Chatgpt:

"is this modus ponens:

A-> ~A
A
~A"

ChatGPT said:

"No, this is not an example of modus ponens. Modus ponens has the form:

→
A→B (If A, then B)

A (A is true)
Therefore,

B (B is true)

In your example, you have
→ ¬
A→¬A (If A, then not A), which leads to a contradiction when assuming

So it's not a valid application of modus ponens. Instead, it illustrates a logical inconsistency."

You somehow got in your head a wrong notion. — TonesInDeepFreeze

Well, one of us does.

You're confused. I'm not "equating" A -> ~A to A -> B.

Let P and Q be metavariables over formulas. Then modus ponens is any argument of the form:'

P -> Q
P
therefore Q

Instantiate P to A. Instantiate Q to ~A. There is no restriction against such an instatiation.

So

A -> ~A
A
therefore ~A

is an instance of modus ponens. — TonesInDeepFreeze

Again, this is incorrect. You cannot substitute P and Q to be a statement with the exact same truth value and maintain logical equivalence because once P and Q are the same, you have a different logical statement.

A -> ~A = ~A. That is, it is reducible to that.
A->~B is not reducible to ~A.

Therefore: A-->~A is not logically equivalent to A --~B.

It's like saying A+A = 4 and since it's generic, I can also say A+B=4. In the first case, A=2. In the second, we don't know what A or B equals.

It's where you disagree with the definition of 'modus ponens'. — TonesInDeepFreeze

Nope, we're in agreement with MP. We're in disagreement that P--> Q = P --> P. The former is a conditional, the latter a tautology.

If P is false, then P -> ~P is true. — TonesInDeepFreeze

If P is false then if P is true then it is true that P is true is a contradiction pretty plain and simple.

Your error lies in equating A --> ~ A to A-->~B because A-->~A = ~A and A-->~B doesn't equal ~A. They're logically different statements.

Then you'd argue incorrectly — TonesInDeepFreeze

This is where we disgree.

A --> ~A <> A --> ~ B because A-->~A = ~A, yet A-->~B <> ~A.

That's wrong.

If A is false then "If A is true then A is false" is true. — TonesInDeepFreeze

If my dog does not have have fleas, then "if my dog has fleas, then my dog does not have fleas" is false.

It's a valid argument with a necessarily false premise and so is necessarily unsound. — Michael

It's a valid argument only if you allow that A --> ~A is of the form A-->~B.

I don't think it follows proper modus ponens syntax. The antecdent and consequent cannot be the same because if they are then it is reducible to simply ~A.

But my point is that one of the ways doesn't require appealing to explosion or even contradiction since the argument is in the form of modus ponens. — TonesInDeepFreeze

I'd argue A --> ~ A is not of the form A --> B as required as a first premise of modus ponens.

The generic modus ponens syntax requires that the antecedent and consequent be different, meaning that A --> A is not logically equivalent to A -->B because the latter is not reducible to a contradiction.

A --> B = ~ A v B.
A --> ~A = ~A v ~A
~A v ~ A = ~A

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

1 is false. "If A is true, then A is false" is a necessarily false statement.
"If A is true, then A is false" is logically equivalent to "A is false or A is false." This means that A is false.

3 follows from 1 and 2 by modus ponens. — TonesInDeepFreeze

1 means "If A is true, A is false." This means A can never be true, despite it being true. It's a walking contradiction. This in itself can be taken to mean A is false because, as noted A -> ~A is logically equivalent to ~A or ~A as a disjunction of the conditional ( A --> B = ~A or B). 1 therefore means ~A.

This can be reduced to:

1. ~ A
2. A
Therefore ~A.

The conclusion is a restatement of #1. 2 is a contradiction of 1..

1. A -> not-A
2. A
Therefore,
3. not-A. — NotAristotle

#1 is a contradiction, reducible to ~ A or ~A. Since it concludes A cannot be true, the antecedent (if A) is always false.
#2 is false and contradicts #1 that establishes ~A.
#3 is not a conclusion, but is a restatement of #1.

