Oooh, yeah, good distinction.
I think "love" indicates soething to do with an actor, not an object. I don't think one can love something which does not have aspects to love. And personally, I don't 'feel' Love applies to ought but deliberative beings. I don't love lower animals, nor I do i think it's open to me. — AmadeusD

Okay, but even with that distinction in hand we could still ask what it is about understanding deliberative beings that predisposes us to love them. Is it that their deliberations become transparent and familiar to us, and this in turn somehow makes it easier for us to love them?

Classical authors have highlighted the interesting fact that there is a positive correlation between understanding and love, and it may be that this fact has value for overcoming the 'is'-'ought' gap, insofar as we associate understanding with 'is' and love with 'ought'.

That seems to do the same as Descartes, dogmatically attributing duration to the soul without deeper justification. — Lionino

So do you then see my claim about wood as 'dogmatic'?

I think we need a more precise definition of what you mean by the word 'soul'.

If we say however that experience is something that flows and cannot exist in a single point time but instead needs to exist in an interval of time, I think doubting the interconnectedness is equal to doubting the self (which Descartes gave the final argument again). For Kant, we must think in terms of space and time, I am willing to accept this idea. If it is true, it may be because there is no snapshot of the mind, it must exist as persisting in time, for as we create a snapshot of it in an instant it is no longer a mind but something else. Like a river, if we create a snapshot of it, it is no longer a river but a lake.
I think the subscriber to substance metaphysics is able to doubt that the interconnected of those experiences exists because it is premised on a snapshot of the soul being possible; while process metaphysics will say that there is no consciousness on an instant of time. — Lionino

You use three different terms here, 'self', 'mind', and 'soul'. Are those three all the same thing in the context of this thread?

The difficulty I see here is that we could concede to the process thinker that the soul can only exist in a duration of time, but this doesn't solve the difficulty. Suppose, for example, that the argument is rephrased in terms of durations rather than instants, perhaps in terms of years. Then we might ask whether the soul from 2020 perdures into 2021, and whether the soul from 2021 perdures into 2022, etc.

Substance metaphysics works under the assumption that there is such a substance that can be located in an instant of time (a snapshot), and for one to say that the substance is not being created and annihilated each instant, one has to say that the soul persists through time. — Lionino

If I recall correctly, many Medieval thinkers equate conservation with creation, such that there is no difference between a substance which is conserved and a substance which is annihilated and created. This is part of what I was getting at with the "no adjudicable way to distinguish these two views" comment.

Process metaphysics however will not commit to there being a substance that can be located in time, but that the soul is something that itself exists through time, and thus is also defined by it. — Lionino

Then the other question comes in. If soul is defined by time, and time does not end at death, then does the soul end at death? If the soul is thought to cease at death then it must be defined by something more than time.

So when I am alive and experiencing, it is not something that happens in an instant but something that happens constinuously, there is no consciousness without time. Therefore process metaphysics doesn't have to prove the persistence of the soul, it is premised in that metaphysics. — Lionino

But what is the difference between building an answer to the inquiry into one's premises, and begging the question? This seems to be precisely what a petitio principii is.

As soon as we prove our own existence, the existence of the self, and we are premised in that self existing as a constinuous entity (process) rather than a discrete one (substance), we know that the self endures. — Lionino

If the question here is whether there is a proof for perdurance, then it is the same as the question of whether the process thinker's premise is provable.

I think this post from another thread is relevant https://thephilosophyforum.com/discussion/comment/895615 — Lionino

Okay, thanks. I agree that there is something goofy about dividing up the soul's temporal experience into instants of time, but I don't think remedying that goofiness solves the question of the perdurance of the soul.

If we want to be more practical we can ask whether the soul perdures in the case of grandma's dementia, or coma, or "brain death," because this is where the ethical rubber meets the road.

I don't find that to be true. In fact for me it is evidently false — Lionino

The problem with physicalism is that it does not address the sensation of "forever here". This is recognised by physicalist philosophers too: — Lionino

Right, but these two statements of yours seem to be in tension. If it is not evident that grandma's previous ability to recognize her family is merely physical, then it cannot be evidently false that her lack of recognition is not a bodily change.

First, this is not a derivation of RAA. It is a putative modus tollens that looks a little bit like an RAA. As I said, there are analogical similarities.

