An interview on God and mathematics

_{Denyse O'Leary

January 17, 2021

Intelligent Design, Mathematics, theism}

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Some of us think mathematics is the best argument for God available. Anyway, here’s Jerry Bowyer’s interview with philosopher Vern Poythress:

The standard modern culture-war revolves around God vs. the mathematical sciences. Take your choice: Faith or physics. Then there are the voices of mutual toleration, which attempt to leave room for science among the faithful and for faith among the scientific. Poythress, though, taps into a different tradition entirely, one which is seldom heard in modern debate: That God and science are neither enemies, nor partners, but rather that God is the necessary foundation for mathematics and therefore of every science which uses it.
The argument is that mathematical laws, in order to be properly relied upon, must have attributes which indicate an origin in God. They are true everywhere (omnipresent), true always (eternal), cannot be defied or defeated (omnipotent), and are rational and have language characteristics (which makes them personal). Omnipresent, omnipotent, eternal, personal… Sounds like God. Math is an expression of the mind of God. Sound strange? It isn’t. Modern natural science was created by people who said that they were trying to “think God’s thoughts after Him.”
Jerry Bowyer, “God In Mathematics” at Forbes

See also: Things exist that are unknowable: A tutorial on Chaitin’s number

Hat tip: Philip Cunningham

Comments

Viola Lee: Do you find the following statement to be absolutely morally true in all possible imagined worlds worlds? "It is wrong to be cruel to others for your own pleasure."William J Murray_{January 23, 2021
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WJM writes, "I was attempting to, via analogy, illuminate for VL and JVL the general structure of KF’s position so that it might be easier to understand why he kept going back to the fundamentals." I understand the general structure of KF's position: that is not a problem. He keeps "going back to fundamentals" because he can't, in fact, explain the leap from math to morals as it applies to real people in the real world.Viola Lee_{January 23, 2021
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I believe KF would make the same argument, that the Bible (or, the DoI or COTUS based on Judeo-Christian morality stemming from the Bible) are analogous to a breakthrough in the understanding of physics, which allowed the building of a civilization/nation unlike any the world has seen before.
I am going to disagree somewhat. While I believe Judeo/Christian principles improve civilization, there were definitely civilizations before each. Greece and Rome depended on neither. So in what way have they led to anything different from that preceding? Also the modern world did not start till the 1800's. What happened in that time era to lead to the incredible advances in material prosperity that also led to large increases in health (age expectancy) and education? The answer is freedom for the common person, first to a limited degree in England and then to the English colonies in North America, especially the United States where there were no such restrictions for immigrants. The reason the United States took off and eventually left Britain far behind is that there was no class restriction in the United States while in England there was a large expansion of rights for individuals but a class system that made it much harder for the common man. Aside: We are a far way from God and mathematics.jerry_{January 23, 2021
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Seversky, I was attempting to, via analogy, illuminate for VL and JVL the general structure of KF's position so that it might be easier to understand why he kept going back to the fundamentals. Although I wasn't arguing my perspective, I think I can make a couple of points from that perspective. First, you do not compare "strengths and weaknesses" of an analogy because analogies are not examples. They are used to illuminate a point, not to be taken as ways of arguing the point or the thing in question. An analogy is not an argument. Second, KF's perspective may be that physics and morality are means of describing the territory of two different realms. It doesn't matter if people in various cultures before, because of a lack of understanding of physics, could not build that which we can build now; the physics were still there, but the comprehension of them was (or is) inadequate. I believe KF would make the same argument, that the Bible (or, the DoI or COTUS based on Judeo-Christian morality stemming from the Bible) are analogous to a breakthrough in the understanding of physics, which allowed the building of a civilization/nation unlike any the world has seen before.William J Murray_{January 23, 2021
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I don’t need a god or anyone else to tell me that I don’t want my nose flattened by your fist.
But suppose someone else enjoyed that your nose was flattened. You may not like it but hundreds of others may enjoy it. So we may have 100 people enjoying it and one person not. So do you want to deprive others of enjoyment for your personal benefit? These can get pretty absurd. So maybe there is some ultimate determination of what is desirable and what is not. Should finding this ultimate determination be a necessity for each person? Suppose there was a God that created us and that God had an objective for our creation. Is frustrating that objective undesirable or of any consequence?jerry_{January 23, 2021
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I regard rights and freedoms as privileges extended by a society to its members, the key consideration here being "society". An individual human being living alone has the freedom to anything he or she chooses within the constraints imposed by the material world. The cannot fly unaided, for example, and they will be killed by the fall if they jump off a tall cliff. John Stuart Mill held that, in a free society, individuals should be able to do whatever they choose up to the point at which their actions could harm to other members of society. As the old saying goes, "your freedom to swing your fist ends at the tip of my nose". Moral prescriptions are created by people not gods for the benefit of the societies in which they live. I don't need a god or anyone else to tell me that I don't want my nose flattened by your fist.Seversky_{January 23, 2021
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William J Murray/105
The engineers rely on physics/math. The community planners rely on morality and ethics. What lies behind all of that is: right reason. If either team doesn’t have the principle of right reason governing their design and planning, the project will most assuredly fail. The building and/or the community will fail.
