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Logic, Math & Morality

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This is an expansion of a post of mine from another thread. Hat tip to HeKS for bringing the debate around to Ontology vs Epistemology.

In another thread, Seversky rejects the objective nature of morality based on the fact you cannot prove its existence or specific values like you can, say, the speed of light or the gravitational constant. Seversky is making a claim that since there is no satisfying epistemological methodology for establishing – precisely – the good or evil value of a moral proposition, then it must be the case that good and evil, ontologically speaking, are completely subjective commodities.

This is not, of course, a logically valid inference. Just because a commodity has no satisfying or precise, repeatable epistemological methodology for measuring its values doesn’t necessarily mean that the commodity itself is subjective in nature. It just means that we do not have a repeatable, precise means of measuring it. It may be that morality is subjective, it may not be.

The question is not whether we have a repeatable, precise way of measuring the good or evil of a proposition, but whether or not morality represents, in ontological terms, an objectively existent or binding set of commodities (good & evil, or right & wrong).

Seversky said:

There are disagreements which can be resolved by appealing to observations of the natural world and there are those that can’t. The first are about objective issues, the latter are subjective. The debate about whether Newton’s or Einstein’s theories offered a better, more comprehensive account of the physics of the Universe was resolved by observation of that Universe, either directly or by experiment.

Seversky is skipping the part about how such disagreements about the natural world are determined. If logic and math were not considered objectively valid determiners of true statements about the natural world, no such disagreement could ever be resolved. Are mathematics and logic part of the natural world? If so, can anyone direct me to where I can find them? No? Can mathematical or logical principles be objectively proven without using math or logic? No?

How are you going to measure the speed of light without logic or mathematics? Why would you “measure” it at all, or consider it a resolution to the argument about how fast it travels, given that both mathematics and logic themselves cannot be found in the natural world? If they are conceptual and exist only in the subjective minds of individuals, they cannot be accepted as objectively true or universally binding … right?

Is there a satisfying (precise and repeatable) epistemological methodology for determining the validity of logical inferences or mathematical proofs? Not without using the very system one assumes objectively valid in the first place, because math and logic are those things by which such satisfying proofs or evidences are established. We cannot prove math or logic valid because “proving” requires math and/or logic. “Proving” or “demonstrating” requires that we assume the validity of logic and mathematics in the first place. We all agree that at least the fundamental principles of mathematics and logic are objectively binding commodities or (1) we have no means by which to resolve disagreements about the natural world, and (2) we have no means by which to measure the natural world in a way that will resolve disagreements about it.

But, why should we agree that logic and mathematics are, ontologically speaking, objective in nature? They are abstract concepts apparently held in individual minds and do not exist in the physical world in a way we can demonstrate them. If we follow Seversky’s logic, how can we possibly consider them to be objectively binding arbiters when it comes to things in the natural world we physically experience?

As I have argued that we operate as if conscience is a sensory ability that can receive objective moral information, so too are the capacities of logical and mathematical thinking. Even though they are abstract and conceptual, we necessarily act as if those capacities are relaying objective, universally-binding information about reality (whether it is limited to what one defines a “natural” or “physical” world or not). When it comes to logic, math and morality, we necessarily act and must argue as if we are perceiving factual, objective, universally-binding aspects of our existence. We already act, and argue, as if they are, ontologically speaking, objective commodities, not subjective ones. That we cannot prove math, logic and morality reflect objective commodities is irrelevant because sane people necessarily accept them as tools or perceptive capacities which reflect objectively true and binding judgements/measurements.

A disagreement about whether your taste in music is “better” than mine cannot be resolved in that way because taste in music is not a property of objective reality but of our response to that reality. It is subjective.

There is a fundamental difference in how we behave when we are operating under the assumption that our views represent subjective commodities, and under the assumption that our views represent objective commodities. We do not behave as if logic, math and morality are categorically the same as personal preferences; we act as if they represent universally binding, objective measurements/judgements.

(Side note: Seversky seems to think that “our response to that reality” is not itself a part of objective reality. I assume this is just a poor choice of wording from what I assume is a naturalist/materialist/physicalist, although this points to another assumption that is necessary to sane human existence: that we are metaphysically distinct from and transcendent over the matter/energy determinism of the physical world. But that’s another argument for another day.)

Seversky continues:

By the same token, our moral judgements or evaluations of human behaviors in the world are subjective. In physics, the speed of light can be measured to see if it is constant, irrespective of the motion of an observer. There is no similar way to measure whether it is always wrong to kill, regardless of circumstances.

Here, again, is where Seversky confuses an ontological argument for an epistemological one. Nobody has claimed that there is a precise, repeatable epistemological methodology for measuring the values of good or evil. Seversky is making a mistake here thinking that unless a satisfying way exists of measuring a thing (epistemology), it cannot be accepted as objective in nature (ontology). Yet, the very core methodologies Seversky demands be used to demonstrate the ontological nature of a thing (math & logic) cannot themselves be demonstrated objective commodities (ontology). They must simply be assumed objective or else absurdity ensues.