Second, this is precisely what we argued about in the middle of the thread, and no one was willing to accept this sort of argument as a straightforward modus tollens. Again, the whole reason you have been so laser-focused on RAA is because the MT is so unconvincing. Recall that in order to run this "modus tollens" one must conceive of the contradiction as false (or 'FALSE') in a manner that is sui generis for a non-simple logical formula. Earlier in the thread you characteristically begged off from entering into that meta-logical dispute, and as a consequence refused to try to prove ~A via modus tollens.

-

Setting this out more clearly:

A corollary of what I have been arguing in this thread is the idea that reductio ad absurdum is a kind of black sheep in the logical family, or that there is a measure of discontinuity between RAA and the other inferences of classical propositional logic, such that there is no straightforward derivation of RAA from these other rules of inference.*

Now someone like yourself who is unwilling to engage in meta-logical discourse will naturally have a hard time seeing my thesis, and for this reason my thesis was directed towards people like Count Timothy rather than you or Tones. You say that I have made a number of well-documented errors in this thread. This is assertion and hot air which can in no way be substantiated, but there is a way for you to show that my corollary is mistaken. The corollary is mistaken if there is a straightforward derivation of RAA from the other rules of inference in classical propositional logic. All you need to do is provide such a derivation.


* What I have said more recently is that the more purely formal a system is, the less this discontinuity of reductio ad absurdum is able to be recognized.

Deriving RAA from MT [...] are common introductory exercises. — Banno

I'll invite you to derive RAA from MT as a way to engage with what I've already written.

And the modern world can be lived in a guilt-free and openly negotiated fashion. If we live in families or societies that can own up to their mistakes and roll with them, then forgiveness gets easier in both directions.

It becomes the smoothly flowing economy of debts incurred and debts paid. Messages received and new attitudes promised on both sides of the equation. — apokrisis

This is interesting in the way that it illustrates the shift from the individual emphasis to the social emphasis.

Guilt is universally recognized as a problem and there are two primary solutions on offer: a culture of admission of mistakes and forgiveness, or a culture which repudiates the concepts of blame and debt.

Along the same lines, in the Nicomachean Ethics Aristotle says that the belief that someone acted at least partially involuntarily is what makes forgiveness possible. Even the simple admission, "My bad: I regret how that turned out. It wasn't what I wanted," is a variety of involuntariness that can go a long way to predisposing the aggrieved party towards forgiveness.

---

"I've looked at how I can defeat them, and I know that if I can understand them, I can love them." - Ender Wiggin — AmadeusD

So then what is it about understanding that predisposes one to love? And it is worth asking whether the principle also holds when we are not speaking about persons or even animals. In understanding the ocean am I disposed to love or appreciate it more? The moon? A motorcycle?

I'd say that the Oxford English Dictionary's philosophy of language requires us to be able to pick out examples in order to derive definitions. — Moliere

There is a problem with Socrates' pet peeve of giving examples instead of explanations, and dictionaries don't generally fall into this mistake, but in fact you haven't given any examples. You are falling into a more basic mistake of using the definiens in the definiendum, something like this:

• "What is science?"
• "It's what scientists do."
• "What do scientists do?"
• "Scientists do science."

In response to an objection you added a rider that exemplified this problem:

Well as long as they are a scientist, then according to your definition whatever they are doing must be science. — Leontiskos

"Science is what scientists do when they are acting as scientists" — Moliere

If we remove the definiens terms the problem becomes even more apparent:

• "What is science?"
• "Science is what someone who does it does when they are doing it." (or)
• "Science is what someone who does it does when they are acting as someone who does it."

And even if it were so, which I doubt, a tautology is always true. "Science is what scientists do" isn't something I could say is true strictly, but rather is a criteria for class inclusion for uses of "science" or "scientist" — Moliere

This is in large part why I wrote my thread on transparency. When we do philosophy we have to take the risk of saying substantive things, even though this leaves us open to critique.

- I have not, but as I read the first few pages of that chapter I think Lutz is right on the money. For Aristotle and Aquinas anger is a social and moral virtue, and therefore the well-developed person must needs get angry in certain situations, and the health of the society can depend on this. Thanks for the article.