Any evaluation of an analogy should take account of both the similarities and the differences. The observed regularities in the behavior of the material/physical Universe, which we call laws, appear to be invariant across time and space. They are the same for the Inuit as they are for the Zulu now and they were the same for Homo habilis 2 million years ago as they are for Homo sapiens today. The same cannot be said for so-called moral laws. They have evolved over a matter of centuries and differ to some degree from culture to culture. Most people would clearly like moral laws to be as invariant and certain as physical laws. The problem is that each person tends to believe that his or her morality is the right one while others believe that theirs is the true one. So is there a right one and, if so, how do we decide?
After the project is finished, people move in and the community begins. Let’s say that the people on the 3rd floor want to make structural changes to the building. The don’t like the high grade steel of the support beams; they want to cut them out and replace them with wood. Let’s say some other people, a group on the 15th floor, doesn’t like the community rules about marriage, gender, family and sex, and want to live by their own rules and preferences.
In the example of occupants of the building being foolish enough to replace steel support beams with wooden beams, they would eventually discover the error of their ways when the building collapsed on top of them. But supposing the occupants began replacing steel beams with lighter and stronger titanium, for example. The building would presumably become stronger and more durable than before. Are the different community rules adopted by the inhabitants on the 15th floor analogous to replacing steel beams with wood or titanium? How does appealing to "right reason" - or science or mathematics - help in deciding moral questions at all?Seversky_{January 23, 2021
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Kairosfocus/103
Emotivism is the view that moral utterances are neither true nor false but are expressions of emotions or attitudes. It leads to the conclusion that people can disagree only in attitude, not in beliefs. People cannot disagree over the moral facts, because there are no moral facts. Emotivism also implies that presenting reasons in support of a moral utterance is a matter of offering nonmoral facts that can influence someone’s attitude. It seems that any nonmoral facts will do, as long as they affect attitudes. Perhaps the most far-reaching implication of emotivism is that nothing is actually good or bad. There simply are no properties of goodness and badness. There is only the expression of favorable or unfavorable emotions or attitudes toward something.
… which is largely my position. Where reason is applied to morality it is usually in the form of post hoc rationalization of emotional postures.Seversky_{January 23, 2021
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I'm not sure how a discussion on God and mathematics got twisted. But I guess there are an infinite number of permutation of each so what is there to be expected. (Here infinite is used as an hyperbole because as we all know infinity does not exist in our universe.) A couple things The Great Courses has several courses on math. One that may be appropriate for this discussion is
Power of Mathematical Thinking: From Newton's Laws to Elections and the Economy
My point has been is that math is a subset of logic and indicates certainties that are true given the premises and will thus show everywhere where there is a relationship. Second, from William Briggs today
This doesn’t mean real science is entirely dead. It will drag along in quiet corners in areas which can’t easily be tied to politics or oligarchic interest.
Could just as well be applied to math and the statement should read
This doesn’t mean real science and mathematics is entirely dead. It will drag along in quiet corners in areas which can’t easily be tied to politics or oligarchic interest.
Interesting that the interview that inspired OP is four years old.jerry_{January 23, 2021
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F/N: Webster's 1828 is helpful on freedom:
LIB'ERTY, noun [Latin libertas, from liber, free.] 1. Freedom from restraint, in a general sense, and applicable to the body, or to the will or mind. The body is at liberty when not confined; the will or mind is at liberty when not checked or controlled. A man enjoys liberty when no physical force operates to restrain his actions or volitions. 2. Natural liberty consists in the power of acting as one thinks fit, without any restraint or control, except from the laws of nature. It is a state of exemption from the control of others, and from positive laws and the institutions of social life. This liberty is abridged by the establishment of government. 3. Civil liberty is the liberty of men in a state of society, or natural liberty so far only abridged and restrained, as is necessary and expedient for the safety and interest of the society, state or nation. A restraint of natural liberty not necessary or expedient for the public, is tyranny or oppression. civil liberty is an exemption from the arbitrary will of others, which exemption is secured by established laws, which restrain every man from injuring or controlling another. Hence the restraints of law are essential to civil liberty. The liberty of one depends not so much on the removal of all restraint from him, as on the due restraint upon the liberty of others. In this sentence, the latter word liberty denotes natural liberty. 4. Political liberty is sometimes used as synonymous with civil liberty But it more properly designates the liberty of a nation, the freedom of a nation or state from all unjust abridgment of its rights and independence by another nation. Hence we often speak of the political liberties of Europe, or the nations of Europe. 5. Religious liberty is the free right of adopting and enjoying opinions on religious subjects, and of worshiping the Supreme Being according to the dictates of conscience, without external control. 6. Liberty in metaphysics, as opposed to necessity, is the power of an agent to do or forbear any particular action, according to the determination or thought of the mind, by which either is preferred to the other. Freedom of the will; exemption from compulsion or restraint in willing or volition. 7. Privilege; exemption; immunity enjoyed by prescription or by grant; with a plural. Thus we speak of the liberties of the commercial cities of Europe. 8. Leave; permission granted. The witness obtained liberty to leave the court.
