If these are truly accidental properties, then they are not in consideration

Why would resemblance and inductive association to the accidental properties in relation to the essential thing not be a consideration? — Bob Ross

Because they are accidental. You're just not properly identifying the situation.

Lets simplify this. Why are the boxes accidental? Lets not just say they are. Lets prove they are. You know that the manufacturer does not care about whether X or Y design has air or not. It is known that they randomly switch between box designs for air and not air, and it turns out the box design X and Y have exactly 50% change of having air or not air.

Thus whether the box is design X or Y is accidental to whether it has air inside. This is a proven accidental property.

Now, lets say that I receive a billion boxes of X, and a billion boxes of Y. low and behold, it turns out all the X's have air, while all the Y's don't. Its an incredibly improbable scenario, but it can be independently verified that yes, its completely a 50/50 chance that either box has air or not.

It doesn't matter the result of the odds, they don't change the odds. Remember that a probability is based off of knowledge, not other inductions.

Here is another way the properties can be accidental. Lets say that X always has air, and Y does not. X is red, and Y is green. You are color blind and can't tell the difference. Within your context, whether its box Y or X is irrelevant to you. It is outside of your distinctive knowledge to know there is a color difference, and outside of your applicable context to tell the colors apart.

Lets take your accidental property that no longer remains accidental.

I am saying that, in this hypothetical consideration, the designs are accidental: it isn’t a question of whether people are implicitly claiming them as essential properties (in this scenario). — Bob Ross

The designs are accidental, not an accidental property then. If you have no foreknowledge of whether box X or Y should or should not have air, then you have not yet decided whether X or Y design are essential or accidental to the identity.

Also, we have to clarify what we're referring to here. If we're referring to the core identity of the box itself as a particular type of measuring tool where air doesn't matter, X and Y are accidental. If we're referring to the probability of whether a X or Y box has air or not, then the box design is no longer accidental to our point!

Taken another way, a type of dog can be green or blue. Whether its blue or green is irrelevant to knowing the identification of the dog. However, you later discover that 74% of these dogs are green, while 25% are blue, and 1% could be any other color. When you are asking, "Is this dog that I cannot see behind a screen green or blue," at that point the probability of the color becomes an essential set or properties in knowing the outcome. At that point, because the point is directly about the color, it is pertinent to the guess at hand. These odds also do not retroactively make the color a primary attribute in identifying this type of dog? No.

To sum up an accidental property - A property which is completely irrelevant to one's assertation or denial of the identity. Meaning that you cannot make an accidental identity suddenly be relevant to the assertation or denial of the identity. As soon as it is relevant, it is no longer accidental.

In the scenario, as I hold the possibility is more cogent than the probability, — Bob Ross

You can decide that you would rather explore the possibility than the probability, but you did not prove that a possibility is more cogent than a probability. Again, all the examples are going to boil down to needing to prove that what one is examining is a known probability, possibility, or plausibility. All that's been done so far is a misunderstanding of the terms.

To see if you understand, take your example again and try breaking it down into clear and provable accidental or primary properties for the context. Second, clearly demonstrate what is a possibility, probability, and plausibility. Only after that careful dismantling, try to prove that you can make a plausibility more cogent than a possibility.

Hello Philosophim,

Why are the boxes accidental? Lets not just say they are. Lets prove they are.

They are accidental because they have been defined as non-essential: distinctive knowledge is definitional. That’s all the proof that is required.

For the personal knowledge within the scenario, I defined a box as “a container with a flat base and sides, typically square or rectangular and having a lid” and defined an “box-with-air” as a “box” + “air”. That is the proof that it is unessential what design the boxes have, because I have defined “box-with-air” and “box-without-air” to have everything but those two factors as unessential.

It is known that they randomly switch between box designs for air and not air, and it turns out the box design X and Y have exactly 50% change of having air or not air.

Firstly, in the scenario I gave, there is no probability known about how many they design in X or Y fashion; so this isn’t analogous. Secondly, that can be your reason for defining a “box-with-air” and “box-without-air” as having designs that are always accidental, but an accidental property is just an unessential property; which does not necessitate that there is a 50/50% chance of it occurring.