On point:

Since [justifiable anger] is literally treated as the moral sensibility of a person, the total absence of [justifiable anger] in an individual could be condemned by others. — Catherine Lutz, Morality, Domination and Understandings of ‘Justifiable Anger’ among the Ifaluk, p. 209

What are you taking this to actually mean to the discussion? — AmadeusD

I don't know. That's a good question.

The first thing that comes to mind is to not appeal to reductionistic or highly theoretical answers before acknowledging the prima facie phenomenon. It seems that something about grandma's core identity has changed, in a way that goes beyond a bodily change. So the first thing we should wonder is whether it is worth making a qualitative distinction between grandma suffering a broken leg and grandma suffering dementia.

Not at all an attack - i just see the pretty stark practical difference between arguing for "bodily" changes manifesting lets say, intangibly, and actually positing an intangible. — AmadeusD

I suppose the rub is that use of the word 'soul' requires a great deal of disambiguation. But then I would wonder how stark the practical difference actually is? An intangible explanatory entity (if this is how we wish to conceive of a soul) in fact seems to have a great deal in common with an intangible explanation. Both possess a healthy share of opacity.

Still, I'm not sure the OP is using 'soul' in the sense of an intangible explanatory entity.

I never know what to make of common-sense-use of language when it comes up against either its actual meaning, or where it illustrates something clearly untrue such as like "His soul left his body at that jump-scare" where it could be illustrating a genuine dissociation (albeit, extremely transient). — AmadeusD

In the first place I would want to make sure we are taking stock of whether a word is being used in its colloquial sense or in a specialized technical sense. Grandma's change may relate to her body in the technical sense, but probably not in the colloquial sense. The bugbear here is catch-all theories, such as, say, string theory. "Oh, her new condition has to do with a change in the vibrations of the strings." Perhaps, but is this really going to help us understand what is happening to grandma? It's hard to see how an explanation that does not involve colloquial meanings can function as an explanation to anyone other than the specialist, or to one committed to an elaborate unified theory.

Edit: Maybe the more straightforward answer is simply, "Does positing something like physicalism provide an answer to the OP, for or against?"

- Thanks, and I think it is worth noting that when one applies a primarily social phenomenon within the bounds of a single individual things can quickly become fraught (e.g. the notion of forgiving oneself).

IEP gives this as the form of the reductio:
If p ⊢ ~p, then ⊢ ~p — Banno

That is interesting and a bit mind-bending, but it goes to my point above that meta-logical justifications of RAA tend to be sui generis. IEP calls Whitehead and Russell's approach "idiosyncratic." I have no doubt that there are any number of creative attempts to justify reductio in classical propositional logic. It does not reduce as easily to the other rules of inference.

A more stark way to put the difference between a direct proof like MP and an indirect proof like RAA, is that in a dialogical context (which is my primary context) a MP cannot be rebuffed, but a reductio can. Laymen and logicians alike are on occasion apt to say, "An absurdity? A contradiction? So what? 'I contain multitudes'."

Deriving RAA from MT, and MT from RAA are common introductory exercises. — Banno

It would be hard to dispatch Tones' army of strawmen. I think they are infinite.

Within the paradigm of classical propositional logic there is a certain parity between RAA and other rules of inference (although, as noted, there are also significant differences). But the way that a different paradigm conceives of reductio vis-a-vis direct inferences will not be the same as classical propositional logic. I almost guarantee that Aristotle will see a reductio as a metabasis eis allo genos (and part of the difficulty here is that an absurdity and a contradiction are not synonyms in the historical senses of reductio ad absurdum. Metaphysical and logical absurdities are both utilized historically under that name.).

Now RAA can certainly be used to derive other classical inferences, but a large part of our discussion in this thread revolved around the question of whether RAA can be derived from MT, and this is not at all apparent. This is the question that I was most interested in, because I think the inference to ~A is based in MT. On my view there is merely an analogy between RAA and MT, such that RAA is not an instance of MT. Again, this question was dealt with at some length in the middle of the thread, and the reason we ended by talking about RAA is because neither you nor Tones were comfortable arguing directly from MT.

Can you show this using Prop logic? If not, then why can't it be dismissed as an artefact of the limitations of Aristotelian logic? — Banno

What I mean is that when logic becomes purely formal, abstracted entirely from natural language, then RAA and the suppositions that attend it take on a more central role. It becomes primarily a way to elaborate and extend a system.

