreement about morality itself and, without that, it is worse than useless to even try to answer these questions because it cannot be done and simply reinforces in the challenger the perception that his position is justified.

It was in trying to deal with such questions that it occurred to me to require the challenger to define his basis for morality, and then reply to his demand by using the ground rules he has specified. So whenever someone asks me (e.g.) why homosexuality is wrong I respond by saying I can only answer his question if he can tell me why murder is wrong. This forces people to address the basis for their morality and quite frankly they have by far the more difficult task.

Ender

 

[Betterave]

I said nothing about it being “merely” unlawful**[False - you said that by definition (i.e., as far as the definition goes) murder was merely unlawful, and not, as far as the definition goes, immoral. This means that it is idiotic to ask the abstract question “is murder immoral?” - in such a case, where murder is not immoral by definition, we require more details, as I’ve repeatedly stated!]**; I said that the definition pertains only to its legality, not its morality. It could be illegal and amoral as well as illegal and immoral; there is nothing incoherent about it. The definition makes no statement one way or the other about the morality of murder.

“If you cannot show that murder is immoral then you clearly cannot claim that morality exists”

this claim implies:

“murder is not immoral” is a sufficient condition for “morality does not exist”

Think about this! Do you understand what you’re saying? Why on earth would you think such an entailment obtains?
It further implies (by contraposition):

“morality exists” is a sufficient condition for “murder is immoral”
i.e.: If morality exists, then murder is immoral.

Now how on earth do you propose to defend that proposition and how is it relevant anyway?

(If “murder is immoral” were true, it would imply that murder is intrinsically immoral (i.e., that murder *qua murder *is immoral) - do you understand that?)

 

[Syntax]

I can’t see how it wold make any sense to say so.

Why? There’s nothing logically inconsistent about it. You mean to say “I don’t want to make any sense of it because I think every property is really a relation.”–But this is just a groundless assumption.

**I keep saying that there is nothing to say about a number that is not to express a relation between 4 and something else, and to refute my claim you tell me 4 is divisible by 2??? I don’t speak symbolic logic, but isn’t it obvious that saying that 4 is divisible 2 is relating the number 4 to the number 2? **Maybe you’ll want to try again to give me a “property” of 4 that is not just as assertion of a relationship between 4 and something else.

I do give you properties of “4”: being-prime, being-divisible-by-2. You just seem to think if you can get away with using “relation” carelessly enough you can demonstrate all properties are relations. This is irresponsible, lazy, and dishonest. I am asking you to specify that relation. Make it explicit. Write it down. Why is this so hard for you? Are you exempt from making critical distinctions? Just because you equivocate word-meanings doesn’t entail your view is correct. Your lazy and haphazard analysis continues to confuse the following kinds of statements as if they were the same thing.

Operations
Relations
Predications

For a statement *to be *a relational statement, it must have one of the following features–and I’m not just “making this up”! The relation must be

reflexive
symmetrical
asymmetrical
transitive

…or some variation of these.

4<5 is a relation because it relates 4 to 5. It is an asymmetrical relation because it holds one way, but not the other (in virtue of 4 and 5 being different numbers–which is immediate evidence for 4 and 5 having intrinsic properties).

4=4 is an identity relation. It relates 4 to itself. All identity relations are symmetrical and reflexive, because when you switch the order of the terms and relate anything to itself, the relation is still true (unlike the above example).
.
If 4<5, and 2<5, then 2<4. This is **asymmetrical **and transitive because the relation holds for one direction but not the other, and this same asymmetry is carried from one set of relata to the other.

But how are the following operations relations???

4+1
4/2
4*3

None of these statments relate the first number to the second, but operate on both numbers to indicate another number. The operations “+” “/” “-” and “*”, along with their numbers flanking them, merely express another sum, quotient, and product respectively, that is, 5, 2, and 12. They are functional descriptions mapping numbers to other numbers, in this case, themselves. So expression like “4/2” indicate one and only one answer, just like “the teacher of Alexander the Great” is a description which indicates one and only one person, namely, Aristotle. But the expression “the teacher of Alexander the Great” itself does not relate “the Teacher of Alexander the Great” to "Aristotle, only the “=” sign does that. You continue to confuse the relation with the relata the relation relates.