I’m posting that video here because I think it challenges us to re-consider what constitutes language. To what extent is an immediate relationship with our non-human surroundings a language? — Joshs

This causes me to want to better clarify what non-essentialism entails. It does not entail an abandonment of definition entirely. It just means there is no one element required to define what langauge is, but it does not suggest that language can be whatever you want it to be. The person in the video was not engaged in any language that could be deciphered from watching her. She seemed to be interacting with her environment to be sure, but that is not langauge. I might skip around and hum and animals of all sorts might do things that explore and feel the things around them, but that's not langauge.

We needn't do a disservice to what it means to engage in langauge in order to show respect to those who think and interact differently than the most of us. That person might lead a life richer in experience and joy than the vast lot of us, but she doesn't engage in langauge, at least not in that video.

The problem is that English doesn't adequately distinguish the counterfactual or hypothetical conditional from the logical conditional of the syllogism and so we confuse ourselves with the ambiguity.

1. Consider the sentence "If God exists, he will answer our prayers."

2. Consider this sentence "If God exist, he will answer our prayers."

Now represent these both formally.

Note the 2nd is not in the indicative, but the obsolete subjunctive and I'd submit incapable of being reduced formally. It does not say what will be. It hypothesizes. #1 has an antecedent. #2 has a hypothesis.

Or, to better clarify:

If I was President, I'd lower taxes.

I was president

I lowered taxes

P -> T.

P

T. Monus ponens.

But not:

If I were President, I'd lower taxes

I were President. (???)

I lowered taxes.

"I was President" can be represented as P.
"I were President" cannot.

The "were" becomes misplaced because it was a hypothetical as written and now it's being modified into an actual.

This is just to say our langauge poorly captures the distinction and the OP ridicules it

There is no purpose. — Michael

This is an aside, but I disagree. It's no more or less logical to choose backward looking reasons (causes) for why things exist as they do than it is to choose forward looking reasons (purposes) for why things exist as they are. In either instance the first cause or the final purpose is unknowable, and both provide explanatory power. The resistence to looking for purpose is that it demands an altered world view where you accept that purpose exists instead of the typical view that accepts that just causes exist, but the acceptance of causation or the acceptance of purpose are both acts of faith.

So we accept that not only is a zygote's "right to life" not absolute but also that their lives are worth less than other things (even things other than something's life). We might disagree with how little/much a zygote's life is worth, but at the very least we must accept that "we ought not terminate a pregnancy because the zygote has an absolute/overriding right to life" is false. — Michael

If someone accepts that a zygote is a second class person, then I do think they'll have a problem not prioritizing the mother's life. A real pro-lifer could not accept that and would have to bite the bullet and do as Alabama did and say that zygotes in test tubes are people and their disposal is murder. If you're getting concessions from pro-lifers that zygotes are red headed stepchildren, then they aren't true believers.

Would you kill 3 barely conscious, immobile, unresponsive people who will never recover in any way in order to save a single child who is in all ways healthy? That is, do you believe that all people are of the same moral worth in terms of preserving their lives or do you value some more than others? That is, you have a trolly with 3 wonderful people barreling towards a cliff in which all will surely die, but if you veer right, you'll save them, but you'll kill a dozen prisoners, all in for violent felonies.

What about killing 1 person to save 50,000 dogs? Would you do that? And they're super cute dogs. They have floppy ears and their entire body wags when they see you. Fucking cute as shit. Are you going to kill those just for one snotty nosed kid?

This second trolly question is important because it might be that pro-choicers can be accused of picking which people they want in society, offering no inherent value to human life. It's just a human choice based upon human priorities at the time.

A lot of people I have encountered who pontificate about the 'sacredness of human life' are simple hypocrites. They're quite comfortable with capital punishment and don't seem to mind if the poor die in vast numbers through lack of affordable services. — Tom Storm

I'd also hold that the sanctity of human life encompasses the right to live to the ability to one's creation, so much so that I would be violating your human rights if I held you against your will in my basement, yet I don't think it hypocritical to incarcerate the guilty. What this means is we draw a distinction between justifiiable imprisonment and unjustifiable imprisonment.

We can do the same for killing. Examples would be war, self-defense, and punishment. I get that you disagree that capital punishment should go in that list perhaps for a variety of other reasons, but someone who is opposed to murder can consistently and non-hypocritically be in favor or capital punishment just as someone can object to an unjustifiable X but support a justifiable X.