As I say, I am not a big fan of the term forgiveness. In relation to the OP I would suggest that the issue is more likely to be one of needing a new way viewing oneself rather than needing to forgive. If we recognize that we are imperfect beings who sometimes make mistakes and inadequate choices, we can roll with challenges and mistakes more readily and improve our approach. — Tom Storm

Your posts make me think you do not understand forgiveness, as they are replete with false dichotomies. For example, you here diminish forgiveness and promote the recognition of imperfection. And yet, without the recognition of imperfection forgiveness is utterly impossible. Recognition of imperfection is not an alternative to forgiveness, it is its prerequisite. This is but one example of the odd dichotomies I see.

There may be something in what you are attempting to articulate. Perhaps a difference between Aristotelian logic and prop calculus could be shown in some interesting way. But quite a few of your comments were simply demonstrably incorrect. This thread was a lsot opportunity for you. — Banno

I think you're just unwilling to consider a closer look at the logic machine. One can paper over the differences between RAA and other inferences and get along fine, but there are also interesting differences to be catalogued. And yes, RAA does present a very interesting juncture between ancient and modern logic. MP and MT are commensurable with ancient (and colloquial) logic in a way that RAA is not. RAA directly leverages the LEM in an entirely unique way. But none of my early posts were written with logicians like you or Tones in mind, so it does not surprise me that they did not resonate with you.

If one looks at the manner that a meta-logician justifies RAA it will quickly be seen that the justification is altogether different from the other rules of inference. Looking back at my phil logic text, the author's proof takes the form of mathematical induction applied to the various levels of RAA (i.e. the number of suppositions that an RAA utilizes).

I haven't found RAA to be the most interesting part of this thread, but it should be emphasized that the OP is not ideal material for RAA. RAA ideally requires a set of axioms, the scope of which is then extended over a new proposition. The OP is really not any such thing, and I maintain that the intuitive inference to ~A has more to do with MT than RAA.

You ignored him for twenty-odd pages? — Banno

"When Tones entered." But his primary complaint has been that I ignore his posts (and not a few times have I logged in to find more than a dozen new posts from Tones alone, which are naturally ignored).

Were there any that were not from you? — Banno

Go back and see. Test your a priori thesis for once.

I mostly ignore users who run into a thread shitting on everyone in sight who is not a mod, and that's what I largely did when Tones entered.

Leon has lost much of his credibility in this thread. You have been remarkably patient and persistent. — Banno

From the moment Tones entered the thread there have been complaints about the way he comports himself. His infantile <third-person> nonsense was the most recent chapter in this book.

Depends what you did and why. I'm not a big fan of 'forgiveness' as such - it often has a Christian flavour to it. I'm more of a fan of contextualising what has happened and understanding one's own behaviour to be the product of situational factors. This allows for understanding rather than forgiving - whatever that means. Understanding gives you the option of doing 'better' next time. Is there a connection for you between forgiveness and personal responsibility? Assuming responsibility and changing one's behavior in the future can be more beneficial than merely assigning blame, which often amounts to a passive judgment. — Tom Storm

People tend to quickly confuse themselves when it comes to forgiveness. A concrete example is best. You run into the back of my car. We both know you are at fault. You say, "Sorry, I will pay for the damages." I say, "Don't worry about it."

That is an instance of forgiveness. You did something wrong and thereby incurred a debt, and then the debt was forgiven. That's forgiveness.

By the definition I posted in this thread probably at least three times. Again:

An inference from a set of formulas G to a formula P is valid
if and only if
every interpretation in which all the members of G are true is an interpretation in which P is true.

For sentential logic, that is equivalent with:

An inference from a set of formulas G to a formula P is valid
if and only if
Every row in the truth table in which all the formulas in G are true is row in which P is true. — TonesInDeepFreeze

So then looking at either example:

1. A -> (B & ~B) {1}
2. A {2}
3. B & ~B {1, 2}
4. ~A {1}

1. A -> (B & ~B) {1}
2. A {2}
3. B & ~B {1, 2}
4. ~(A -> (B & ~B)) {2} — TonesInDeepFreeze

Or:

1. P -> Q {1}
2. P {2}
3. ~Q {3}
4. Q {1, 2} — TonesInDeepFreeze

Either way, your claim is not fulfilled. In the first two arguments (4) does not follow from the truth of (1) and (2), and in the third argument (4) does not follow from the truth of (1), (2), and (3). As I've noted multiple times, your appeal to the "truth table" involves an arbitrary selection of certain premises and an arbitrary exclusion of others.