Now “4+1”=5 is a relation, namely, the relation of identity of a thing to itself. And no thing can have this relation unless it is, in fact, identical to itself. But “4+1” is not a relation because it is not relating “4” to “1”; instead, it is an operative description of another number, namely, the number 5,

So “+” “-” “/” and “*” are operations which, together with their numbers, indicate another number. So the expression “4/2” is a description, not a relation because there’s nothing about it expressing the (a)symmetry, (ir)reflexivity, or (in)transitity between the two different numbers! Where are these features, Leela, that qualifies these operations as relations? You provide no demonstrations.

“<” “=” are relations

“being-prime,” “being-divisible-by-2,” and “being-irrational” are predicates

 

[Syntax]

I made an honest blunder: being prime is not a property of four.

But this property is a good example, nevertheless. I would like you, Leela, to give me a re-write of the statement “1 is a prime number” using a relation that expresses exactly what it says preseving the statement’s original meaning. If you can’t, then “being prime” is **not **a relation: Q.E.D

 

[Syntax]

Leela, I strongly recommend reading Frege’s famous “Foundations of Arithmetic” and “Function and Concept,” both of which provide an in-depth analysis of the distinctions in mathematics between,

properties like being prime, being even
relations like < and =
formula like 2x=y which admit of multiple answers mapping numbers to a line.
functional descriptions like 4+1 which maps numbers to the true and the false.

For instance, 4+1 is a functional description mapping numbers to the true and false. In this case, the only number that satisfies the description is 5. So if you plug in 5 as in 5=4+1, you get the answer “the true.” If you plug in 2, 3, 1 to the function as in 2=4+1, 3=4+1, and 1=4+1 you get the answer “the false.”

 

[Leela]

I made an honest blunder: being prime is not a property of four.

But this property is a good example, nevertheless. I would like you, Leela, to give me a re-write of the statement “1 is a prime number” using a relation that expresses exactly what it says preseving the statement’s original meaning. If you can’t, then “being prime” is **not **a relation: Q.E.D

1 is not a prime number

 

[Leela]

I do give you properties of “4”: being-prime, being-divisible-by-2. You just seem to think if you can get away with using “relation” carelessly enough you can demonstrate all properties are relations. This is irresponsible, lazy, and dishonest.

Irresponsible, lazy, and dishonest? Can’t you be charitable enough to imagine that we may just have an honest disagreement?

I am using the word “relation” in a very usual way that the dictionary supports. When you say that 4 is divisible by 2, you are expressing one way in which these two numbers relate to one another.

I’ve lost sight of what your point is. Is it important to you to say that 4 is not related to other numbers for some reason? Is there something important that I need to know about 4 that does not involve telling me how 4 is related to other numbers? If so please tell me!

And does any of this have anything to do with the existence of morality? If not we should probably start a new thread.

I am asking you to specify that relation. Make it explicit. Write it down. Why is this so hard for you? Are you exempt from making critical distinctions? Just because you equivocate word-meanings doesn’t entail your view is correct. Your lazy and haphazard analysis continues to confuse the following kinds of statements as if they were the same thing.

I really don’t know what you are getting at here. You are asking me to specify how 4 is related to 2? You’ve already alluded to one way in that 4/2 is is an integer (which is equivalent to saying that 4 is divisible by 2). There are lots of other ways such as the fact that 6-2=4. There is no single relation if that is what you are trying to get me to “specify.” My point has been and still is that there is no particular way of relating 4 to other numbers that should count as the essence of 4-ness since all such relations are on a par.

For a statement *to be *a relational statement, it must have one of the following features–and I’m not just “making this up”! The relation must be

reflexive
symmetrical
asymmetrical
transitive

…or some variation of these.

The above shows a lack of imagination. These are not the only ways that a number can relate to another number. In fact, there are at least as many ways that a number can relate to another number than there are numbers, which is a pretty far out though no less true thing to say as than are an infinite number of numbers. I think it is even a “bigger infinity” as Georg Cantor talked about such things.

4<5 is a relation because it relates 4 to 5. It is an asymmetrical relation because it holds one way, but not the other (in virtue of 4 and 5 being different numbers–which is immediate evidence for 4 and 5 having intrinsic properties).

This is not evidence of intrinsic properties of 4-ness unless all you mean by intrinsic property is any particular way of relating 4 to other numbers. Such intrinsic properties are a dime a dozen. But then I wonder why you would call such a thing an intrinsic property when it only manifests as a relation to such numbers as 5 and 17?

4=4 is an identity relation. It relates 4 to itself. All identity relations are symmetrical and reflexive

, because when you switch the order of the terms and relate anything to itself, the relation is still true (unlike the above example).