Now, lets say that I receive a billion boxes of X, and a billion boxes of Y. low and behold, it turns out all the X's have air, while all the Y's don't. Its an incredibly improbable scenario, but it can be independently verified that yes, its completely a 50/50 chance that either box has air or not.

This is irrelevant, because you don’t know in my scenario that it is a 50/50 chance; and it is not, by definition, true that something which is an accidental property has a 50/50 chance of occurring.

This contradicts your own definition of accidental properties:

The properties which I find are important to me for my memory, the curly fur and hooves, are identities of the sheep I call essential properties. Properties I observe which are irrelevant to my identity of the sheep, I call accidental properties. Accidental properties allow me to remark on how the identity is affected beyond its number of essential properties.

Your definition simply does not equate “accidental properties” with “something which is proven beyond definition as non-essential”. It clearly defines it as “that which isn’t an essential property of the thing in question”. Regardless, in my scenario, when I say that the designs are accidental, I do not mean that they have an equal chance of occurring nor that there is a defect in my ability to identify (such as you color blind analogy): I mean more broadly that the designs are unessential properties.

The designs are accidental, not an accidental property then. If you have no foreknowledge of whether box X or Y should or should not have air, then you have not yet decided whether X or Y design are essential or accidental to the identity.

Firstly, by your own definition of it, any non-essential property is an accidental property (i.e., “ Properties I observe which are irrelevant to my identity of the sheep”)—it is irrelevant if you have foreknowledge of all the potential properties of a thing. If you define a sheep as [X, Y, Z] essential properties, then it is necessarily the case that a property which is not X, Y, or Z is unessential and thusly accidental. Now, you can refurbish accidental properties to become essential ones given new knowledge; but that is different than your lack of knowledge of a property being undecided yet.

Secondly, whether the first point is true is irrelevant for the scenario I gave: I said definitively that what I am distinctively calling a “box-with-air” and “box-without-air” is those two aforesaid properties, and all the rest are unessential ones. So you can’t validly claim that my accidental properties are no longer accidental. It is a matter of definition, which is distinctive knowledge.

Also, we have to clarify what we're referring to here. If we're referring to the core identity of the box itself as a particular type of measuring tool where air doesn't matter, X and Y are accidental. If we're referring to the probability of whether a X or Y box has air or not, then the box design is no longer accidental to our point!

I think you are thinking beyond the scenario, when I am looking for you to address specifically the scenario given. I am saying that the core identity of a box and “with-air” vs. “without-air” is those two aforesaid properties, and everything else is an accidental property. I can do that because it is distinctive (and not applicable) knowledge in the scenario, which is definitional.

No. In the scenario when you are determining the most cogent solution, the box design is not an essential property of anything. I am specifically saying that the design is irrevelant to the definition thereof: I am not saying that the design for the airless box has some necessary component to it that enables it to vacuum out the air.

Likewise, you aren’t calculating the probability of it having air in the box: you can’t. You will never be able to calculate the numerator and denominator for that question: the only probability you know in the scenario is that there is a 51% chance that the box does not have air.

Taken another way, a type of dog can be green or blue. Whether its blue or green is irrelevant to knowing the identification of the dog. However, you later discover that 74% of these dogs are green, while 25% are blue, and 1% could be any other color. When you are asking, "Is this dog that I cannot see behind a screen green or blue," at that point the probability of the color becomes an essential set or properties in knowing the outcome

It is not an essential property of what a “dog” is (which I think you agree with me on that) and it is not an essential property of anything—it is essential to answering the question nevertheless. An essential property is a property first and foremost, which is of a concept (i.e., distinctive knowledge of a thing): you have no concept here to attach the color to. This is implicit in your example: “ The properties which I find are important to me for my memory, the curly fur and hooves, are identities of the sheep I call essential properties”. I think you are confusing something being essential for answering purposes with an essential property.

To sum up an accidental property - A property which is completely irrelevant to one's assertation or denial of the identity.

This contradicts your definition in your OP:

Accidental properties allow me to remark on how the identity is affected beyond its number of essential properties.