The same is true of morality; if we do not assume that certain core properties of morality are objectively true (love is good, cruelty is evil), then morality is an absurd proposition.

I see no way to escape the subjectivity of morality.

By Seversky’s argument, then, I see no way to escape the subjectivity of mathematics and logic, and so I should disregard them as objective determiners of true or factual statements about the world and start regarding them as subjective preferences. Right?

The way to “escape” the idea that morality is subjective in nature is via correct critical thinking which may require that Seversky, at least for the sake of argument, set aside certain ideological commitments that may be preventing him from a proper rational analysis.

First, he’s thinking about morality incorrectly; it is not proposed as something that can be measured, but rather as something that does the measuring, like logic or math. Morality is like logic or math and conscience is like our capacity to apprehend/perceive logical and mathematical principles and apprehend logical validity and mathematical equations. Yes, we can make erroneous equations and come to logically unsound conclusions, but such disagreements and errors do not mean that logic and math themselves are subjective in nature. There are some things we know are evil just as certainly as we know 1+1=2 or know that A=A. It is undeniable to pain of absurdity to claim that love is evil or cruelty is good. Morality provides sane people with self-evident truths in precisely the same way as do math and logic, and it is from these self-evidently true statements that we must accept, on pain of absurdity, that systems of objectively measuring and judging other things can be and are established.

Second, Seversky needs to recognize that a lack of precise, repeatable epistemological methodology for measuring good and evil (right and wrong) does not mean good and evil are not themselves objective commodities. Just because we cannot precisely-repeatably measure a thing doesn’t mean that we cannot have any credible objective knowledge of a thing at all. We all understand that torturing a child for fun is more evil than not opening a door for an elderly woman (showing her kindness and respect); we all know that unconditional, self-sacrificing and forgiving love is more good than just about any other good one might engage in. Our conscience can perceive general moral measurements we know to be true, even if many moral measurements are difficult to make.

Third, Seversky needs to acknowledge the profound experiential and categorical difference between moral behavior and behavior with regards to subjective preferences and feelings, and that only sociopaths/psychopaths can act as if morality is subjective in nature. He (and others) need to acknowledge that the very idea of forcing subjective feelings/habits/preferences on others is antithetical to the nature of morality. IOW, if morality is nothing more than living according to one’s personal, subjective views and forcing them others when you feel like it, then there is no principled moral difference between Gandhi and Hitler or between the golden rule and might makes right.

“Escaping” the “subjectivity of morality” simply requires being honestly willing to consider the idea that morality represents an objective capacity to judge good and evil, just as one accepts that logic and mathematics represent systems that make objectively valid and universally binding judgements and measurements. One does not have to explain how or why logic, math and morality exist or are objectively binding and valid; one only has to accept that they do exist and are objective in order for their behavior to be rationally consistent with their premises and to avoid existential absurdity.

To deny math, logic or morality represent objectively binding systems of judgement and measurement is to adopt existential, solipsistic anarchism and absurdity. No sane person can even act as if any of those things are subjective in nature. No sane person can even organize a coherent sentence, much less make an argument, that does not reflect the assumption that morality, math and logic are objectively valid, universally binding methods of measurement and judgement.

(However, I doubt Seversky, CF or others can pry themselves away from their ideological commitments sufficiently to honestly consider what it means to deny the objective nature of morality, or to promote the idea that morality is subjective in nature.)

Lacking any evidence to the contrary, even a moral code handed down from on high inscribed on tablets of stone is just another – albeit divine (allegedly) – opinion.

Even though we cannot find any of the principles of mathematics and logic in they physical world, we are capable of recognizing self-evidently true logical and mathematical statements that serve as the axiomatic, objective root of our capacity to make systems of measurement and judgement we consider objective and universal in nature. We cannot prove them; we cannot find them in the physical world; yet it is by their existence that we are able to prove other things and resolve disagreements about other objectively existent commodities.

The same is true of morality. There are self-evidently true moral statements (love is good, cruelty is evil) the denial of which result in absurdity, just like denying that 1+1=2 or denying the principle of identity results in absurdity.

Denying that conscience can perceive objectively valid judgements of good and evil is the equivalent of denying that logic can be used to make objectively valid judgements of truth or denying that mathematics can be used to make objectively valid measurements and equations. It moves one’s worldview into a position that is in absurd contradiction to how they must behave, think and speak, and renders their every moral act the in-principle equivalent to Hitler and Dahmer, by justifying as “good” the forcing of one’s own subjective, personal views on others because, ultimately, one feels like it.