For example, in the third example the "truth table" would be one where the first three premises are true, and no such truth table exists. Given that it doesn't even exist, it surely is not going to help us in the way you claim that it will:

To say ∴Q instead of ∴~P is to selectively consider the truth table for (1, 2), rather than the truth table for (1, 3). To think that a truth table settles the matter is to ignore the contradiction, which in this case is present in (1, 2, 3). — Leontiskos

Yes, the idea of the body being the best picture of the soul seems right to me. I am also reminded of Spinoza's "the soul is the idea of the body".

And what else can the idea of hylomorphism pertain to but the body? — Janus

Suppose you had a nice cup of coffee with grandma at the nursing home yesterday. You go back today and she doesn't recognize you at all, and she is suspicious of your claims to be related to her.

Now the commonsensical interpretation is that her body is the same but her soul is different. If the difference in her soul was manifest in her body then simply upon seeing her you would have noticed the difference, but you didn't.

The objection is presumably something like, "Oh, well the difference is her memory, and her memory is part of her brain, and her brain is part of her body. So it is a bodily change after all." But this is a strange and non-commonsensical way to talk. It is really an elaborate theory of the relation between grandma's lack of recognition and the putative underlying physical causes, and when we talk about "body" we aren't usually talking about such things. For example, you wouldn't go home to your family and tell them, "Grandma experienced a bodily change today."

But sticking to perdurance, it strikes me as a subset of the induction problem. If one takes Humean premises then proof of perdurance is impossible. If one takes Aristotelian premises then familiarity with the nature of the soul can allow one to understand that it has the property of perduring. These are two top-level approaches. — Leontiskos

The point here is that I want to ask the question, "What kinds of arguments could be thought capable of adjudicating the question of the soul's perdurance?"

There seem to be two main camps, one where the soul's perdurance is obvious and perhaps properly basic, and a second where there can be no possible argument in favor of the soul's perdurance. It's hard to understand how this thesis is something that can be properly argued about. It reminds me of the arguments for or against Occasionalism in that way.

In the sense that "From that I am the same person I was before, I can't infer that I will be afterwards."? — Lionino

In the simple sense of, "How do I know that what I have known myself to be will perdure into the future?"

My question is a bit more extreme, it denies the first premise. Though the focus is indeed on the future, as the past is past, the question also applies to the future: ¿how do I know I am the same person I was minutes ago, but not another person with the same memories due to us sharing the same bodily brain? — Lionino

This sounds like a concrete objection to a perdurance view, namely, "But what if you were recreated as a separate person who has the same memories because they possess the same bodily brain?" If such an objection obtains then perdurance fails, but to ask about the objection is different from asking about perdurance per se.

This gets to the separate argument that perdurance is the prima facie view, and that it should stand if there are no good objections.

How so? — Lionino

Familiarity with the soul shows that it perdures, just as familiarity with wood shows that it burns. This familiarity comes both with respect to our own souls and with respect to other person's souls. For example, I can continue my chess game with my friend from yesterday because his soul and mine perdured from yesterday to today.

The alternative is that it is constantly being annihilated and created through time; though it is not an appealing alternative, he does not address or refute that possibility. — Lionino

I don't know if it's the same excerpt, but your quote from page 1 seems to conclude in the idea that one is dependent for their existence, and "that conservation and creation differ merely in respect of our mode of thinking and not in reality." This gets at the idea of distinctions without any difference. If one person says that we are conserved in existence at each moment and another says that we are recreated at each moment, and there is no adjudicable way to distinguish these two views, then what are we even talking about at that point?

The process is the perdurance through time, so, if there is such a thing as some experience in time, and each point in time there is this same element, the soul is the interconnectedness of those experiences, that gives rise to a sense of self which is the subject. — Lionino

We can define 'soul' as "the interconnectedness of those experiences," but in that case the original question seems to simply morph into the question of whether this "soul" exists.

Since all perceptions are subjective responses, you can't claim any property to exist objectively, except to just say the perceptions must be being elicited by something. — Hanover

Isn't it just that there are objects of knowledge and there are the means by which we know these objects? The chair is an object of knowledge, and vision (and color) are the means by which we know this object. A mosquito is an object of knowledge, and pain is a means by which we know this object. The object impresses itself upon us via some faculty we possess.

