it is not possible to know whether or not categorical imperatives exist

Defense: rehashing of the defense of premise 2: let X be a world with categorical imperative C. let Y be a world with categorical imperative not-C. Let Z be a world without categorical imperatives. C states that one ought to do action 'a'. (C <=>0a) not-c states that one ought not to do action 'a' (not-C <=> 0~a) thus '0a' is an element of X and not an element of Y and '0~a' is an element of Y and not X and both '0a' and '0~a' are not elements of Z. Let P1 be an observer in all three worlds and let P2 be a conveyer in all three worlds. P2 tells P1 '0a' in all three worlds. Note: while we have the about the imperatives in X, Y and Z; P1 does not. How would P1 be able to justifiably assign a truth value to C (justifiably believe C is true)? First let’s imagine the case of a hypothetical imperative with the same imperative that is in C: hypothetical imperative h(C) is in X, Y and Z. h(C) states "if one desires outcome 'b' and one has sufficient reason to assume that action 'a' will result in 'b', then one ought to perform action 'a'" [h(C) <=> ([D(b)&K(R(a,b))]->C); where D is the desire property, K is sufficient reason property, and R is the relation between two arguments where the first results in the second.] P1 will be able to justify assigning one truth value or the other to h(C) depending on whether or not he conforms with h (that is, whether or not he desires outcome b and has sufficient reason to assume that the action will result in the attainment of that outcome) the conditional ‘h’ in h(C) allows P1 to justifiably believe (or not believe) h(C), because h represents the condition of h(C)’s truth value. Given this, we know that we cannot use this method to find the truth value of C, as h(C) =/= C. C is an 'ought' without condition. Applying that condition and using it to justify the application of a truth value to C would be fallacious as such justification would only apply to the special case of C; h(C) but not C alone. Imagine P1 and P2 again. If P2 states C and P1 asks why, the answer 'because it’s a categorical imperative' is not a sufficient reason. If P2 gives an answer like "because you desire result 'b'" and then presents sufficient reason to believe that doing ‘a’ will result in ‘b’, P2 will have turned c into h(c). He has given a reason to assign a truth value to h(c) but not to c alone. For any action 'a', that you are categorically obliged to do, any reason given to explain why you ought to do so will be of the same form. You must first turn the categorical form of the imperative into a hypothetical form, before you provide a reason. Paradoxically, doing so does not provide a reason for the categorical form, but only to hypothetical form. Take away the conditional, and the reason no longer applies. For a human to have knowledge, they must have a justification for believing, a reason, be it empirical evidence or some line of logic to concludes to that statement. in the case of categorical imperatives, all such attempts to give a reason for believing the categorical imperative is true, without qualification, must first grant qualification to the categorical imperative, but doing so inevitably turns the categorical form of the imperative, into a hypothetical form. because of this, there is no way to provide a reason for granting a truth value to a categorical imperative, as all attempts will be granting such values to hypothetical forms of such imperatives rather than categorical. as there is no condition upon which P1 can justifiably assign a truth value to C alone (without adding the hypothetical) there exists no method in either X or Y that would help indicate the truth value of C. thus, (as we assume X, Y and Z are the same in all other ways except the truth value of C) X and Y are indistinguishable to any observer. X and Y represent worlds with opposing imperatives. Since those two world are indistinguishable, it follows they cannot be distinguished from a world where neither imperative is true (such as Z); Z us also a world without any categorical imperatives. Since the form of this explanation allows one to extrapolate to any number of such imperatives in any set of 3 such worlds, One may conclude that: p2)'a world with categorical imperatives and a world without categorical imperatives are indistinguishable from one another.' This is perhaps the most explicit way of demonstrating my second premise. My previous defenses were basically less rigorous forms of this. counter argument: my opponent claims that first my claim about something being controversial does not make it true and second, morality has been 'established' by theory of mind, cognitive empathy and moral inferential systems. This leads me to believe that my opponent misunderstands my objection. I was not using controversial in the sense he seems to think I was, and the idea that those things establish the basis of morality was the very thing I was attacking. after explaining how morality is not comparable to scientific practices (as there is no standard theory) and that they are at best comparable to mathematics (by this I was eluding to how there can be multiple, mutually exclusive but equally valid systems given certain postulates) my next statement was to elucidate that even that may not be the case due to the ‘controversy’ of the term 'morality'. What two people call 'moral' can be two entirely different things; that isn’t in dispute. Where the first person uses something like the bible as a moral compass, the second may use human wellbeing as his compass and the two may both coincide and contradict on different occasions. this is not unlike how the parallel postulate in Euclidian geometry leads to certain conclusions that its absence would not allow (such as in parabolic geometry). The problem of ‘controversy’ presents itself, because in cases of mathematics, postulates are assumed to be true. Whilst the results of the postulates will be objective given the postulates, the postulates themselves may or may not reflect reality. The objectivity/subjectivity of the postulates is irrelevant to the mathematician; they are simply extrapolating what would occur IF the postulates were true. The reason such axioms are not 'controversial' is because it is accepted amongst mathematicians that the postulates are assumed and that they may or may not reflect reality. This is not and cannot be the case for morality. That human wellbeing is 'the correct' basis for morality is not assumed by all. That is what I meant by 'controversial'. Unlike in mathematics where it is okay to assume something (since pure math isn’t talking about reality, its talking about the results of definitions of numbers and numerical systems) we cannot simply assume that in reality we have some universal categorical obligation to value human welfare. My opponent uses theory of mind, cognitive empathy and moral inferential systems as examples, but morality is first a word, and thus will mean something different depending on how two separate people use it. Morality is not like the word 'physics' or 'chemistry' where people that have different definitions may be ignored due to the existence of a standard theory. Since no standard theory of morality exists, there is no standard by which we may ignore other people’s disagreements upon definitions. the three examples and their related studies, all define morality exclusive to their own systems, but that those are the 'correct' definition of morality is ultimately relative (and thus subjective) to those given systems. --- With regards to the pomegranate example: both examples are subjective, because how the individual defines moral goodness. Examine: 'pomegranates are good because I like them" here there is one objective thing and one subjective thing, but my opponent seems to think they are switched. The objective thing is the person making this sentence likes pomegranates. Regardless of what my view of reality is this person still likes pomegranates (unless he’s lying). Though his liking of pomegranates may vary over time, and 'the liking of pomegranates' may be subjective to his state of mind, that he has that state of mind is still a statement about reality (again, unless he’s lying). The subjective part of the statement is 'pomegranates are good'. The definition of good is ultimately dependent on the person making the statement about pomegranates. he may be defining good as 'is desirable' or beneficial to health or any number of other uses of the term good, the definition of good in this case, is the subjective thing. Examine: pomegranates are good because they contain anti-oxidants the objective thing about this statement is again the statement about anti-oxidants. It is a factual statement about reality. The subjective thing is the meaning of good. You could be saying that you find antioxidants desirable or you could be saying that antioxidants are beneficial to your health. I agree with what you say about god. but when you go on to say that if things are (morally) good because the effects they have on the real world, then goodness is objective, you are making a false statement. Look at all these statements: "things are good because of the effects they have on the world", "thing are good because god likes them'", "pomegranates are good because I like them"; "pomegranates are good because they contain antioxidants". Each could be one of two things; statements of definition, or statements attributing properties. If they are definitions, then they are definitions subjective to the person making the statement. That is, another person could disagree and neither would be wrong. If they are assignments of properties then we still need to figure out why such properties are being assigned. Why are things that god likes good, or why are things that effect the world good', become questions that require answers, and in my opponents case, answers that have yet to supplied.