These definitions are incompatible with each other. If an accidental property is actually something which is completely irrelevant to its assertation of the identity of a thing, as opposed to merely being not within its set of essential properties, then not all non-essential properties are accidental (i.e., not all non-essential properties meet your first quote here of a definition just because they meet the second quoted definition). I think you are thinking that in virtue of a property being non-essential it doesn’t matter for identifying the said thing, but that is a separate claim than that it is non-essential (and currently in dispute).

I am saying that, although it doesn't matter for meeting the definition of a thing, the accidental properties play a role in identifying it pragmatically (and am thusly questioning your separate claim that non-essential properties are irrelevant for identification purposes).

To see if you understand, take your example again and try breaking it down into clear and provable accidental or primary properties for the context.

I already did this in my post outlining the scenario:

2. You hold that the only essential properties of a box-without-air is that it is a box (i.e., a container with a flat base and sides, typically square or rectangular and having a lid) and it is not filled with air in its empty space (within it).
3. You hold that the only essential properties of a box-with-air is that it is a box (i.e., ditto) and it is filled with air in its empty space (within in).

I am shaping an identity distinctly out of discrete experience. There’s no further proof needed. If I say, for this example, “green” is “the number one”, then the set of essential properties for “green” is [“1”]. There’s no further proof required.

Second, clearly demonstrate what is a possibility, probability, and plausibility.

A possibility is something which has been experienced before at least once. In the scenario, the billion experiences of each are the experiential context for it being possible that the box presented is filled with air or not.

A probability is a quantitative likelihood: a numerator divided by a denominator, where the latter is the whole quantitative sample size and the former is the selected items within the sample size that one wants to know the likelihood of occurring. In the scenario, the only probability given is that there is a 51% chance that the box is a “box-without-air”, and any deducible information therefrom (e.g., there’s a 49% chance that it is a box-with-air).

Only after that careful dismantling, try to prove that you can make a plausibility more cogent than a possibility.

I am saying that:

Since the probability that it is a box-without-air is negligible (because it is only a 1% difference) and the experiential association of the box-with-air with design X, although the design is not a part of its essential properties, so many times (viz., a billion) warrants claiming that the first random box pulled from this sample, being of design X, is a box-with-air.

In this scenario, the incredibly strong correlation between design (X or Y) and the box type (air or airless) outweighs merely going off of the probability. This doesn’t mean that a strong correlation between design and box type always outweighs probability.

Bob

Hi Bob, I think a little too much is being thrown around by both of us, so I'm going to narrow the scope to your exact example.

1. Probability is 51% that the box does not have air.

To be clear, this means that any box given has a 51% change that it does not have air in it. So regardless of box design, its a 51% chance that it does not have air.

I'm going to simplify the others.

The only essential property for a box is that it is a six sided box. If it has air, its a box with air. If it doesn't, its a box without air. Anything else is non-essential.

We'll call call a box with air a BWA, and a box without air a BWOA because I'm tired of typing those phrases. :)

Any box you pick has a 49% chance of being a BWA, while it has a 51% chance of being a BWOA.

Now lets include some non-essential properties. What they are is irrelevant. Lets call them properties X and Y.

So I can have a BWA with a X, and a BWA with a Y. Does this change the probability of the BWA being picked? No. Its still a 49% chance. What about a BWOA with a X and a BWOA with a Y? No, still a 51% chance of being picked. This is because we know that X and Y are non-essential the the probability.

Lets say that I pull any number of boxes. It turns out that I only pull BWAs with X's and WBOAs with Y's. I've never pulled a BWA with a Y or a BWOA with a X, but its still within the odds that I can.

Is is possible that I could? Of course. But does that change the probability? No, non-essential properties don't affect the probability. If they did, they would be essential properties of the probability. Therefore it is still more rational to assume over the course of picking more boxes that I should always guess that I'll pull a BWOA, whether that's a X or a Y.

If you believe that because every BWA you've pulled so far is a X, therefore its more reasonable that a box with a X is going to be a BWA, that's not rational, its just confirmation bias. Your biased results don't make something more or less cogent. It is always more rational to believe that the box will be a BWOA whether its an X or a Y.

Confirmation bias isn't new either. https://www.verywellmind.com/what-is-a-confirmation-bias-2795024#:~:text=For%20example%2C%20imagine%20that%20a,supports%20what%20they%20already%20believe . Its an easy trap for all of us to fall into.