Ok. These are pretty boring sort of relation, aren’t they? But they are important to mathematics. If we didn’t declare them as true, we couldn’t get much done.

But how are the following operations relations???

4+1
4/2
4*3

I follow that these are not really relations until you say what hey are equal to, just as the statement “4 is divisible by 2” relate 4 and 2 by pointing out that there quotient is an integer, but just saying “4/2” just puts the two number near one another and suggests what we ought to do with them.

Fun fact! Do you realize that in mathematics functions are special types of relations?

So expression like “4/2” indicate one and only one answer, just like “the teacher of Alexander the Great” is a description which indicates one and only one person, namely, Aristotle. But the expression “the teacher of Alexander the Great” itself does not relate “the Teacher of Alexander the Great” to "Aristotle, only the “=” sign does that. You continue to confuse the relation with the relata the relation relates.

The fact that there is only one answer suggests a special kind of relation called a function.

Now “4+1”=5 is a relation, namely, the relation of identity of a thing to itself. And no thing can have this relation unless it is, in fact, identical to itself. But “4+1” is not a relation because it is not relating “4” to “1”; instead, it is an operative description of another number, namely, the number 5,

So “+” “-” “/” and “*” are operations which, together with their numbers, indicate another number. So the expression “4/2” is a description, not a relation because there’s nothing about it expressing the (a)symmetry, (ir)reflexivity, or (in)transitity between the two different numbers! Where are these features, Leela, that qualifies these operations as relations? You provide no demonstrations.

“<” “=” are relations

“being-prime,” “being-divisible-by-2,” and “being-irrational” are predicates

Your mistake in all this other than the prime business you already mentioned is that “being divisible by 2” is not “4/2” but rather “4/2 is an integer.” If you have more questions, I can probably help. I’m pretty good at math.

Best,
Leela

 

[Syntax]

reflexive
symmetrical
asymmetrical
transitive

**The above shows a lack of imagination. These are not the only ways that a number can relate to another number. **…I am using the word “relation” in a very usual way that the dictionary supports. When you say that 4 is divisible by 2, you are expressing one way in which these two numbers relate to one another.

I can’t think of any other relations that don’t satisfy at least on of these structural forms. If you think there are more types of relations, then tell me what they are and give examples.

The “dictionary”? Does there exist some colloquial use specified in the dictionary that I am not aware of that doesn’t fall into one of the other structural features of relations I’ve listed above? Are you privy to some kind of unique relations that are neither (a)symmetrical, (ir)reflexive, (in)transitive, etc? Tell me what they are. Your colloquial dictionary business doesn’t help here.

I’ve lost sight of what your point is. Is it important to you to say that 4 is not related to other numbers for some reason? Is there something important that I need to know about 4 that does not involve telling me how 4 is related to other numbers? If so please tell me!

Of course not. Numbers have relations to other numbers; I’ve already listed examples. I am claiming that the intrinsic properties of numbers are not reducible to their extrinsic relations to other numbers (which is what you are proposing). E.g. being-prime.

I really don’t know what you are getting at here. You are asking me to specify how 4 is related to 2? You’ve already alluded to one way in that 4/2 is is an integer which is equivalent to saying that 4 is divisible by 2. There are lots of other ways such as the fact that 6-2=4.

The bold-faced is false. The statement that “4 is divisble by 2” does not have the same meaning as “4/2 is a description that designates the number, 2.” The first is a predicative statement saying 4 has a property of being divisible-by-2. The second expresses the** identity relation **that a number has to itself 4/2=2.

There is no single relation if that is what you are trying to get me to “specify.” My point has been and still is that there is no particular way of relating 4 to other numbers that should count as the essence of 4-ness since all such relations are on a par.

This is the problem: you seem to think 4 must stand in relations to other numbers in order to “count as having an essence,” as you say. I am saying the reverse: 4 cannot stand in relations without having intrinsic properties. (I don’t like the use of “essence”–“intrinsic properties” is a better label.) The structural form “Rx” is both logically and explanatorily prior to “xRy.”

This is not evidence of intrinsic properties of 4-ness unless all you mean by intrinsic property is any particular way of relating 4 to other numbers.]