Note the natural freedom of the human person, as an agent, and that judicious balance in sound civil society. KFkairosfocus_{January 23, 2021
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In another thread I said we don't have the right to life. I also don't think we have their "right" to liberty or the pursuit of happiness. Let me explain. I consider the term "right," in this context, to be entirely misleading. Life, liberty and the pursuit of happiness are not external things we have rights to; these are innate, essential qualities of our being. We are fundamentally, essentially living, free and in pursuit of our happiness. These aspects of us are not confined to physical bodies, worldly laws or social constructs. I live, am free, and pursue my happiness regardless. Killing me or imprisoning me does not change these aspects of what I am. The physical world cannot extinguish my life, only my presence in this world. Chains can only imprison my body; they cannot imprison my mind. My mind is free, and it is free to pursue happiness even while the body is in chains. I am not my body; this world is not my home. The Constitution does not grant these things, it recognizes them as inherent truths about all humans. The term "unalienable Right" is not the same kind of thing as a mere "right," because it's referring to a truth about all humans. When people say they have a "right" to healthcare, housing, not being offended or equal outcomes/pay, and think it is "the same as" an unalienable Right, they have no idea what they are talking about. The DoI was recognizing innate truths about our existence, and declaring these truths to be the necessary foundation for a proper society. A society not built on those truths will be corrupt and fail because it would ignore the true reality of what a person is. The Constitution is a "best attempt" at an essential codification of basic structure of law based on the recognition of these fundamental truths. IOW, "these are truths about our nature, this document recognizes those truths and calls them Rights." But, we don't have a "right" to them (small "r",) we are those qualities.William J Murray_{January 23, 2021
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WJM, that is in fact highly relevant -- and worrying. My context on ethics actually comes through sustainability, and things that raise questions of what is enduring or chaotically destructive. I have been led to recognise just how important it is to align what we say with reality, and to see that the principle of distinct identity is truly central, a thing is what it is, i/l/o its distinct characteristics, i.e. there is such a thing as what it is to be a given thing; to have a nature. Which, we have a duty to recognise and respect, playing ill-advisedly with I beams in a building framework is analogous. In that context, I came to recognise that in our debates, decisions, reflections we implicitly pivot on certain first duties that give our thought traction, duties that we simply cannot evade and which, thus -- as stated -- are statements of truth and are also self-evident. They literally come before debates or arguments or logical demonstrations etc as when we do these things we implicitly pivot on them. Duties to truth, to right reason, to prudence and to that inner witness, sound conscience are relevant to more academic and technical reasoning. The duty to neighbour who is as self bridges to community, law and government, as it brings up fairness and justice etc. What I find interesting is the lack of traction in pointing to how even the objector cannot evade, which puts him/her in an immediately absurd position, showing self-evidence. I am inclined to think there is a paradigm shift involved, requiring recognising that morality rises above subjectivity, emotion and shifting balances of community opinion, on grounds of the utter incoherence of such views. Paradigms, notoriously, are incommensurate and until one recognises that there can be enduring, universal moral principles, one will not see the point coeval with our rational ensouled freedom and linked responsibility. KFkairosfocus_{January 23, 2021
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JVL & VL, I have an analogy that I think may give you a better understanding of what KF has been saying and arguing in this and prior threads (like the one about civilization, moral duties, right reason. I think it will also be enlightening in terms of how what KF is saying relates to specific social and moral cases. Let's say you're an engineering firm contracted to design a skyscraper. The building must be designed using sound engineering principles translated into a design incorporating the proper materials that can withstand all of the physical stresses and tensions, such as gravity, wind, bearing the load of people. The engineering firm works with building management in order to provide the infrastructure necessary to sustain the community. Both teams - the engineers and the founding community planners - must work together to create not only a building that can stand the test of time, but also the infrastructure that can provide for a successful, thriving community. The engineers rely on their knowledge of math, materials, and physics to make sure the building can stand the test of time; but the community planners must rely on something as fundamental as the engineers knowledge to build a strong, successful community that endures the stresses, challenges and issues that are certain to arise. The engineers rely on physics/math. The community planners rely on morality and ethics. What lies behind all of that is: right reason. If either team doesn't have the principle of right reason governing their design and planning, the project will most assuredly fail. The building and/or the community will fail. After the project is finished, people move in and the community begins. Let's say that the people on the 3rd floor want to make structural changes to the building. The don't like the high grade steel of the support beams; they want to cut them out and replace them with wood. Let's say some other people, a group on the 15th floor, doesn't like the community rules about marriage, gender, family and sex, and want to live by their own rules and preferences. Would you feel comfortable with allowing non-engineers and non-mathematicians negotiate for changes in the design, materials and structure of the building? Probably not. You might think that the physical building and the community housing it are two entirely different things, but they are not. Remember the building and infrastructure was designed to serve the needs of a particular kind of community, not any and every community. In #100 above you said you're interested in negotiating compromises with people in terms of the rules and expectations and future