# How is logic utilized in constructing ethical arguments?

Forgive me if this sounds ignorant. Although I am an applied person, my experience in using logic in academia is through mathematical proofs, primarily in the real analysis. I have a friend who is a philosophy major who tells me that philosophy and mathematics has a lot of overlap (which I am heavily aware of). I can see the logic aspect of philosophy used widely in proofs about the behavior of functions, I am in no doubt denying that. Without logic, there is no mathematics.

However, I understand there are other subdivisions of philosophy other than logic. These include ethics and metaphysics among others. Do all subdivisions of philosophy use formal logic in mathematics? I am very open to changing my perspective and by my own admission I might come off as abrasive not because I am defensive, but because I am ignorant. How can you use logic in ethics for example?

Isn't the construct of logical argument biased to the beliefs held by the arguer? For example, 2 people could argue on what has a correct truth value. For example, assume you are trying to argue against the right to die.

Someone pro euthanasia could say A⇒B∨C

Where A is "Patient is very sick", B = "Can live with assistance", C = "Allowed to die with dignity"

But, someone who is very pro-life could say

D=∅, where D is the set of justifiable conditions that can warrant humans to take another human's life.

Both have used logic, but both have different views. Who is to say once side of an "if, then" statement has a truth value of T or F? Again, I apologize for my ignorance. It's just that I am used to doing proofs with universally accepted definitions with constraints, like "a is in the rational set iff it can be expressed as the quotient of p and q, with p and q being in the set of integers such that q is not equal to 0".

• You could really edit down a lot of your question to just "I am trained in formal logic but not philosophy and was wondering if formal logic is used in ethics" then you could put your example. Commented Sep 26, 2015 at 2:45
• Outline of an answer: no, formal logic is not used in ethics (you might be able to find an exception somewhere if you really look hard), but a background in logic is necessary for doing ethics in philosophy. Put another way, normal logical connections are used but not as formalization. Disjunctive syllogism is applied but not symbolized, etc. etc. Commented Sep 26, 2015 at 2:47

That depends on what you mean by logic.

In a looser sense of logic, certainly philosophers argue "logically" about ethics, i.e. give arguments relating to ethics and ethical questions. For example Hume argued that you can't derive normative conclusions from factual premises.

In a stricter sense of logic we have deontic logic (a formal language, axioms and inference rules, and semantics). These logics are interesting because there are certain minimal and plausible principles relating to deontic concepts, for example: "P is permitted iff not-P is not obligatory".

Of course the larger question is whether ethical statements have truth values. Because one might claim that logical relations between statements presuppose that those statements have truth values.

So for example emotivists (a version of moral non-cognitivism) claim that ethical statements simply express emotional attitudes, which plausibly means that there can't even be ethical disagreements: me emoting "hurrah voluntary euthanasia" does not contradict you emoting "boo voluntary euthanasia". But emotivism has its problems, and there are alternatives.

Also another larger question is how do you demarcate ethics from other topics? So one might plausibly claim that even mathematics and science involve norms. Arguably logical consequence is partly a normative notion: truth is the norm of assertion and belief.

• Ok, I undeleted it, the reason was that I forgot something essential for ethics and the question: practical reason. I tried to include it to my answer, but it just wasn't working. Commented Sep 26, 2015 at 6:35

I don't think formal logic is really necessary for ethics. However, logical reasoning has played a large role in modern ethical thinking, usually expressed in terms of rules for political-social organization of a "just society."

Examples include Kant's categorical imperative, Bentham's felicitous calculus, and Rawls' theory of justice. It is simply a matter of setting your axioms and rules of "the good," then reasoning towards those ends.

Hobbes, for example, begins with the axiomatic assumption that "all men fear being murdered" and "any man is capable of murdering any other." He then proceeds with a systematic development based, in his words, on Euclid'd geometry. Rawls was responsible for reintroducing ethics and justice in analytical philosophy. He commences with the axiomatic, "veil of ignorance" in which the reasoning agent seeks his own ends, but begins in absolute ignorance of what position, body, or talents he/she might possess. He then adds other decision "rules."

Prior to Rawls, ethics had been largely abandoned on the analytical side, where mathematical logic reigned supreme under a strict division of "fact" and "value." This, incidentally, was a welcome state of affairs for the supposed economic logic of the "market" under theories of marginal utility. A calculus of all values.

It was the eventual erosion of a secure foundation for "facts" that whittled away the "fact/value" divide and reopened ethical and other "value" topics on the Anglo-American side. Logical systems, such as game theory, can certainly apply as long as certain fundamental values are axiomatically accepted as "ends." However, as I say, modern symbolic logic may be of limited use here.

Deontic arguments appear to have logical form though they deal with values or imperatives not facts. (Vide Jorgensen's dilemma) Logic is useful in showing why such arguments are fallacious though, by the same token, they can't positively disprove it. Ross's paradox deals with a situation where a non sequitur has higher instrumental value e.g. saying 'don't post the insurance letter- just burn down the house already!' Moore's paradox deals with situations where some one says 'I believe x but know x is not the case'. This arises all the time in the real world, indeed Newcombe type problems- like Kavka's toxin- prove surprisingly common in Game Theoretic analysis of various bargaining situations. Cognitivism appears a promising way of taming Ethical problems but it generally turns out that such approaches make absurd computational demands or require P=NP or there is a way to discriminate pseudo random from random strings or some thing of that sort. Moral Philosophy is hilarious in that, in general, the more rigorously 'logical' a theory the more atrocious its prescriptions. This is because its first order language has to include at least one impredicative term because any word that relates to human intentionality is going to feature 'holophrastic indeterminacy'and the researcher tends to forget this inconvenient truth and soon ends up with an ex falso quodlibet snowball of silliness.

• You may wish to reread the question as it's not asking if people make arguments in ethics. It's asking about the use of formal logic in ethics. Commented Sep 27, 2015 at 5:13
• I have given a brief introduction to the stumbling blocks to the use of formal logic in ethics. Your suggestion that anyone would be foolish enough to ask if 'people arguments in ethics' is risible. Commented Sep 27, 2015 at 10:55
• Not sure why you're misquoting me. Are you sure you know what formal logic is? As referenced in the question, it's ideas like speaking of null sets and using existential and universal quantifiers. As someone who works in ethics for a living, I can say this is not very common... I don't see anywhere in your answer that moves beyond elementary logic which is used implicitly... Commented Sep 27, 2015 at 12:10

Reasoning is used in ethics; but it isn't formalised. For example, the law of the excluded middle is generally accepted: one does not accept both following unqualified statements:

Thou shalt not kill

And

Thou shall kill

In a just war theory - a code of military ethics - one qualifies and justifies when one can go to war, the code of conduct during war, and more recently how post war, peace-treaties are to be negotiated and how settlement and reconstruction are to be handled.

• If what you mean is that one cannot accept both statements of the form A and ¬A then perhaps you wanted to say that the law of contradiction is generally accepted? Commented Feb 8, 2020 at 20:29