I have this said before: intrinsic properties are the only way we can specify the truth-confitions of mathematical relations–relations alone cannot do this because they don’t have that capacity. For instance, the only reason we have for explaining why 5>4 is true and 4>5 is false, is that the numbers 4 and 5 are intrinsically different from the other. We can’t account for the truth of the one and the falsity of the other by appealing to the relation of “>” alone. The relation itself doesn’t tell us why “4>5” is false and “5>4” is true. This should be obvious.

I follow that these are not really relations until you say what hey are equal to

That’s correct.

just as the statement “4 is divisible by 2” relate 4 and 2 by pointing out that there quotient is an integer.

The first part is false. “4 is divisible by 2” is a statement predicating divisibility to 4; it is not a statement relating 4 to the number 2. In addition, “4/2” is an operative description that designates a number, namely, 2; neither is it a relation nor a name for a number like “2” is a name for 2.

I am pretty sure there are many more semantic distinctions going on with these expressions than you are willing to admit. I really disapprove of the colloquial gloss that every expression is a relation–simply because this idea doesn’t hold water at all when you begin analyzing all the structural and syntactical differences of these expressions.

but just saying “4/2” just puts the two number near one another and suggests what we ought to do with them.

That sort of sounds right…

 

[Syntax]

Fun fact! Do you realize that in mathematics functions are special types of relations?

I wouldn’t call functions “relations.” I would call them “functions.” Functions require (name removed by moderator)uts to generate outputs, so functions without (name removed by moderator)uts are “unsaturated,” whereas relations are “saturated.” Functions map (name removed by moderator)uts to outputs, but they aren’t static like relations are because they admit of multiple values or (name removed by moderator)uts.

For instance, 5>4 is a static relation which informatively tells us the explicit relationship that holds between the numbers 5 and 4. On the other hand, 2x+x is a function that admits of multiple (name removed by moderator)uts generating multiple outputs. So when the (name removed by moderator)ut is the number 2, the corresponding value is 6. So the function maps 2 to 6 and its corresponding object is a line. But the same function also maps 3 to 9 when the (name removed by moderator)ut is 3. So a function is not informing us of the particular relationship that holds between any two numbers. It simply pairs different **sets **of numbers together to form a line.

Your mistake in all this other than the prime business you already mentioned is that “being divisible by 2” is not “4/2” but rather “4/2 is an integer.” If you have more questions, I can probably help. I’m pretty good at math.

I already explained the differences between the three expressions above.
(1) “being divisible by 2”–is a predicate…like “being red”

(2) “4/2”–is an operative description which indicates, or refers, to an integer…like “the teacher of Alexander the Great.”

(3) “4/2 is an integer”–is a proposition which ascribes the property “being an integer” to the the object designated by the operative description “4/2.” This has the exact same form as “the teacher of Alexander the Great is a philosopher.”

(The number 1 was considered prime by mathematicians up until the 19th century, by the way.) The point is that you can’t re-translate the predicative statment “3 is a prime number” by using the syntactical structure of a relation. I’d like to see it if you could succeed.

 

[Syntax]

Leela,

Here are some further distinctions.

Functions like 2x+x=y have relations as instances, but the function itself is not a relation:

2(2)+2=6 is a relation
2(3)+3=9 is a relation

Morever, the truth-conditions for functions and relations are completely different:

The truth condition for a function is the line indicated by that function.

The truth condition for a relational equality is simply the self-identity of the number indicated by the expressions flanking the equality sign.

The truth condition for the relations “<” and “>” are the numbers indicated by the expressions flanking the relation and where they are placed. This is precisely why numbers can’t be relations. Like I’ve said, the relations alone don’t tell us why these different expressions are true or false. We also need to appeal to the numbers themselves as partly consisting of the truth conditions for the expression.

 

[Greg27]

I think it depends on what is meant by ‘objective’ and ‘subjective.’ Does objective morality mean moral norms and laws are objective only if a God promulgates them? If this claim is correct, then obviously morality is ‘subjective’ if by subjective you mean humans are the creators of moral principles and norms if God does not exist.

But I think we need to take care in arguing that the non-existence of God means that everyone is a law unto themselves and no moral principles exist. Clearly atheists don’t go around killing, robbing or harming other people, and most obey the law. So clearly it is possible to believe moral norms exist and it is necessary to obey them, even if you are an atheist. Many atheists also lead good lives.