of the community. A successful community requires moral, ethical and behavioral expectations and rules, a fundamental common goal, a social contract, laws, etc. What KF is arguing is that unless people begin with right reason, they cannot hope to find successful moral and ethical principles that can create and maintain a successful community. You wouldn't begin to argue with mathematicians and engineers about what it takes to support the building, yet you somehow think you're qualified to argue about what can be put into or taken away from the rules of the community successfully. Why is that? Are you educated in moral philosophy, history, ethics, human behavior, logic and psychology? What are the foundational moral and ethical principles that guide your negotiations? Let's take this to specific instances: marriage, family and steel support beams. Would you be okay with a group of people in a certain location in the building cutting out their section of a steel support beam and replacing it with wood? Of course not; you get enough people doing that and the building will collapse. It cannot be allowed. Let's look at marriage and family. These concepts are rooted in something as real as engineering: biology. Can a change be allowed, here and there in the community of the building, that ignores biology? KF's argument, I think, would be that you're letting people do the social/community equivalent of cutting out sections of support beams here and there and replacing the biologically-required (engineering-required) material with something else. What makes you or anyone think that will work in terms of the sustainability of the community? What is that idea based on, rooted in? What principle of morality, social psychology or ethics does it logically flow from? Is there a historical precedent? What are the potential ramifications from this fundamental change? Have you thought that through? I'm not saying I share anyone else's perspective on these subjects, I'm just pointing out that if you can't do the (i)moral math on this,(/i) you're just saying stuff that isn't rooted in anything meaningful or significant. You two are like laymen challenging an engineer to explain why wood wouldn't be acceptable as a replacement for the steel beam running through your apartment and rolling your eyes when the engineer starts talking about the physics of load-bearing materials, stress factors, the principles involved. Would you accept it if he said: wood isn't strong enough to support the building? No, you'd ask ... why not? Then KF goes into an explanation about engineering principles as it relates to load bearing materials and structures, and you roll your eyes and say he's not talking about the specifics. What would his attention to the specifics about wood vs steel mean unless you understand what he's saying and why he's saying it? I apologize if I didn't represent well, KF.William J Murray_{January 23, 2021
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PPS: It is probably worth noting a classification by Clarke & Rakestraw, which will help us to clarify ethics and morality, two strongly overlapping terms, the second introduced in Latin by Cicero to render the first, a Greek term, but which now have subtle distinctions:
Principles are broad general guidelines that all [responsible] persons ought to follow. Morality is the dimension of life related to right conduct. It includes virtuous character and honorable intentions as well as the decisions and actions that grow out of them. Ethics on the other hand, is the [philosophical and theological] study of morality . . . [that is,] a higher order discipline that examines moral living in all its facets . . . . on three levels. The first level, descriptive ethics, simply portrays moral actions or virtues. A second level, normative ethics (also called prescriptive ethics), examines the first level, evaluating actions or virtues as morally right or wrong. A third level, metaethics, analyses the second . . . It clarifies the meaning of ethical terms and assesses the principles of ethical argument . . . . Some think, without reflecting on it, that . . . what people actually do is the standard of what is morally right . . . [But, what] actually happens and what ought to happen are quite different . . . . A half century ago, defenders of positivism routinely argued that descriptive statements are meaningful, but prescriptive statements (including all moral claims) are meaningless . . . In other words, ethical claims give no information about the world; they only reveal something about the emotions of the speaker . . . . Yet ethical statements do seem to say something about the realities to which they point. “That’s unfair!” encourages us to attend to circumstances, events, actions, or relationships in the world. We look for a certain quality in the world (not just the speaker’s mind) that we could properly call unfair. [Readings in Christian Ethics, Vol. 1: Theory and Method. (Grand Rapids, MI: Baker, 2002), pp. 18 – 19.]
Such of course leads into the IS-OUGHT gap, which as Hume highlighted can only be bridged at root of worlds. I take a further plunge:
However we may define the good, however well we may calculate consequences, to whatever extent we may or may not desire certain consequences, none of this of itself implies any obligation of command. That something is or will be does not imply that we ought to seek it. We can never derive an “ought” from a premised “is” unless the ought is somehow already contained in the premise . . . . R. M. Hare . . . raises the same point. Most theories, he argues, simply fail to account for the ought that commands us: subjectivism reduces imperatives to statements about subjective states, egoism and utilitarianism reduce them to statements about consequences, emotivism simply rejects them because they are not empirically verifiable, and determinism reduces them to causes rather than commands . . . . Elizabeth Anscombe’s point is well made. We have a problem introducing the ought into ethics unless, as she argues, we are morally obligated by law – not a socially imposed law, ultimately, but divine law . . . . This is precisely the problem with modern ethical theory in the West . . . it has lost the binding force of [truly rational, intelligible] divine commandments [--> rooted in a reality-source that is inherently good and utterly wise, a maximally great necessary being] . . . . If we admit that we all equally have the right to be treated as persons, then it follows that we have the duty to respect one another accordingly. Rights bring correlative duties: my rights . . . imply that you ought to respect these rights [--> 2/3 way towards seeing justice as due balance of rights, freedoms and duties]. [Ethics: Approaching Moral Decisions (Downers Grove, IL: IVP, 1984), pp. 70 – 72, 81.]