The death due to lack of services I know occurs worldwide, but much less so in the West. I'm not suggesting all is well and that there isn't room for improvement, but I don't see where people don't mind unavoidable death occuring all around them or where that mindset is more pronounced among the religious. Are you saying the religious shrug their shoulders to worldwide hunger and withhold support where their non-religious counterparts are trying to assist?

That presents the opportunity to explain that the life of a zygote has less moral weight than the woman's bodily autonomy. — Michael

I don't see where this conclusion comes from. I agree the trolly problem can show that there are certain circumstances that justify the killing of an innocent person, but I don't see how that changes the weight a pro-lifer would afford an embryo.

I would assume that if the question is whether one should kill one person to save five, that question would be answered by the pro-lifer the same whether "person" is defined as an infant of an embryo.

The trolly argument (as typically presented) doesn't ask you evaluate the lives that would be killed versus those saved before you decide how to steer the trolly. Questions like "who do I throw off the sinking ship to save it, the nun or the thief?" are typically answered by the Kantian that you cannot morally decide to throw anyone off and both the nun and the thief have to die.

In any event, I don't see how we can make the trolly problem fully applicable to the abortion issue because the only true instance where a choice of life has to be made is when there's a question about saving the mother, which even the most pro-life folks usually defer to saving the mother. That is, most would argue the trolly should be steered to save mom and to run over the embryo. The bigger question is why some sick fuck would put an embryo and a mom on the railroad tracks in the first place

As a general matter, I advocate for sanctifying life, not just in a humanist way, but in a way that truly seperates life and humanity in a mystical way. It's not enough for me to simply say we're humans so therefore we afford ourselves priority, but it means something more to me, where I hold each person out in the universe as a child of God with special purpose.

That argument does hold sway with me, and I can understand why some want to avoid stripping that special assignment from the deserving. I don't think it helps though to assign it where it isn't deserving. To say that the value of my life and your life is infinite is true, but to then to say that also of the zygote doesn't just benignly elevate the zygote to special status, but it demeans my status. It suggests that the loss of the zygote is truly is as monumental as the loss of a child.

As in really? You read of a child drowning and that evokes the same thoughts as a zygote being disposed of at the fertility clinic?

And this is where I think the pro-choice get rightly offended, even if it's doubtfully based in anything I've said about the sacred and holy. It's not in the idea that zygotes are afforded great value. It's in the idea that living breathing people are reduced to the value of a zygote and the rights of each must be weighed as if my life is of no more woth than a zygote.

And I say all this because I am about as religious a poster as posts here, but I find this pro-life position hard to swallow. It just seems the result of some dogma that demands zygote = person without much thought into what that means and it obviously comes from a religious tradition foreign to my own that violates my views of the who we all are.

As the article notes, it seems a lot like the electoral college system. I place both of them under the classification of “seemed like a good idea at the time.” — T Clark

I agree with their similiar structures, but I'd say the Georgia unit system was more openly nefarious than the electoral college. Georgia's was created to stem the growing power of metro Atlanta and the decreasing power of the historical racist ruling class.

The electoral college was created as a compromise between having Congress elect the President and a direct democracy, with no other nation at the time electing the President directly. It was based upon distrust of the Chief executive. You can argue it has done nothing to control the power of the President and that it does nothing other than to change the way voting works in the US, but it hasn't predictably helped one group over another. It's just a strange way the game gets played.

What I like about it is that my vote really matters and no one cares about yours. Massachusetts is a slam dunk for Harris, but Georgia is a swing state. Everyone is begging for my vote, but yours is a given and so you don't get dozens of fliers in your mailbox every week.

I'd also add that even when we do divide the districts into equal numbers of voters, we divide the districts in a way to maximize power of one group or the other by gerrymandering.

An interesting instance in unit voting: https://en.m.wikipedia.org/wiki/County_unit_system

Referendum and initiative SOMETIMES lead to very bad law, and sometimes to very good law. — BC

A referendum will capture the subjective preference of the majority at the moment, but whether a decision is good or not isn't always just a subjective question, but it's often something that can be assessed objectively. There's no reason to think the average half engaged voter will be better able to assess that than an elected representative.

You have this "democracy" now, and in fact, the President and expesically the Senate use their powers for serving the financial aristocracy ("300 familities"), they have the full power and do not allow other people to become their competitorr; and it is becomes clear that smart people are not allowed to become presidents in US, because a smart president can become a threat for the power and money of these people. — Linkey

My question was whether we could vote this system back in by referendum or whether you're limiting the power of referendum based democracy.