I also think the notion moral absolutes or laws cannot exist without God’s existence can be refuted. Many philosophers, i.e. Immanuel Kant, Aristotle, or the Buddha, proposed moral norms that were absolute (i.e. the categorical imperative or the duty to not harm others) without appealing directly to God. It can be admitted that Kant’s moral philosophy didn’t dispense entirely with theism, but Kant ruled out direct knowledge of God by reason, which in effect means the principles of morality must be determined by human practical reason and rationality. Similarly in law, Hugo Grotius proposed as far back in the 17th century that absolute legal norms derived from natural law can still exist and bind even if God did not exist (though Grotius was not an atheist). The Stanford Encyclopedia article on Grotius for example writes “Instead of emerging from or being otherwise dependent on God, the fundamental principles of ethics, politics and law obtain in virtue of nature.”

Likewise, John Finnis proposes his natural law theory is not necessarily dependent on prior recognition of God’s existence, and he is a Catholic jurist. See Beverly Hinton, (2003), ‘A Critical Look at Finnis’s Natural Law Ethics and the Role of Human Choice’, 37 Journal of Value Inquiry 68, 68-91, springerlink.com/content/wx140002qx443861/fulltext.pdf

I think then it is on the onus of theist to demonstrate that objective morality is impossible without God, and (the somewhat more unrealistic claim) people won’t behave morally unless theistic morality prevails. I personally think the moral principles the best of theistic and religious thinking develops is similar to the best principles of secular ethical systems. This is probably because rational analysis of ethical and moral problems on either theistic or non-theistic grounds develop similar principles (i.e. the sanctity of life).

The major difference is divine command systems of ethics, i.e. based on a revealed text. Secular ethicists seem less willing to condemn acts like homosexuality, contraceptive use or abortion than Catholic ethicists are willing to do on the grounds of divine revelation and divinely revealed natural law. It is harder in this case for secular and religious ethicists to agree since to the secular ethicist, the prohibitions against things such as abortion on divine revelation or church tradition seem irrational and arbitrary, while to the theistic ethicist, the acceptance or approval of such things can seem to manifest the worst of heathen sin and ignorance of divine and natural law.

I think it is possible for religious and non-religious people to agree general principles and norms of morality and justice exist and should be recognised and protected in any rational system of morality (i.e. that human life should be valued and not taken away arbitrarily) but the application of such principles in specific situations and cases (i.e. abortion, self-defence, just war, euthanasia, etc) diverge because different theistic and secular systems of morality give different answers to problems posed in specific cases.

I think the task for theist and secular moralists is to give a rational ethical framework which is not absolutist and inflexible to the extreme and allows some grounds for mutual acceptance and recognition. The problems with ethical matters like abortion, the disputes over the rights of homosexual people to have legally recognised relationships, war and peace, povery and inequality, etc require more consensus and agreement across different religious and ethical divides. The extreme and hardline stance taken by religious people on these issues as well as the extreme relativism of some aspects of postmodern thinking don’t offer decent rational principles ordinary people can use for good moral decision making in these situations. It is also vital for society to have some conception of virtue and the common good in order to flourish.

I think then that moral absolutes can be defined, but it has to be done independent of proposing the existence of God or a divine source, since many people don’t believe or accept on the evidence God exists. Then in that case it will be easier for non-theists to accept moral absolutes if it is rational and not offensive to their conscientious decision not to believe in a deity for whatever reason.

 

[Leela]

The bold-faced is false. The statement that “4 is divisble by 2” does not have the same meaning as “4/2 is a description that designates the number, 2.” The first is a predicative statement saying 4 has a property of being divisible-by-2. The second expresses the** identity relation **that a number has to itself 4/2=2.

I’ve spent a lot of time in math classrooms, and “4 is divisible by 2” is always taken to be equivalent to “4 divided by 2 has a quotient that is an integer.” If that is not what you mean, then the only other possibility is that you are taking “4 is divisible by 2” to mean “4 can be divided by 2” and asserting this as an intrinsic property of 2. If this is what you mean, this is what you you should say, because divisibility has a more specific meaning. Anyway, is that what you mean?? If so, this is a particularly lousy candidate for an intrinsic property of 4 since literally any number can be divided by 2.

This is the problem: you seem to think 4 must stand in relations to other numbers in order to “count as having an essence,” as you say. I am saying the reverse: 4 cannot stand in relations without having intrinsic properties. (I don’t like the use of “essence”–“intrinsic properties” is a better label.) The structural form “Rx” is both logically and explanatorily prior to “xRy.”

No, I am not saying that for 4 to have an essence it must stand in relation to other numbers. Not at all. I am saying that 4 has no essence to speak of–that all there is to know about 4 is how it relates to other things.