With that simplified, does that answer your question?

Hello Philosophim,

1. Probability is 51% that the box does not have air.

To be clear, this means that any box given has a 51% change that it does not have air in it. So regardless of box design, its a 51% chance that it does not have air.

Correct. The box is, at random, picked from the group and presented to you. The probability is 51% that it does not have air.

The only essential property for a box is that it is a six sided box.

This definition is circular. But I get the point and, for intents and purposes, let’s go with that for now.

If it has air, its a box with air. If it doesn't, its a box without air. Anything else is non-essential.

Correct.

We'll call call a box with air a BWA, and a box without air a BWOA because I'm tired of typing those phrases. :)

Lol. Sounds good! (;

Any box you pick has a 49% chance of being a BWA, while it has a 51% chance of being a BWOA.

Correct.

Now lets include some non-essential properties. What they are is irrelevant. Lets call them properties X and Y.

They are not irrelevant: they are irrelevant to the identity of the thing. That is not the same thing as them being irrelevant flat out.

So I can have a BWA with a X, and a BWA with a Y.

Yes it is logically possible (I am not using “possibility” in your sense here). On top of that, in your terms, it is possible that a BWA has design X and not proven to be possible it has design Y (because you have only experienced it with X). It is, likewise, possible that a BWOA has design Y and not proven to be possible that it has design X (ditto reasoning).

Does this change the probability of the BWA being picked? No. Its still a 49% chance

Correct.

What about a BWOA with a X and a BWOA with a Y? No, still a 51% chance of being picked.

Correct.

This is because we know that X and Y are non-essential the the probability.

For fear of you equivocating here, I am going to stress that all this means is that the probability is independent of whether they have design X or Y. The wording “non-essential” could be equivocated there as having to do with non-essential properties, which has nothing to do with this claim.

Lets say that I pull any number of boxes. It turns out that I only pull BWAs with X's and WBOAs with Y's. I've never pulled a BWA with a Y or a BWOA with a X, but its still within the odds that I can.

Is is possible that I could? Of course.

It is not provably possible under your terms that a BWA could have a design of Y because you haven’t experienced it before. Just to clarify.

But does that change the probability? No, non-essential properties don't affect the probability.

Correct.

Therefore it is still more rational to assume over the course of picking more boxes that I should always guess that I'll pull a BWOA, whether that's a X or a Y.

No. You are forgetting that you have experienced this correlation a billion times each (and none vice-versa). Yes, it is logically possible (note: I am not using “possible” here in your terms) that, even after experiencing X with BWA a billion times, the box is design X and BWOA but you are more justified in inferring that it is a BWA since the probability is so close to each other.

Let’s make it even more obvious what I am getting at: imagine that in the scenario you also know that, although you don’t know which design the box will definitively have (because it is a non-essential property), only design X and Y have ever been associated with either a BWA or BWOA. Now, to clarify, this does not make the designs essential properties: I am saying that these unessential designs have, by happenstance or purpose, been associated (correlated) with them in the past. Maybe there’s a law in place that you have to make BWA’s with X and BWOA’s with Y, but the actual definition of them both doesn’t include X and Y as essential properties (which is entirely possible).

Now you have really good reasons to believe that when you see a box presented to you with design X, although designs aren’t essential properties, that it is a BWA. Is it logically and actually possible that someone broke the law (or what have you) and made a BWOA with X? Absolutely. But guessing BWOA on the X designed box when there is merely a 1% more chance it is such isn’t very cogent given these circumstances.

If you believe that because every BWA you've pulled so far is a X, therefore its more reasonable that a box with a X is going to be a BWA, that's not rational, its just confirmation bias.

Firstly, I am not saying that you have drawn a billion times from the sample of 100. I am saying that you have experienced, independently of drawing from the 100, a billion times each correlation.

If I were saying that just because I pulled a BWA last time that the next will be BWA, then I would agree that is irrational and confirmation bias: that’s not what I’ve been saying.

Secondly, if you would like to call what I just clarified as irrational, then you would have to say all inductions and abductions are irrational because that is how they work. Take Hume’s problem of induction, which you mentioned in your OP: you would have to say it is equally irrational to hold that the future will resemble the past. But this is nonsense: it isn’t irrational to induce or abduce: it can be quite rational.