If you're limiting it, you're writing a constitution. I vote we write in the right to free speech.

Can we vote to create a representational democracy where we have a House, a Senate, and a President so we no longer have to vote on everything personally?

Natural rights are enforced by nature, but not necessarily in a timely fashion — frank

I don't follow this.

The position I am aware of is that governments have the duty to protect natural rights. For example, my right to free speech isn't given to me by the government, but the government must recognize it and protect it else it's an immoral government.

You seem to be describing some sort of karmic system where mother nature is going to send its wrath if not respected and that will result in eventual compliance with her dictates.

The problem is that you have all sorts of horrible governments that openly deny rights and this can only be stopped by intentional intervention and uprising, if at all, but never just by the consistent hand of nature.

So, if people have the natural right to respect in death, it's obvious the dead can't enforce it, but that doesn't mean it doesn't exist. It just means someone else must enforce it for the dead, just like an infant couldn't enforce its own rights without assistance.

Antigone was Jewish? You learn something every day. — Banno

Everyone will eventually be proven to be Jewish.

https://www.independent.co.uk/life-style/christopher-columbus-dna-sephardic-jew-b2630798.html

Scientists in the study of human origins place a lot of significance to burial of the dead. I've never thought through what that really means. — frank

For what it's worth, Jewish law:

"The obligation to bury applies to every corpse, even criminals who have been put to death, the unclaimed slain, suicides, and strangers to the community. To be denied burial was the most humiliating indignity that could be inflicted on the deceased, for it meant “to become food for beasts of prey”.

https://rohatynjewishheritage.org/en/culture/death-burial-mourning/#:~:text=The%20obligation%20to%20bury%20applies,food%20for%20beasts%20of%20prey%E2%80%9D.

am asking you why you believe that a zygote does not have the same fundamental right to not be killed when innocent like a woman does; and you refuse to engage — Bob Ross

You didn't ask @Banno to clarify if the blastocyst he posted was created by fertilization or electronically created parthenogenesis. If the latter, is it not human due to its lack of viability? If so, does that mean viability is a relevant criteria for personhood?

Bob Ross has dragged the discussion back to essentialism again. "It's human, so you mustn't kill it", ignoring capital punishment and war and euthanasia. — Banno

The pro-life argument is not "thou shall not kill." It's not to kill unjustly, which would exclude killing the innocent.

We all agree, for example, that holding someone against one's will ought be prohibited, yet we distinguish between false arrest and legal arrest and between kidnapping and incarceration. We allow certain actions in response to other actions, so it's not hypocritical to permit capital punishment yet prohibit abortion. One person has been found guilty and deserving, and the other not.

What constitutes the just taking of a human life (or deprivation of any human right) might be complicated and nuanced, but that doesn't mean the allowance of some deprivation of human rights in some cases means it must be allowed in all cases.

This is consistent with the biblical commandment at Exodus 20:13 that says לֹא תִּרְצָח (do not murder) which is obviously different from לא להרוג (do not kill). That is, killing is sometimes ok, but never murder because murder has a specific definition that excludes war, capital punishment, but I doubt euthanasia. I point out the biblical passage because I am not confused into thinking the pro-life position isn't aligned with it, but I don't think the position is internally hypocritical.

Crop milk isn't from a maary gland. — Benkei

At least properly use you M key when you correct me.

While all mammals provide milk, not all providers of milk are mammals.

Gentlemen, I introduce you to pigeon milk: https://en.m.wikipedia.org/wiki/Crop_milk

Delicious in Froot Loops and a frothy cappuccino. Those birds will fight you though when you try to milk them.

even bachelors are not as analytic as we like to pretend it is. But hey, everything frays at the edges of language. I'm not too worried about it. — Benkei

That's the Quine argument. https://iep.utm.edu/quine-an/

There isn't a problem with the logic. The problem is that the premise isn't saying what it superficially seems to be saying. — Michael

I've agreed that the deductive logic within the OP is valid. I disagree that it's inductively valid. As in your reduction of the argument to:

"if I do not pray then God exists, I do not pray, therefore God exists."

that is deductively correct.