Comments
I wonder Has Ellazimm ever heard of Gödel's incompleteness theorems?Andre
June 6, 2016
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ellazimm said:
I’ve got this feeling you haven’t seen many mathematical proofs. But if I’m wrong I’d love to hear about your experience.
I've got this feeling you don't have anything of substance to add to this thread. But if I'm wrong I'd love to hear your salient rebuttal to any point in the O.P.William J Murray
June 6, 2016
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Always like this quote from Sir Arthur Eddington, who of course was smarter-than-the-average-bear on both mathematics and the speed of light, having been the one to confirm Einstein's theory by observation: “Dismiss the idea that natural law may swallow up religion; it cannot even tackle the multiplication table single-handed.” Swarthmore Lecture in 1929. He refers, of course, to the metaphysical assumptions that must, necessarily, underlie maths, and even more empirical science.Jon Garvey
June 6, 2016
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Querius@7: Excellent points.Truth Will Set You Free
June 5, 2016
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WJM wrote:
It moves one’s worldview into a position that is in absurd contradiction to how they must behave, think and speak, and renders their every moral act the in-principle equivalent to Hitler and Dahmer, by justifying as “good” the forcing of one’s own subjective, personal views on others because, ultimately, one feels like it.
Relativism was once used to attack the absolute Judeo-Christian ethics. Once victorious, relativism adopted a set of supposedly self-evident, immutable truths that are ferociously enforced by political correctness mobs on campus. No dissenting rational discussion or debate is tolerated."She's a witch" has been replaced with "he's a fascist." The irony is completely lost on them. However, the way to defend yourself against one these self-appointed vigilantes of political correctness is easy, but usually overlooked. As you've seen here on occasion, appeals to logic, pointing out contradictions, or presenting historical facts are all completely ineffective. What is highly effective is to take up the Shield of Genetic Fallacy to deflect any attacks and the Sword of PC Orthodoxy to find in them the smallest deviation in PC conformity, and to start hacking them on that point alone without mercy until it becomes apparent to their friends that they are heretics. Their former friends will then eat them alive. No one escapes the new Inquisition! -QQuerius
June 5, 2016
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WJM
Is there a satisfying (precise and repeatable) epistemological methodology for determining the validity of logical inferences or mathematical proofs? Not without using the very system one assumes objectively valid in the first place, because math and logic are those things by which such satisfying proofs or evidences are established.
I've got this feeling you haven't seen many mathematical proofs. But if I'm wrong I'd love to hear about your experience.ellazimm
June 5, 2016
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PPS: should I mention the simple but useful RION framework for scales of measurement, and that comparative judgement is involved directly or indirectly in measuring? Ratio, interval, ordinal, nominal? The presence of Likert scales or polytomous Rasch scales for ordering that routinely appear in contexts of evaluation?kairosfocus
June 5, 2016
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WJM, attn Sev:
[Sev:] There are disagreements which can be resolved by appealing to observations of the natural world and there are those that can’t. The first are about objective issues, the latter are subjective.
This fails, most likely by equating empirical experience of the physical world with reality. WJM is right to point to mathematics as an abstract, objective domain of knowledge in answer. Math is the study of the logic of structure and quantity, which is wholly abstract, is accessed by subjects using their faculties for rational, responsible thought and is objective. That is, the findings and grounding warrant transcend the particular perceptions, views, likes, tastes and experience of any one individual or group. And at the core of grasping the reality of morality and Mathematics alike there are self-evidently true assertions that are seen as true on pain of absurdity. Nor are they unconnected. In fact the sense of urgency towards mathematical truth is just as much an expression of the voice of conscience as the sense of urgency towards truth in general. There is deep wisdom in the old saying that all [genuine] truth is God's truth. KF PS: There are also objective principles of aesthetics. Indeed, with the Pythagoreans, it was discovering the mathematical structure of music that led them to look for explanation of the harmony of the heavens in the same domain, and onward to the mathematical vision of the sciences. So, no, it is not true that beauty is a chaotic, irrational wholly subjective phenomenon.kairosfocus
June 5, 2016
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An interesting question here is: why would one assume math and logic objectively binding, and not morality? All three are subjectively held abstract concepts; all three rely upon non-demonstrable, so-called "intuitions" about correct thinking, all three demand that we act, argue and think as if they are indeed objective commodities. So, why is it any easier to accept logic and mathematics as objectively binding systems of judgement and measurement, and not morality, when we can state moral principles that are as self-evident and as indispensable to our experience and behavior as 1+1=2 or A=A?William J Murray
June 5, 2016
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daveS said:
I think I understand where you’re going here, but perhaps this should be rephrased? There are indeed methods for determining whether mathematical proofs are valid.
What methods are those, daveS? I see what you mean, though, so I edited the above statement in the OP:
Is there a satisfying (precise and repeatable) epistemological methodology for determining the validity of logical inferences or mathematical proofs? Not without using the very system one assumes objectively valid in the first place, because math and logic are those things by which such satisfying proofs or evidences are established.
William J Murray
June 5, 2016
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WJM,
Is there a satisfying (precise and repeatable) epistemological methodology for determining the validity of logical inferences or mathematical proofs? No, because math and logic are those things by which such satisfying proofs or evidences are established.
I think I understand where you're going here, but perhaps this should be rephrased? There are indeed methods for determining whether mathematical proofs are valid.daveS
June 5, 2016
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