Your biased results don't make something more or less cogent. It is always more rational to believe that the box will be a BWOA whether its an X or a Y.

Wrong. If I know that the designs X and Y have always been associated with either box and that there is a colossal correlation between X → BWA and Y → BWOA and the probability of one is only 1% greater than the other of occurring, then I am rationally justified in thinking that an X will be accompanied by a BWA (although I could most certainly be wrong). So when they present one at random to me and I see it is an X and only 1% less likely that it is a BWA, I am justified in claiming it is a BWA.

You are basically hedging your bets on a minuscule 1% difference and expecting, given the contextual background knowledge you would have, that this next one will be the only one out of a billion and out of every single one that you have seen that will break the correlation.

I think you are right to assume that if we were to keep drawing, returning, amd re-shuffling the boxes that it would even out over time to 51% being BWOA—but we are talking about one selection here.

With that simplified, does that answer your question?

No. I think the above explains why I think that.

Bob

Now lets include some non-essential properties. What they are is irrelevant. Lets call them properties X and Y.

They are not irrelevant: they are irrelevant to the identity of the thing. That is not the same thing as them being irrelevant flat out. — Bob Ross

It is not provably possible under your terms that a BWA could have a design of Y because you haven’t experienced it before. Just to clarify. — Bob Ross

Ok, I think we've narrowed down the point of contention. I think we're seeing two different contexts here. When you say, "The odds of any box being without air are 51%, and the only thing that matters to the identify of the box, is that its a box," then the non-essential properties of the box do not matter to the probability. If X and Y are non-essential, they don't matter to the probability then. I think that's a straight forward conclusion right?

Your context doesn't quite seem to fit this though, and that's what I'm trying to piece together here. Are you saying that the probability of 51% is only a guess? Or that we only think that the design of the box is irrelevant? In other words, is our 51% open to change, and do we not know if it depends on X or Y?

This is where I'm having trouble seeing your argument. You may have a good argument, but I'm just not understanding it yet. From my point, if X and Y are unessential to the probability, then they are unessential to the probability. Any results from experience, if we know the probability is correct, would not change the probability. Therefore no matter if we simply pulled 99/1 airs to no airs, that doesn't change the probability. The outcome of the probability does not change the probability.

I don't consider confirmation bias irrational by the way, I think that's a bit harsh. Its simply less rational then relying on knowledge we know. If we know the odds, its more rational to play the odds over the long term then not right? Even if we're currently beating the odds, it won't last over long term if the odds are correct.

Back to your point where I feel you changed the context a bit. You noted that it wasn't possible for you to have experienced a Box with Y that did not have air. I had assumed you had. That's true, you don't know if its possible for you to pull that box. Despite the odds, you never have. And yet you know its probable that you will, and its only incredible luck that you haven't so far. If the odds for the air or not air do not depend on X or Y, then each X and Y has a respective 49/51 split as well. This is just a logical fact. Results defying the odds do not negate the odds if the odds are known.

Now you have really good reasons to believe that when you see a box presented to you with design X, although designs aren’t essential properties, that it is a BWA. — Bob Ross

No, you don't. Because it is more rational to stick with the odds that you do then the possibilities that you don't. If you flip a coin ten times and it comes up heads ten times, does the non-essential property of you being in your living room change the odds of the coin's outcome? Of course not. If you start saying, "Every time I flip a coin in the living room, it changes the odds to where I always flip heads," then the living room is no longer a non-essential property to the coin flip, but has now become, in your head, an essential property of the coin flip.

Same as if after you count all the X and Y boxes that have ever been made, and sure enough, it turns out that all X's are airs, while all Y's are not airs. The odds didn't change, that's just one extremely unlikely outcome out of many possible outcomes. At that point since you know all of the boxes, and you've noted something special with the property of X and Y with the box, you could say that all boxes with X have air, while all boxes with Y's don't, and applicably know this. It just so happens that there are 49 billion X's, and 51 billion Y's.

In all of this, you have not shown a case in which it is more rational to not go with the odds beyond confirmation bias. But feel free to try again, as perhaps I'm missing something that you're seeing.