However, "if you do not pray then God exists" is a false statement if treated as a contingency. The reductio, for clarification purposes, was creating an absurdity, as in, "if I don't scream then I will be a billionaire, I do not scream, therefore I am a billionaire."

That is false because everyone knows that my defining characteristics are that I scream and that I am a billionaire.

If you don't produce milk, of what use are your nipples?

They are completely different. The implicit connotation in the OP makes perfect sense. Your parallel is perfect nonsense. Not all parlor tricks are created equal. The parlor trick of the OP is a great deal better than your attempt regarding billionaires. Your argument possesses no plausibility because it is so obviously unsound. You are trying to make yourself a billionaire with specious reasoning. The OP is not praying on the supposition that God does not exist. — Leontiskos

I was trying to clear away the enticing parlor trick that made the OP appear plausible so that the error could be revealed. If it can be shown that the use of the logic within the OP will lead to absurd results in other instances, then that is a valid disproof of the logic within the OP. Such is a reductio ad absurdem.

Logical equivalence is not determined solely by symbolic representation, especially in light of the interpretive choices made when translating from natural language to formal logical symbols. — Benkei

"If A then B" is logically equivalent to "if C then D." You're going to have offer a proof that is not the case without equivocating between deductive and inductive logic. I don't see how that can be done.

Deductive logic ensures that if the premises are true, the conclusion must also be true. Obviously when the premises are true, a valid deductive conclusion will say something about the world. — Benkei

This offers an equivocation of the term "true." The sylIogism "If A then B, A, therefore B" is true. The statement "I am at work today" is true. It's the analytic/synthetic distinction. It's for that reason why a statement can be deductively true and inductively false, which is what the OP showed. Analytic validity says nothing about synthetic validity.

Your second argument is not inductively supported because the conclusion is supported by the definition of mammal. It's like saying, all bachelors are single, John is single and therefore a bachelor. There's no probability involved that a single man isn't a bachelor. — Benkei

The definition of "mammal" was arrived at a posteriori as opposed to "bachelor" which, as you've used it, (i.e. there is no probability a bachelor can be married) is a purely analytic statement. That is, no amount of searching for the married bachelor will locate one. On the other hand, unless you've reduced all definitions to having a necessary element for them to be applicable (which would be an essentialist approach), the term "mammal" could be applied to a non-milk providing animal, assuming sufficient other attributes were satisfied. This might be the case should a new subspecies be found. For example, all mammals give birth to live young, except the platypus, which lays eggs. That exception is carved out because the users of the term "mammal" had other purposes for that word other than creation of a legalistic analytic term.

"All penguins are black" means something very different as an analytic statement versus a synthetic statement. The former holds it true as a matter of definition. The latter as a matter of fact. Necessary versus contingent.

Another hot button issue as an example, "Can a man give birth?"

So I guess what's the bigger picture? — schopenhauer1

I'd say the main point of the OP was snark, hitting back at those ancient proofs for the existence of God that can't seem to go away. It points out that attempts to bootstrap something from from logic alone lead to whatever foolishness you desire.

No, I don't think so. The OP is nowhere near as "ridiculous" as your argument about billionaires. The English argument of the OP makes sense in a way that you haven't recognized. I don't see that any of this has to do with deduction vs. induction. — Leontiskos

The two arguments (mine and the OP) are logically equivalent under deductive logic. They are represented symbolically the exact same. For one to be more ridiculous than the other means you are using some standard of measure other than deductive logic to measure them, which means you see one as a syllogism and the other as something else.'

Inductive logic references drawing a general conclusion from specific observations and it relates to gathering information about the world, not just simply maintaining the truth value of a sentence. To claim that statement of the OP is more logical than mine means that the conclusion of the OP bears some relationship to reality. If that is the case, it is entirely coincidental.

Deductive logic says nothing at all about the world.

(1) All dogs are cats, all cats are rats, therefore all dogs are rats. That is true, except for the fact that dogs aren't cats and cats aren't rats.

(2) All dogs are mammals and all mammals provide milk to their young; therefore, all dogs provide milk to their young. That is true, both deductively and inductively.

(1) and (2) are represented the exact same way deductively and are therefore both true deductively. (1) is inductively false and (2) is inductively true.

In a syllogism, the premise is a given. In an informal statement, it is a contigency.

That's what the OP plays upon.