I have this said before: intrinsic properties are the only way we can specify the truth-confitions of mathematical relations–relations alone cannot do this because they don’t have that capacity. For instance, the only reason we have for explaining why 5>4 is true and 4>5 is false, is that the numbers 4 and 5 are intrinsically different from the other. We can’t account for the truth of the one and the falsity of the other by appealing to the relation of “>” alone. The relation itself doesn’t tell us why “4>5” is false and “5>4” is true. This should be obvious.

Yes, and I’ve addressed this before as well. The “why?” you are looking for is simply that
5>4 and 4>5 both have inferential relationships with other relations. We could only say 4>5 if we were willing to give up our beliefs about these other relations such as 4=2+2 and 4=3+2 and 3>2, but neither of us are willing to do so.

Best,
Leela

 

[Leela]

I wouldn’t call functions “relations.” I would call them “functions.”

That is certainly up to, but in mathematics a function is a special kind of relation. A relation is just any mapping of a set of numbers to another set of numbers while a function is a relation where there is only one y-value in the range for every x-value in the domain.

Here’s a quiz. See if you can tell which of these relations is a function…

a. y equals the square root of x
b. x equals y squared
c. y equals x cubed

Fun fact! if the function also has the property that there is only one x-value for each y-value we can say that the function is one-to-one.

(a. is a function, b. is not, and c. is one-to-one)

I already explained the differences between the three expressions above.
(1) “being divisible by 2”–is a predicate…like “being red”

As mentioned earlier, in the way you seem to be using the term “divisible,” all you are saying is that 4 can be divided by 2 just as any number can be, so this so-called property doesn’t distinguish 4 from any other number, so it makes no sense to call it a property.

(2) “4/2”–is an operative description which indicates, or refers, to an integer…like “the teacher of Alexander the Great.”

(3) “4/2 is an integer”–is a proposition which ascribes the property “being an integer” to the the object designated by the operative description “4/2.” This has the exact same form as “the teacher of Alexander the Great is a philosopher.”

How is “being an integer” an intrinsic property? Isn’t saying that a given number is an integer a way of relating that number to a larger set of numbers. When you say “4 is an integer” you are saying that 4 is like others numbers in some way. Is there anything you can tell me about 4 without relating it to other numbers?

(The number 1 was considered prime by mathematicians up until the 19th century, by the way.) The point is that you can’t re-translate the predicative statment “3 is a prime number” by using the syntactical structure of a relation. I’d like to see it if you could succeed.

Saying that 3 is a prime number means that 3 is only divisible by 1 and itself. Saying so it to say how 3 stands in relation to 1 and itself as well as to all other integers, X, with regard to whether or not the quotient 3/X is itself an integer.

Best,
Leela

 

[Prodigal_Son]

Leela,

Perhaps we could boil down your conversation with Syntax into the following question: If number is merely expressive of relations, then what are these relations between? How can there be a relation without some *things *which are being related?

 

[Betterave]

The major difference is divine command systems of ethics, i.e. based on a revealed text. Secular ethicists seem less willing to condemn acts like homosexuality, contraceptive use or abortion than Catholic ethicists are willing to do on the grounds of divine revelation and divinely revealed natural law. It is harder in this case for secular and religious ethicists to agree since to the secular ethicist, the prohibitions against things such as abortion on divine revelation or church tradition seem irrational and arbitrary, while to the theistic ethicist, the acceptance or approval of such things can seem to manifest the worst of heathen sin and ignorance of divine and natural law.

Hi Greg,

I think this is off topic for the thread, but Catholic ethicists do not ground their analysis of the acts you mention in divine revelation, and ‘divinely revealed natural law’ doesn’t even make sense - to say that it is ‘natural’ just means that it can be known without divine revelation.

 

[Ender]

Now how on earth do you propose to defend that proposition and how is it relevant anyway?

You’re dithering. Either you can explain why murder is immoral or you can’t and if you can’t - or won’t even try - then you ought to acknowledge the probability that your position is unsustainable.

(If “murder is immoral” were true, it would imply that murder is intrinsically immoral (i.e., that murder *qua murder *is immoral) - do you understand that?)

Yes, that was the point of asking you to show that murder is immoral. If you can do it then you will have shown that objective morality exists … but if neither you nor anyone else can do it then it is a good indication that objective morality does not exist. That was the whole point of opening this thread.

Ender