This distantly reflects, Cicero on core of law:
, On the Republic, Bk 3: {22.} [33] L . . . True law is right reason in agreement with nature , it is of universal application, unchanging and everlasting; it summons to duty by its commands, and averts from wrongdoing by its prohibitions. And it does not lay its commands or prohibitions upon good men in vain, though neither have any effect on the wicked. It is a sin to try to alter this law, nor is it allowable to attempt to repeal any part of it, and it is impossible to abolish it entirely. We cannot be freed from its obligations by senate or people, and we need not look outside ourselves for an expounder or interpreter of it. And there will not be different laws at Rome and at Athens, or different laws now and in the future, but one eternal and unchangeable law will be valid for all nations and all times, and there will be one master and ruler, that is, God, over us all, for he is the author of this law, its promulgator, and its enforcing judge. [--> where, as already noted, the concept of God here involves the inherently good and utterly wise so that the principles are intelligible and rational, not arbitrary; notice, the first duties as repeatedly listed pervade reasoned argument inescapably, once we incline ourselves to look: to truth, to right reason, to prudence, to sound conscience, to neighbour, to fairness and justice [= due balance . . . ] etc ] Whoever is disobedient is fleeing from himself and denying his human nature, and by reason of this very fact he will suffer the worst penalties, even if he escapes what is commonly considered punishment [--> coeval with rational, ensouled creaturehood] . . . . – Marcus Tullius Cicero
These are broad, drawing out a richer understanding of morality and helping us to see how first duties can rise above one's subjectivity or shifting sands of a place and time, as we here see root level principles coeval with our human nature as rational, responsible creatures. In which context, despite obvious discomfort, first duties of reason clearly extend to reason applied to [the study of] the logic of structure and quantity. A definition of Mathematics that clearly emphasises right reason as core to the subject. That underlies say an exploration of Wigner's amazement on the pervasive utility of Mathematics and much more, including explorations on axiomatisations and limits of axiomatisation post Godel. Recognising due limits is of course part of the judicious use of reason. Recall, the pivot of my point is about self-evident first duties of reason, which apply to Mathematics, as a province of reason in action. Reason, is duty-bound, inherently, it is an aspect of the government of freedom, freedom implies choice and choice ought to be towards the good. But it cannot be forced, or it is no longer choice. What that points to at root of reality is an onward matter, it is not primary.kairosfocus_{January 23, 2021
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JVL (& attn VL), you are now projecting and personalising distractively. The difference is not in the Math, it is in what mathematical reasoning as a case of reasoning is governed by. An obvious thing is that we should believe things as true for good reason, i.e. on warrant, especially as we are prone to error. But, should already points to duties, here to truth, then to warrant so to both right reason and prudence. Right reason, of course, is a longstanding term for the body of knowledge and best practice on reasoning, involving logic, sound judgement, and pointing to discernment, judicious temperament etc. Where, these duties of reason are not shifting matters of preferences or emotions or social consensus, apparently a key part of a common, flawed conception of morality -- such reductionism has long been shown to be incoherent (and yes, I am pointing to key duties of reason to dismiss a particular flawed theory on morals). We are here drawing out duties of reason coeval with there being rational creatures. Those duties are permanent, inescapable, inescapably true, self-evident. They pervade any rational context,. specifically including the practice of Mathematics. KF PS: A reminder -- I have pointed this out before in your presence -- on certain failed theories of morality:
Excerpted chapter summary, on Subjectivism, Relativism, and Emotivism, in Doing Ethics 3rd Edn, by Lewis Vaughn, W W Norton, 2012. [Also see here and here.] Clipping: . . . Subjective relativism is the view that an action is morally right if one approves of it. A person’s approval makes the action right. This doctrine (as well as cultural relativism) is in stark contrast to moral objectivism, the view that some moral principles are valid for everyone.. Subjective relativism, though, has some troubling implications. It implies that each person is morally infallible and that individuals can never have a genuine moral disagreement Cultural relativism is the view that an action is morally right if one’s culture approves of it. The argument for this doctrine is based on the diversity of moral judgments among cultures: because people’s judgments about right and wrong differ from culture to culture, right and wrong must be relative to culture, and there are no objective moral principles. This argument is defective, however, because the diversity of moral views does not imply that morality is relative to cultures. In addition, the alleged diversity of basic moral standards among cultures may be only apparent, not real. Societies whose moral judgments conflict may be differing not over moral principles but over nonmoral facts. Some think that tolerance is entailed by cultural relativism. But there is no necessary connection between tolerance and the doctrine. Indeed, the cultural relativist cannot consistently advocate tolerance while maintaining his relativist standpoint. To advocate tolerance is to advocate an objective moral value. But if tolerance is an objective moral value, then cultural relativism must be false, because it says that there are no objective moral values. Like subjective relativism, cultural relativism has some disturbing consequences. It implies that cultures are morally infallible, that social reformers can never be morally right, that moral disagreements between individuals in the same culture amount to arguments over whether they disagree with their culture, that other cultures cannot be legitimately criticized, and that moral progress is impossible. Emotivism is the view that moral utterances are neither true nor false but are expressions of emotions or attitudes. It leads to the conclusion that people can disagree only in attitude, not in beliefs. People cannot disagree over the moral facts, because there are no moral facts. Emotivism also implies that presenting reasons in support of a moral utterance is a matter of offering nonmoral facts that can influence someone’s attitude. It seems that any nonmoral facts will do, as long as they affect attitudes. Perhaps the most far-reaching implication of emotivism is that nothing is actually good or bad. There simply are no properties of goodness and badness. There is only the expression of favorable or unfavorable emotions or attitudes toward something.