Secondly, if you would like to call what I just clarified as irrational, then you would have to say all inductions and abductions are irrational because that is how they work. Take Hume’s problem of induction, which you mentioned in your OP: you would have to say it is equally irrational to hold that the future will resemble the past. But this is nonsense: it isn’t irrational to induce or abduce: it can be quite rational. — Bob Ross

No, I don't. I simply rely again on the hierarchy of inductions, which rests on applicable knowledge as noted. All inductions ARE inductions, but it simply notes which inductions are more rational to believe in when compared to each other. It is more rational to believe that known rules and laws will remain as they are until we first experience them breaking. Then we will know its possible for a rule or law to break. The sun has always risen in the East and set in the West. It is in induction to believe it will do so tomorrow, but it is the only possible outcome which has ever happened. As such, it is more rational that we believe the possibility over the plausibility that it will rise in the West and set in the East.
My counter to you is to note that the hierarchy holds, so it does not destroy it.

You are basically hedging your bets on a minuscule 1% difference and expecting, given the contextual background knowledge you would have, that this next one will be the only one out of a billion and out of every single one that you have seen that will break the correlation. — Bob Ross

This is isn't hedging a bet. This is simply taking the most rational induction I know of, a probability, and holding it over my confirmation bias of the results I've obtained. My desire has nothing to do with what is more rational. However, being less rational could be less stressful for me right? Perhaps the issue you're really holding here is that you want to make decisions that are less rational sometimes. That's fine. There can be a host of reasons to be less rational in one's inductions. Perhaps you're just tired of examining the boxes and want to get through them faster. Perhaps the penalty for guessing wrong is irrelevant. What you really seem to be saying is that the 1% doesn't matter to you. Which is fine. But it is still 1% more likely, and therefore the more rational choice.

Hello Philosophim,

"The odds of any box being without air are 51%, and the only thing that matters to the identify of the box, is that its a box,"

To clarify, I am saying that the odds of any box being without are is 51% and the only thing that matters to the identity of the box is that it (1) is a box and (2) has or does not have air in it.

Something can be useful to identifying a thing without it having to do with the identity (essence) of that thing. For example, it is not a part of the identity of being human to draw art. You can be a human and never have drawn art and you may be so disabled that you literally can’t do it. However, if I am walking in the park and see some extravagant art (perhaps graffiti), then I can reasonably inductively infer that that was a human that did it. Philosophim, I identified the origin of the art to be human, while never conceding that the identity (essence) of a human is that it draws art. Likewise, it is actually and logically possible that an alien drew the art, or it formulated naturally as a freak accident.

Accidental properties of a thing, such as experiences a strong correlation between humans and drawing and never experiencing anything else doing it, can influence rationally what we identify as being the case.

then the non-essential properties of the box do not matter to the probability. If X and Y are non-essential, they don't matter to the probability then. I think that's a straight forward conclusion right?

That is correct. But I think you are perhaps misunderstanding: the probability is given to you by a person who knows whether each box (out of the 100) has air in it. They are using strictly essential properties to calculate the probability because they can know whether the boxes meet those 2 essential properties. However, when they present it to you, you can’t know if the box meets your criteria because you don’t know if it has air in it: that’s the whole point!

Now, the probability being unaffected by the unessential properties does not entail, in itself, that it isn’t rational, depending on the circumstances, to use them to infer what you think it is.

Are you saying that the probability of 51% is only a guess?

No. It is the actual probability of pulling a box without air.

Or that we only think that the design of the box is irrelevant?

Irrelevant to what? To the probability that was calculated? Yes. To your evaluation of what you think it is, no.

The scenario is only granting implicitly the former, not the latter.

In other words, is our 51% open to change, and do we not know if it depends on X or Y?

The probability stays the same regardless of what design they have because the guy in the back room knows whether they are (1) boxes and (2) they have air in them. Those are the essential properties, so he uses that to calculate the probability. We, on the other hand, only know they are boxes and that they either do or do not have air; but with consideration of the rest of the context as well (e.g., we’ve experienced them strongly correlated with those designs a billion times each).

, if X and Y are unessential to the probability, then they are unessential to the probability. Any results from experience, if we know the probability is correct, would not change the probability. Therefore no matter if we simply pulled 99/1 airs to no airs, that doesn't change the probability. The outcome of the probability does not change the probability.