Then in knowing the means we can also objectify it. Thus we can have knowledge of vision, or color, or pain, and this knowledge is obtained by some subtler means.

Elaborating, we can understand that a red chair exists via our visual perception of the color red, but then when we go further and consider "red" in itself we arrive at ambiguities. Does 'red' mean an experience, or a wavelength, or something else? If we consider redness as a wavelength then it is an object of knowledge that will have causal effects on even those substances which are not conscious. If we consider redness as the experience of a conscious subject then obviously it will not. Of course it is in fact both, and at each successive stage of inflection upon the means of knowing this duality will emerge. QM shows that even our knowledge is not merely "mental."

I haven't really been following this thread, but presumably at the bottom of Michael's claims is the idea that there are some objects of knowledge that are only accessible to certain types of knowers (e.g. knowers that possess taste and a certain type of taste bud can know that lemons are sour). Drawing a hard mental/non-mental line is almost certainly not possible or productive.

Otherwise, I will remain in doubt, and in absence of any evidence of permanence, I will default to the position that it does not stay at all, and that we are constantly as always dying, as the comic posted in the first page depicts. — Lionino

It seems like you are asking about perdurance, not permanence. The word "permanence" tends to lead to these sorts of considerations:

I’d cite the abundance of veridical near death experiences as evidence of the soul and an afterlife. — Captain Homicide

It seems to me that whether the soul exists from moment to moment and whether the soul exists after death are related questions, with related arguments.

But sticking to perdurance, it strikes me as a subset of the induction problem. If one takes Humean premises then proof of perdurance is impossible. If one takes Aristotelian premises then familiarity with the nature of the soul can allow one to understand that it has the property of perduring. These are two top-level approaches.

Thus, in process philosophy, the soul (or mind or whatever you wanna call it) would be not the substances that stay through time but as an integrating process. — Lionino

Wouldn't the same questions arise, but in this case about the process rather than the substance? It seems that we would simply move to asking whether the process perdures over time.

If blame is not possible then accountability is not possible.
Therefore, if accountability is good then blame is good.

Should one do it? and if one does it then the next obvious step must be to forgive yourself. But why even blame yourself when you're coming to terms with yourself later on anyway.. — Nimish

You seem to be asking, "Why accuse if you are going to forgive?"

Wrong. By the definition of 'valid' in context of classical logic, they are valid. — TonesInDeepFreeze

According to what definition are both proofs valid?

Or if you like, when I asked what rule of inference allows you to draw (4), you simply said, "RAA." What do you suppose the inference rule "RAA" means? "RAA" is no answer at all, and appealing to the mere name begs the question at hand.

On my reading reductio ad absurdum ("reduction to absurdity") is the idea that a supposition can be rejected if it leads to an absurdity. What is necessary for a reductio is <an isolated supposition> which can then be "reduced" to an absurdity. Without a supposition there can be no reductio, for premises are equal one to another. If two premises contradict then our system is inconsistent. A reductio is not what happens when premises contradict.

- Without you and Tones the thread would have been filled with good-faith argumentation, and that's a sobering fact. Can you at least answer a simple question, or is that too much?

Is this statement true or false:

Tones thinks that ¬(1) and ¬(2) both follow from (1, 2, 3). — Leontiskos

So as things stand, 41% of folk got it wrong. Pretty sad. — Banno

That rare combination of hubris and senility. Gotta love it.

I would suggest reading Lionino's first post on page 1, but that would require reading. I see that in the last page or two you managed to misread all sorts of things re: Peirce and Wittgenstein.

- At this point it is a very real question, whether you are even capable of reading at all.

The simple version, for your benefit:

Two premises and an inference:

1. A -> (B & ~B) {1}
2. A {2}
3. B & ~B {1, 2}

What can be drawn from these claims? <According to Tones> one can draw two different, contradictory conclusions (and this pertains to the misunderstanding of RAA). Further, when I ask Tones why he drew one conclusion rather than the other, he tells me to look at the truth table, which is the sort of nonsensical statement that I had thought only you were capable of, for earlier in the thread you had to stick your foot in your mouth any number of times over this same issue.