kairosfocus_{January 22, 2021
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Thank, JVL. I think letting these folks talk among themselves as much as possible is probably for the best. I get addicted, so it's my own problem if I can't quit. We'll see - sometimes math topics come up that are interesting to me, but I they haven't really led to good discussions, either.Viola Lee_{January 22, 2021
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Kairosfocus: I have nothing more to say to you about mathematics and morals. Clearly you have not experienced higher level mathematical education because if you had you would not say the things you do. The fact that you still want to tell those of us who have had that experience what we should and should not think speaks volumes about your preconceived notions and biases. Math is not a spectator sport. Sitting on the sidelines or watching the game on the telly is not really understanding what is going on. Until you can put on the cletes and the pads and take your place on the field you are just a pretender, a spectator. And spectators never get to determine the score. Players do. When you're ready and able to get on the field and play the game then you get to influence the outcome. Until then . . . If you want to test your mettle then tell us what steps you would take when approaching something like the Goldbach Conjecture. What is step one when dealing with that topic?JVL_{January 22, 2021
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Viola Lee: Thanks for the encouragement. Love you really!! It's an odd thing . . . I consider myself a skeptic in that I think all ideas should be scrutinised strongly, especially if they run counter to well understood and well established knowledge. And I do try and spend time listening to those whose views differ from mine. I'm interested in trying to find some common ground, some central place where conflicting views can be discussed and examined and compared. And I think that when it comes to making social and ethical decisions some compromise is essential; no one will get everything they want but if we try a bit we all might get enough to form a cohesive and strong centre. When I first came to Uncommon Descent I thought it would be good for me to try and understand what people who I disagreed with were saying and thinking so that we could work towards a workable consensus, an agreement to work on the problems we all recognise in a way that we could all support. I know I'm probably sounding a lot like President Biden in his confirmation speech but, like him, I guess I'm a child of the 60s: let's talk things out, let's be honest and straight, let's work together. Sadly, after quite a long time trying to get to that point it seems that, for some, it's just not going to happen. Some people are so sure they are right, are so convinced they know 'the truth' that there's no discussion or debate possible. I didn't want to believe that because it's such an irrational call IF one is really interested in working together to solve problems. This forum is not the place for compromise or giving ground. I should forget it as well. I don't know why I continue to try and gain even minor concessions. It never happens. No one in charge here wants it to happen. They know they are right and the rest of us can pound sand. Thank you for being a dissenting voice whose posts have been insightful, intelligent, smart and ones I very much look forward to. You done good. Very good. I'm sorry it didn't make any difference. Except to me.JVL_{January 22, 2021
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JVL, Let's see, just your first sentence:
>>That is not correct.>> - appeal to duty to truth, and also to warrant thus both prudence and right reason, right from your opening words - the objection pivots on what it objects to - I note on the way that these duties are coeval with creatures having sufficient freedom to be rational, posing the is-ought challenge. >>Theorems are true because they have been proven to be true>> - appeal to duty to truth and to warrant, again >>and unless you can find fault with the proof>> - appeal to duty to right reason >>then they stay true forever and always. >> - appeal to duty to truth and to right reason cumulative to sound warrant, thus prudence
The inescapability shines through in the objection itself. KFkairosfocus_{January 22, 2021
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Thanks for the encouragement.Viola Lee_{January 22, 2021
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Viola Lee: Forget it, I say to myself. If you keep repeating it you might believe it one day!JVL_{January 22, 2021
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Kairosfocus: why a proof, a particular type of warrant? Ans, because we are prone to error so we seek reliable confirmation of accuracy and derivation from axiomatic start points taken as true. That is not correct. Theorems are true because they have been proven to be true and unless you can find fault with the proof then they stay true forever and always. It's not a matter of warrant or point of view. I don't think you really understand how mathematicians think. the root claim is not on mathematics but on reasoning, which then embraces mathematics as a form of reasoning. No, the root claim is on mathematics. For example: a common method of proof in mathematics is proof by contradiction. I doubt there are many real-world situations where that method is even applicable. I can't think of one time in my life I reasoned my way through a situation based on that process. The style of reasoning is partly based on the subject at hand, mathematics. ask yourself, why should anyone pay slightest heed to a supposed proof? Ans, because of said duties. You really don't understand how mathematics works. I took several courses taught by a modified Moore method: the professor would give us a series of statements which we had to either prove or find a contradiction for. The propositions were cumulative over a year meaning that something we proved in September was still true, still applicable and still useable in May. The whole point of the course was to consider possible proofs, figure out if they were true or not and then establish our decisions. No morals, no dictated behaviour, any and all approaches and methods