"They probably wouldn't, because the grammar of ordinary language does not follow the rules of propositional logic.

In propositional logic, the following is a valid argument:

P → ¬P
∴ ¬P"

Exactly. And if someone wouldn't make such an inference, I am suggesting that that is a logical mistake of some sort, which is a way of saying the argument is not valid.

Michael, the argument is simply this:

If it is raining then it is not raining.
Therefore, it is not raining.

Who in there right mind would conclude the conclusion from the premises in a conversational setting?

(It is a different argument from the original argument in the first post).

I am referring to the "it is raining" example; the conclusion in that argument appears to be a logical leap. I get that the argument is formally valid, that's the entire point - while formally valid, the conclusion does not appear to "follow."

I may be using "equivocal" incorrectly; what I meant is that there may be two senses of the term "valid" in a logical context; one formal, the other informal and that evaluating an argument with either definition may cause different conclusions as to whether a given argument is valid.

I think you are right that material implication is a problem in the example I stated; the premise appears to not be true (and to never be true).

Still, it also appears that the conclusion is an unwarranted logical leap from the premises, so that is why I think there might be room to argue that the argument is not valid according to some informal definition of logical validity. That is to say, the conclusion doesn't follow or doesn't lead to the conclusion. I understand that this is not the definition of validity formally speaking.

I am not entirely sure what the original post is asking.

This comment does not directly answer the original post's question:

It seems that, if you accept the historicity of Jesus, and accounts given of the apostles such as the martyrdom of Peter, and if you also deny that Jesus rose after suffering a brutal execution at the hands of the Romans, then Peter would have to be just the least intelligent person imaginable to continue to preach about Jesus.

So either early Christians like Peter were all complete idiots, or he was an individual of heroic virtue. But where would such heroics originate? In other words, if someone considers as though they were Peter, why bother preaching if none of it is true?

Okay, but I can actually see how the edited conditional could be true. For instance, if Michael is a really great citizen, then maybe he would end up being President were he American, if so, then in the ordinary sense, the sentence can be "true" based on what it means.

I am not sure what you mean by saying "If I am American then I am the President" is true in propositional logic. But I do appreciate that that conditional is not true in ordinary language.

Yes, because I have a better understanding of how to define validity in a formal context. No, because in a non-formal ordinary sense, and in a natural language context, the argument still seems invalid.

If I uttered: "If it is raining then it is not raining." ... If formal logic is "mappable" onto ordinary language, then you should be able to infer "oh okay, it's not raining." But no one speaks like that and no one would make such an inference. At least, no one would consider such an "argument" "valid." That being so, while I would prefer there not to be equivocal definitions of validity, it appears that there are, one formal, the other informal.

and @Hanover, and @Banno, and @all participants to this thread,

I was hoping this thread would be a discussion investigating deduction, implication, and validity. I am thankful that that is what everyone is discussing and other topics. I wish I had more to add to the discussion, but I am not as well-versed in logic. I have learned what I think is a strong definition of validity, which TonesinDeepFreeze stated earlier in the thread. I encourage respectful discussion of these topics by all parties.

Insofar as the things you mentioned are objectively bad for the organism, I would argue that they are morally bad, or are at least morally worse than a situation wherein the organism was not so harmed.

It seems to me that science may not be very good at defining an act as right or wrong. On the other hand, I think it may be quite good at saying what is good or bad (for an organism). "Cigarettes cause cancer" is a scientifically established fact.

Perhaps it may be asked whether what is bad for an organism is morally bad, but, to my eyes, the answer seems to be "yes."

Follow-up question: when we say "ethics isn't a science" do we mean ethics does not require any kind of scientific knowledge and can be applied through a kind of a priori cognition/intuition? Or do we mean that the kind of knowledge that science supplies is either insufficient for ethics or does not apply to ethics at all?

I myself can be sympathetic to the view that scientific knowledge may be applicable-but-insufficient for ethics due to something like a normativity objection.

I also tend to think scientific knowledge is unnecessary for ethics even though it may be able to provide evidence concerning moral facts.

Is it a problem that "not-(A and not-A)" is also a valid conclusion of the argument? According to the definition proffered by Hanover, it would seem to be a problem given that "the negation of the conclusion flows from the premises."

Can you provide a citation for that criterion of validity? I did not find it in the wiki article.

Also, Hanover, thanks for articulating an argument against validity as I was not sure how to do so.

Are there any domains (I'm thinking of ethics) where you think methodological naturalism would not be instructive, or would you recommend it as a complete and holistic approach for understanding all of reality?

Nevermind, "A and B Therefore C" would be an invalid argument where the conclusion does not contradict the premises.

Can anyone think of an invalid argument where the conclusion does not contradict one of the premises?

It is an interesting problem to me because according to this website -- https://www.umsu.de/trees/#(A~1~3A)~5(A~1~3A) -- the argument is apparently valid. Even though you and I can plainly see that such an argument can never be true. It is an obviously bad argument in a way that:

not (P->Q)
Therefore, not-P

is not an obviously bad argument (bad argument though it is).

I would also note that the argument "A->not-A, Therefore not-A", though it is apparently a valid argument, does not make much sense in natural language; it would be like saying "if it is raining then it is not raining." Maybe someone could infer from that statement that it is not raining, but the statement seems more like a contradiction then a "valid" logical statement.

I can see why the premises imply G. I agree with Michael that there is a translation issue.

I think I meant to say:

1. not-G -> ( not (P->A) )
2. ( not (P->A) )
3. not-A
Therefore,
4. P

My understanding of a valid argument is that it is one such that if the premises are true, the conclusion must be true. Sounds like you are saying the initial argument is at least inconsistent; does that prevent it from being a valid argument? Or is it valid, just unsound?