I agree with you here, but I think you are focusing too much on the calculation of the probability and not that it is a minuscule difference in probability. Imagine there was a %50.00000001 chance that you will pull a BWOA. Now imagine that you’ve experience in your lifetime (1) only BWAs having design X, (2) design X only being on BWAs, and (3) you have experienced #1 and #2 a BILLION times. Imagine, likewise, same thing for BWOA but with design Y. This extra info doesn’t change the fact that you are 0.00000001% more likely to pull a BWOA.

Now, imagine that the box pulled has design X. Given that there is only a 0.00000001% chance more of pulling a BWOA and the sheer incredibly correlations you’ve experienced inductively of BWA → design X. I think that you are warranted in claiming it is a BWA instead of going with the probability. It is more probable that it will be a BWOA, but by 0.00000001%.

Take away the probability for a second, just think of the inductive aspect I am talking about. If you only ever saw design X on BWA and never anywhere else a BILLION times throughout your life. All through society where you have gone and travelled, it’s always the same o’le design X → BWA. You confirmed each time (a billion times) that the box did have air in it and it had design X. The next time I show you a box with design X, forgetting about probability for a second, what would be the most cogent answer? Clearly that it is a BWA. This is no different than thinking that gravity will work the next time you drop something. Actually, in this case, since it is a billion times, you have stronger reasons to think that a design X → BWA than gravity working next time you drop something (as I doubt you’ve experienced thinks drop a billion times yet in your life).

Now, the only extra information we add into the scenario is that there is actually a 0.00000001% in the sample of 100 that this design X is not BWA (as its BWOA). By my lights, if you go off of the probability, then you are saying that you would rather hedge your bets on a 0.00000001% difference that this design X box presented to you is the first box out of a billion and 1 that is going to break that life-long correlation you have experienced. To me, that 0.00000001% difference doesn’t outweigh.

Now, if the person told me that after each guess the presented box is not returned into the sample and they tell me if my guess is correct, then each time I guess I do have to consider that the probability is changing and eventually that outweighs my experiential knowledge of the correlation. If there’s a 99% that it is a BWOA, then I am definitely going with that.

I don't consider confirmation bias irrational by the way, I think that's a bit harsh.

As far as I’ve understood confirmation bias, it is the tendency to seek out a result without sufficient justification for it. It’s like placebo effect: if I think that aliens are ruling the world and I start actively seeking out reasons to believe it, then I will definitely find them. Not because it is true, but because I am intensely trying to fit the world to my narrative. This is irrational.

Confirmation bias is not, as far as I understand, the same as inductive and abductive reasoning. You can assume rationally that gravity will work for the next thing you drop because you have sufficient evidence, which wasn’t just a result of you trying to fit the world to you wants, that that will be the case.

Back to your point where I feel you changed the context a bit. You noted that it wasn't possible for you to have experienced a Box with Y that did not have air. I had assumed you had. That's true, you don't know if its possible for you to pull that box. Despite the odds, you never have. And yet you know its probable that you will, and its only incredible luck that you haven't so far.

I was just clarifying that, under your terms, you couldn’t claim to know it is possible for a BWOA to have design X.

Likewise, in the scenario, I am not saying that you know that there actually is at least one BWOA which has design X. You don’t have that information. You just know that it is logically and actually possible that a BWOA could have a design X: but “possible” here is being used in the standard philosophical sense and not your sense (because you hold that you have to experience it for it to be possible). So, in your terms, you cannot claim it possible despite it being logically and actually possible.

If the odds for the air or not air do not depend on X or Y, then each X and Y has a respective 49/51 split as well. This is just a logical fact.

No they don’t. The probability of one having design X or Y is completely unknown to you. The probability of picking a BWOA or BWA is irrelevant to the probability of it having a particular design. To know that you would have to know how many in the actual sample have design X and how many have design Y and divide that by 100: you simply do not know this in the scenario.

If you flip a coin ten times and it comes up heads ten times, does the non-essential property of you being in your living room change the odds of the coin's outcome? Of course not

That’s disanalogous: I am not saying that non-essential properties always weigh in or outweigh the probability of something occuring. That’s why I picked this very specific example scenario.