were allowed and anything we did that did not pass muster could be shot down by other members of the course or our instructor. No where, never, did anything outside of the pure mathematics matter at all. The only time I can remember anyone saying anything about morals or behaviour was when we were told we had to have a kind of killer instinct for things; go for the kill, take your best shot. Do you see, have to language? That’s a clue. why is it important for conjectures to be confirmed? Ans, the same duties. No, no, no! That's how mathematics works! You throw out an idea, you try and show it true, other people look at your work, see if there are any obvious faults or flaws, etc. No morals, no social issues, just the math. do you notice the duties poking through here: “establish the truth” “correcting reasoning” In a Mathematical sense! Not in a moral or societal or any other sense. and BTW, that is the point of my observation and recognition all along: even attempts to deny, object, dismiss etc end up inescapably appealing to said first duties of reason. No, either your math is correct or it isn't. That's the only criteria. You clearly have never actually taken higher level math courses, had to take a shot at proving an unknown conjecture in a room full of peers, lived with the times when you got it wrong, enjoyed getting it right. No morals, no philosophy, no societal standards or mores, none of that. That's the beauty of mathematics. It's free from all of that. why does something need to be founded, but that per duties of prudence in a world of error we find ourselves duty-bound to warrant claims as reliable via appeal to duty to right reason and to truth? Again, clearly you haven't taken a 'proof' class where you learn to speak mathematics. A self-evident truth is not proved but recognised. There are no self-evident truths in mathematics. Only axioms, conjectures, lemmas, corollaries and theorems. First, based on sufficient experience and maturity, we understand it, and see that it is so, is necessarily so and is such on pain of immediate patent absurdity on attempted denial. This is the crux of the matter: nothing in mathematics is given or accepted without scrutiny. That's the part I think you don't understand and why mathematics is different. And besides, some of your necessary truths are not universally accepted and we've been trying to get you to address that issue for weeks but you refuse to consider that your most deeply held beliefs are just that, beliefs. That other intelligent and rational and reasonable people can and do disagree with you. The link is not directly Arithmetic to morals, though just arithmetic and a just system of quantities is part of just weights and measures. No, it is that arithmetical reasoning is a sub-species of reasoning. It is reasoning, in general, in toto, that is governed by first duties of reason. That's just you trying to shoe-horn math into your moral world view. It doesn't work that way, it never has. Euclid's work stands above his social and moral and historical situation. It's independent of those things. They have no hold on the math. Strange, yes, seemingly bizarre yes, absurd no. It is the attempted denial that will inevitably show the absurdity. Your continued attempts to harness mathematics for your own ends is absurd. I do not understand why some folks who are clearly much less experienced in a very specialise field try to insist their interpretation of the work in that field serves some purpose that they are interested in promoting. You cannot, you must not, impose your view on something which you have much less experience of than others who are telling you that you are mistaken. What kind of hubris, what kind of elitism drives someone to do that? The utter and complete conviction that they are right? In which case they stop listening to what others have to say and just keep insisting that they are correct and those with years of academic and other experience don't understand. Why don't you start listening for once instead of dictating and dismissing? Because you cannot possibly accept that you might be incorrect? You are not going to change. You are not going to give an inch. You've already decided and the theatre of a conversation or discussion or debate is just theatre, a comedy, maybe a tragedy. But nothing you will ever take seriously. And you wonder why people find it hard to take you seriously about some of your beliefs? You don't take them seriously, you dismiss them over and over and over again because, in your mind, you know you are right so they must be wrong. Must be.JVL_{January 22, 2021
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Forget it, I say to myself.Viola Lee_{January 22, 2021
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VL, that we can and do use canons of logic and warrant routinely is not at issue [see Copi's textbook for a good first reference), what this is about is where they take force from, and recognition of the nature of such first duties; they are oughts, they are self-evident, they are pervasive, they call us to training and development of sound judgement etc. Insofar as on another focus, they shape the core of lawful government, they are guidestars for much needed reform of current praxis of law and government to restore sounder approaches that for example will check the Jacobins. KF PS: Judging by some of the above, not everyone recognises that first duties apply to all rational action, including how we compose and respond to mathematical arguments.kairosfocus_{January 22, 2021
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What you don't address is how human beings ares to use those to reach various judgments about real-world situations, and how people who are equally committed to those duties can reach different conclusions, and how we are to live well in a world where people do reach conclusions.Viola Lee_{January 22, 2021
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KF, we accept that! You don't need to repeat it again.Viola Lee_{January 22, 2021
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VL, sorry, I am not suggesting that someone here questions use of right reason. I am pointing out that we find ourselves duty-bound to right reason and linked duties. So much so, that the attempt to deny that duty boundedness is itself an implicit appeal to said duties. Thus, the duties are inescapable, inescapably true and self-evident. KFkairosfocus_{January 22, 2021