Am I understanding you to be saying, similarly to unenlightened, that one of the premises must be false given that they are "inconsistent?" The argument is valid but unsound you are saying?

If so, can you say which premise is false and why?

I think adding content to the logical propositions definitely demonstrates the absurdity of the argument; but it seems to me that the absurdity is implicit in the structure of the argument itself - we don't really need the content to see that.

The argument seems a bit less problematic if the second premise were changed to: "Sue is not sitting" because then it seems to me that the argument can at least be true in some sense.

I agree that A -> not-A seems like a questionable premise; perhaps that is the premise you think is untrue. But what makes " A -> not-A " a premise that is not true? Does it have something to do with truth tables?

Okay, what about this argument -- https://www.umsu.de/trees/#((A~5~3A)~1A)~5~3A

A -> not-A
A
Therefore, not-A.

There must be a difference between implication and deduction, right?

not-G -> ( not- (P -> A) )
not - P

does not imply

G.

in fact, the premises do not actually tell us anything. On the other hand,

not- G -> ( not- (P -> A) )
not- A

does seem to imply..

P.

But again, it still does not imply G.

On the other hand,

not- G -> ( not- (P -> A) )
A

does seem to imply

G.

I am against abortions for religious reasons.

A lot of people seem to think consciousness is important to deciding whether abortions should be allowed. I guess my question is: are you proposing we have a "consciousness test" for fetuses? And will this test be 100% accurate, or will it sometimes mistake whether a fetus is conscious?

If the consciousness test is not 100% reliable, that would be a reason against allowing abortions. One could only still support abortions if one were willing to sacrifice an innocent person, a morally repugnant decision.

I think this reasoning defeats any condition stipulated that purportedly would have rendered abortions permissible.

Third: what type of computing power would be required to 'house' this virtual universe? Are we talking about computers that are bigger than the universe itself? Is this possible even in principle? — jasonm

My understanding is that a nucleotide of DNA is the best way of storing information. A nucleotide of DNA is about 2 nanometers in diameter by .33 nanometers in length; it stores 1.8 bits of information. The earth, according to some estimates, now contains approximately 10^44 bits of information or something in that ballpark. If you took all the information contained by earth, cultural artifacts, digital information, etc. and stored it on nucleotides of DNA, you would need, if my math is right, about 1^28 cubic meters of nucleotides, The sun is only 1^27 cubic meters. That means, our hypothetical simulated world needs to be stored on a device that is no less than 10 times the size of the average star.

Let's put aside the fact that there is no good reason to build a simulated world in the first place, the sheer size of storing the data to build this simulated world seems preposterous.

whether determined to deliberate or not doesn't really matter. I am content to say that a determinist who deliberates is acting irrationally and he will agree with me that he is acting irrationally; that is, that he is not acting according to his deterministic convictions.

Perhaps there is a way to integrate POM with the idea of freer choices having priority when there is a dispute over preferences.

As I said, not choosing, rather than choosing, provides the most freedom, because every choice made restricts one's freedom with respect to that choice already made. And, since the measure of value is freedom, as you say, then the highest value is to not choose, because this provides the most freedom. And, not choosing is what enables deliberation and contemplation. This is consistent with Aristotelian virtue, which places contemplation as the highest activity. — Metaphysician Undercover

I'm not sure I follow this Metaphysician Undercover. You mean to say that when I act according to my free choice, I am actually less free than when I am figuring out what I want to do?

The concern is that when we say "this free choice to use my arm is more important than that free choice to use the cheese grater," one choice cannot be more important for being free. Both choices are free so freedom is not what is making one choice more important; there has to be some external criteria that is the basis of "more important." In terms of consequences, it is not the freedom that differentiates the choices but some other factor.

That being said, I suppose one might insist that one choice is more important because it is a freer choice.

Dan, I am not a professional philosopher, but here are my thoughts on the document you posted:

As I read, I asked myself, how do you define "good?" It seemed to me that you went on to answer this question. It is as if you had said, "the good is when someone is maximally free, and free of any constraints on their choices; the freedom to make choices is good." But then you asked a question about weighing freedoms and about the "importance" of choices. And I found myself very much with the same question I had started with. The "freedom is good" paradigm seems to require further criteria that make the consequence good that is quite separate from the freedom derived as a consequence, an independent standard for the rightness or wrongness of a consequence. But isn't that antithetical to the freedom consequentialist project? If freedom does not make a consequence good, what does?

That being said, it is easy to be a critic of another's writing and there may be nuances to your view that I didn't catch.

Anyways, thanks for sharing the idea.

P.S. This comment is from someone who is skeptical that a comprehensive moral theory is ever forthcoming.

That is exactly what I am doing by showing that belief in determinism is consistent with the belief that one should not waste time deliberating. The point being, of course everyone should deliberate on important questions, therefore the deterministic worldview leads to imprudent decisions.

noAxioms, you said my decision will be different after deliberation then what it would have been had I not deliberated, will it also be better for having deliberated?

I understand the position that my feelings concerning what I could have done could be mere illusions. What doesn't make sense to me is why someone who believes in determinism would ever take the time to deliberate.

Deliberating can either change one's decision or it cannot not. If determinism is true and I am someone for whom deliberation does make a difference, then it seems like I could save myself a lot of time by simply choosing the opposite of what I otherwise would have chosen without deliberating.

It would be foolish, but yes.

Yes.

Here is an argument:

If determinism is true, then there is no good reason to deliberate because such thought will not change how I decide (I must choose, or "act" the same way whether I deliberate or not).

Then, deliberation is pointless and no one should ever take the time to deliberate.

But that is terrible advice; therefore, belief in determinism is counter-productive.

:ok: :up: I myself did not catch that.. good point.