An odd thing to say, since a contradiction will have "F" all the way down it's main operator — Banno

The question here is the validity of a conclusion. See:

Tones thinks that ¬(1) and ¬(2) both follow from (1, 2, 3). — Leontiskos

A truth table does not adjudicate between (1) and (2). It does not perform the and-elimination of the reductio for us. What Tones is doing is just arbitrarily ignoring inputs to the truth table:

If you want to bring clarity you should explain what inference you used to draw (4). As it happens, truth tables don't adjudicate contradictions. I don't get to say:

1. P→Q
2. P
3. ~Q
4. ∴ Q {See truth table for 1, 2; avert eyes from 3 at all costs. I repeat: do not allow 3 a seat at the truth table!}

(The fact that you think this sort of thing can be adjudicated by a truth table is proof that non-truth-functionality is in your blind spot.) — Leontiskos

To say ∴Q instead of ∴~P is to selectively consider the truth table for (1, 2), rather than the truth table for (1, 3). To think that a truth table settles the matter is to ignore the contradiction, which in this case is present in (1, 2, 3).

1. A→(B∧¬B) assumption
2. A assumption
3. B∧¬B 1,2, conditional proof
4. ~A 2, 3 reductio — Banno

1. A -> (B & ~B) {1}
2. A {2}
3. B & ~B {1, 2}
4. ~A {1} — TonesInDeepFreeze

The reason these are not RAA is because there is no supposition taking place (and again, Tones' original attempt in this thread did not suffer from this problem). Banno and Tones will not understand RAA until they understand that the first step of the reductio portion of a proof (the "supposition" or "assumption") is different from a premise.

For example:

[ ∴ (P v ~P)
1. __Suppose: ~(P v ~P)
2. __∴ ~P {from 1}
3. __∴ P {from 1}
4. ∴ (P v ~P) {from 1; 2 contradicts 3}

Rho is assumed and Mu is supposed, and if someone doesn't know the difference between an assumption/premise and a supposition then they won't understand a reductio. — Leontiskos

If you had a definition for "scientist" do you believe that the person who does not know what a scientist does will be able to identify scientists? — Moliere

That's just what a definition is.

Let's say "Scientists are the people who produce knowledge about the physical world", to use Merriam-Webster. So "Science is what scientists do, and what scientists do is produce knowledge about the physical world, and that production process changes over time" fits with what I've said. — Moliere

"X is what Xers do" is a tautological and uninformative statement.

The "changes over time" idea is similarly uninformative and unhelpful. If the use of a term changes over time then we have equivocation, and in that case in order to talk about the same thing one needs two different terms, and in order to understand what older texts mean by the older definition, one requires linguistic historical knowledge.

He skips that I stated exactly why the argument is valid. If he won't look at a truth table as suggested, then there's little hope he'll understand anything here. — TonesInDeepFreeze

So many of your claims have already been debunked in this thread. The truth-table approach to reductio was dispatched almost ten pages ago!

Has everyone agreed by this point that ↪Banno's truth table does not fully capture what a reductio is? (See bottom of post for truth table)

((a→(b∧¬b)) ↔ ¬a) is truth-functionally valid, but the implication in the first half of the biconditional is not the same implication that is used in a reductio ad absurdum. — Leontiskos

And in bringing clarity to what classical logic actually is, one needs to explain. — TonesInDeepFreeze

If you want to bring clarity you should explain what inference you used to draw (4). As it happens, truth tables don't adjudicate contradictions. I don't get to say:

1. P→Q
2. P
3. ~Q
4. ∴ Q {See truth table for 1, 2; avert eyes from 3 at all costs. I repeat: do not allow 3 a seat at the truth table!}

(The fact that you think this sort of thing can be adjudicated by a truth table is proof that non-truth-functionality is in your blind spot.)

https://thephilosophyforum.com/discussion/comment/922432 — TonesInDeepFreeze

https://thephilosophyforum.com/discussion/comment/922468

The poster continues to indicate that he does not know what validity is in this context and that he is unwilling to read the posts to which responds. He skips that I just stated exactly why the argument is valid. If he won't look at a truth table as suggested, then there's little hope he'll understand anything here. — TonesInDeepFreeze

The poster continues to substitute rhetoric for argument, utterly failing to engage in rational argumentation or inferential reasoning. Why such a course is taken, one does not yet know. Diagnosis continues.