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Hi JVL. KF seems incapable of understanding that no one is questioning the use of right reason. He is very much a Don Quixote, tilting at imaginary enemies and not seeing the reality of the issues that he is not addressing.Viola Lee_{January 22, 2021
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JVL, I will again highlight how, yet again, your intended objection -- as is true of any reasoning -- inescapably depends for its force on first duties to reason:
>> If I claim to have a proof>> - why a proof, a particular type of warrant? Ans, because we are prone to error so we seek reliable confirmation of accuracy and derivation from axiomatic start points taken as true. - this appeals to duties to right reason, truth and prudence. Unsurprising as mathematical reasoning is reasoning. - the root claim is not on mathematics but on reasoning, which then embraces mathematics as a form of reasoning. - ask yourself, why should anyone pay slightest heed to a supposed proof? Ans, because of said duties. >> for a mathematical conjecture (thereby turning it into a theorem) I have to>> - Do you see, have to language? That's a clue. - why is it important for conjectures to be confirmed? Ans, the same duties. >> exhibit correcting reasoning to establish the truth.>> - do you notice the duties poking through here: "establish the truth" "correcting reasoning" >>Nothing to do with morals at all. >> - err, nope, the duties are there - even this failed conclusion is an appeal to right reason, truth and warrant thus prudence. - and BTW, that is the point of my observation and recognition all along: even attempts to deny, object, dismiss etc end up inescapably appealing to said first duties of reason. >>Why you keep insisting it does is bizarre>> - attempted dismissal, but it only manages to be a failed appeal to said duties. You are actually projecting the absurdity to the other. >> and clearly unfounded>> - why does something need to be founded, but that per duties of prudence in a world of error we find ourselves duty-bound to warrant claims as reliable via appeal to duty to right reason and to truth? >>based on>> - appeal to right reason, to warrant (so prudence) and truth >> a multitude of examples>> - failed, attempted disproof by counter-example, tracing to the implication logic, a principle of right reason
The point is, yet again, shown. A self-evident truth is not proved but recognised. First, based on sufficient experience and maturity, we understand it, and see that it is so, is necessarily so and is such on pain of immediate patent absurdity on attempted denial. Not, that we go through a chain of warrant to conclude but that the absurdity is instant. That is why such are start points. We saw that with Epictetus in Discourses, when someone challenged the validity of logic. That is a subset. Further to all of this on reflection we will see how we do feel an inner witness drawing us to truth, right reason, prudence [including warrant and much more], all reflecting duty to sound conscience. Of course, such could be delusional, after all that error exists is patent fact and is in fact self evident. We find the urge to avoid error, to accurately describe reality and to show good grounds that we are so doing, the duties are calling out to us in the song of the heart. But moreso, were we to deny these, we would be in absurdity. This is the context of the observation that the objector finds her-/him-self inextricably entangled in these duties. Why object, why not you do your thing, I do mine it does not matter. Because, the said duties are at work in the very fabric of the objection. It is not a mere trick of language and if one were clever enough one could phrase an objection to the truth claim that does not appeal to duties to truth, right reason etc. That is, we see inescapable duties, inescapable truths, self-evident truths. Not, proved from axioms but prior to even axioms. We construct axioms and we state principles of reason using a fabric pervaded with these duties. To try to prove them, we must use them. To try to deny them, again, we cannot escape using them. They are primitives of rationality antecedent to warranting exercises. This points to the underlying issue, it seems bizarre because it is on the other side of a paradigm shift. The link is not directly Arithmetic to morals, though just arithmetic and a just system of quantities is part of just weights and measures. No, it is that arithmetical reasoning is a sub-species of reasoning. It is reasoning, in general, in toto, that is governed by first duties of reason. Which has been the argument of invitation to recognise what we so easily overlook, from the beginning. Strange, yes, seemingly bizarre yes, absurd no. It is the attempted denial that will inevitably show the absurdity. KFkairosfocus_{January 22, 2021
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Kairosfocus: no, you made several claims, and indeed the norm you just appealed to is another appeal to first duties, that claims should be warranted. Again, truth, right reason, prudence. A further example of the inescapability of the first duties of reason. Sigh. If I claim to have a proof for a mathematical conjecture (thereby turning it into a theorem) I have to exhibit correcting reasoning to establish the truth. Nothing to do with morals at all. Why you keep insisting it does is bizarre and clearly unfounded based on a multitude of examples, i.e. any theorem you can think of. Not a single theorem has anything to say about morals, is not dependent on morals to be true, does not affect or influence moral behaviour, etc. You'll just repeat the same thing you've been saying for weeks and weeks. You can't actually address the question of how EXACTLY mathematics and morals are connected. 'Right' reasoning is not the answer because you are already lacing that statement with a moral stance. You have to go back to the beginnings of mathematics and show that learning how to add 2 + 2 was a moral exercise. No 'first duties', no prudence, no claims; just draw the link between arithmetic and morals.JVL_{January 22, 2021
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