The poster seems to not know what validity is and that he is unwilling to read the post to which he responded. He skips that I stated exactly why the argument is valid. If he won't look at a truth table as suggested, then there's little hope he'll understand anything here. — TonesInDeepFreeze

The poster seems to suffer from psychological delusions and grandiosity. When faced with simple questions he retreats into himself, opting for 3rd-person rhetorical strategies and failing to engage in inferential reasoning.

/quoteWhat rule of inference do you think you used to draw (4)? (4) adjudicates the and-elimination.quote — TonesInDeepFreeze

The poster continues to evidence a significant difficulty in using fairly basic forum features, such as quotes.

1. A -> (B & ~B) {1}
2. A {2}
3. B & ~B {1, 2}
4. ~A {1} — TonesInDeepFreeze

The poster continues to assert his baseless arguments without answering the question and providing the rule of inference he purports to use in order to arrive at conclusion (4). Ongoing observation recommended. He seems to have no understanding of the difference between his truth-functional formalisms and reality, or even how to properly utilize his formalisms.

The truth-functional logicians have no sense of the difference between these two arguments:

The modus tollens and the reductio are two different things:

A1. μ→¬ρ
A2. ρ
A3. Therefore, ¬μ

B1. ρ
B2. Suppose: μ
B3. Contradiction, therefore ¬μ

You can say that "the RAA is logical," but the fact remains that B3 is not as secure as A3... — Leontiskos

...much less 's half-baked reductio:

• ρ
• μ
• Contradiction, therefore ¬μ

- More drool. The sort of confusion and self-contradiction you are exhibiting in this thread within a few short posts is unprecedented.

You made the claim that this was RAA: — Banno

The conversation I am having with Tones revolves around <your argument>, which is an instance of the form of reductio that I gave.

Which, as Tones pointed out, leaves out 3: — Banno

"3" is present in the word "contradiction." :roll: You are and were nitpicking.

And again, as far as I can tell Tones was quoting me without using the quote feature, as he responded to a post where I said:

There is no rule of inference that allows us to draw (4) from (1) and (2). — Leontiskos

From a different angle, Tones says:

1. A -> (B & ~B) {1}
2. A {2}
3. B & ~B {1, 2}
4. ~A {1} — TonesInDeepFreeze

If one looks at previous posts by me, one would see that I also directly, explicitly and formally addressed the matter that RAA also provides:

1. A -> (B & ~B) {1}
2. A {2}
3. B & ~B {1, 2}
4. ~(A -> (B & ~B)) {2} — TonesInDeepFreeze

Tones thinks that ¬(1) and ¬(2) both follow from (1, 2, 3). It goes without saying that there is no rule of inference that forces one rather than the other. I would simply say that both of these proofs are invalid. There is no rule of inference to justify (4) on either count. This all goes to the misunderstandings of reductio ad absurdum in this thread, and in particular to Tones' recent claim that there is no need to advert to a difference between an assumption/premise and a supposition.

This is inane. (4) cannot be invalid on its own. — Banno

A proposition can be invalid qua conclusion, and that's precisely what I said. :roll:

The argument is valid in classical prop logic. — Banno

Again and again the simple questions go unanswered:

What rule of inference do you think you used to draw (4)? — Leontiskos

I didn't. — Banno

You quoted my words and then you said, "Yep..." You just didn't know they were my words. :roll:

There is no rule of inference that allows us to draw (4) from (1) and (2).
— TonesInDeepFreeze

Yep. The example Leo gave is not an example of RAA. — Banno

Tones was quoting me, and he should have used the quote feature. If he had you would not have inadvertently agreed with me. Because as this thread shows, you would say any number of stupid things rather than do that.

Note that (4) is originally your conclusion, and we now both agree that it is invalid. My example was a quote from you, where you claimed to give a reductio.

It is valid. — TonesInDeepFreeze

But it's not.

Every interpretation in which "A -> (B & ~B)" is true is an interpretation in which ~A is true. — TonesInDeepFreeze

All you are saying is, "ρ→¬μ," but this does not make the proof valid. What rule of inference do you think you used to draw (4)? (4) adjudicates the and-elimination.

The argument doesn't draw (4) from (1) and (2). The argument draws (4) from (1) as (2) is discharged. — TonesInDeepFreeze

Heh. Why is (2) "discharged" and not (1)?