Also, you being in your living room wouldn’t be a non-essential property because it isn’t a property of the probability. Is an unessential reason or factor: not a property.

However, if you’ve experienced a billion times living rooms having a strong gravitational pull than non-living rooms, then, yeah, I think that unessential factor becomes at least a relevant factor. I think this is what you mean by:

"Every time I flip a coin in the living room, it changes the odds to where I always flip heads," then the living room is no longer a non-essential property to the coin flip, but has now become, in your head, an essential property of the coin flip.

Same as if after you count all the X and Y boxes that have ever been made, and sure enough, it turns out that all X's are airs, while all Y's are not airs. The odds didn't change

Sure. I already agree that the probability itself wouldn’t change.

you could say that all boxes with X have air, while all boxes with Y's don't, and applicably know this. It just so happens that there are 49 billion X's, and 51 billion Y's.

No, the sample size for the scenario that you are drawing from a sub-collection of them in the real world. You don’t know that there are 49 billion X’s and 51 billion Y’s but, rather, only that in this sample of 100, there are 51 BWOAs and 49 BWAs. That’s it.

Perhaps the issue you're really holding here is that you want to make decisions that are less rational sometimes.

No philosophim, I am saying it is less rational to go with the 1% chance or 0.00000001% chance that it is a BWOA as opposed to a BWA in this specific scenario.

Bob

To clarify, I am saying that the odds of any box being without are is 51% and the only thing that matters to the identity of the box is that it (1) is a box and (2) has or does not have air in it. — Bob Ross

Here is where you also have to clarify. Does the design of X or Y have anything to do with the probability? For example, if the ration of X airs to Y airs was 3/4, then X and Y are essential properties to the probability. Both of these can co-exist.

So on one hand we could say overall, there's a 51% chance of no airs vs airs, not considering X or Y. Then we can drill down further, make X and Y a part of our observations, and note that X has a 75% chance of being no air, while Y has a 25% chance of being air. These are two different probabilities, and we could even math them together for an overall probability if we wanted to.

Once you start including an attribute in your probability, it is now essential to that probability. While you are considering X and Y, you're not considering the how heavy they are right? Anything you don't include in the probability is non-essential. Since you don't care about the weight of each box, it doesn't matter. Once you notice X and Y designs, and start actively noting, "Hey, X's so far have all been with air," then you've created a new probability, and X is essential to that probability.

No they don’t. The probability of one having design X or Y is completely unknown to you. The probability of picking a BWOA or BWA is irrelevant to the probability of it having a particular design. — Bob Ross

If it is known information that the X or Y is irrelevant to the design, then you cannot make a probability based off of it when referring to the boxes in general. If it is unknown whether the X or Y is relevant to the air inside of the box, then you could start to note a probability that is again, separate from the box disregarding the design.

I think the part of confusion Bob is you keep making non-essential properties essential to an induction, but think because its non-essential in another induction, its non-essential in your new induction. That's simply not the case. Once you start including the X or Y as a consideration, it is now an essential consideration for your new induction. That's your contradiction.

If you flip a coin ten times and it comes up heads ten times, does the non-essential property of you being in your living room change the odds of the coin's outcome? Of course not

That’s disanalogous: I am not saying that non-essential properties always weigh in or outweigh the probability of something occuring. — Bob Ross

Its completely analogous. Non essential properties never weigh in or outweigh the probability of something occurring. If they do, they are now essential to that probability. That's why the living room is non-essential to the probability.

Also, you being in your living room wouldn’t be a non-essential property because it isn’t a property of the probability. Is an unessential reason or factor: not a property. — Bob Ross

A reason or a factor is a property of something. If you wish to interchange it, its fine. The point still stands.

I am saying it is less rational to go with the 1% chance or 0.00000001% chance that it is a BWOA as opposed to a BWA in this specific scenario. — Bob Ross

Only if you consider the X, Y design of the box. In which case, it is now an essential property of your induction, and you've made the separate probability as I noted earlier.

Hello Philosophim,

Here is where you also have to clarify. Does the design of X or Y have anything to do with the probability?

No they do not. It is a 51% chance that it is a BWOA, and that is calculated solely of it’s essential properties, which is that it (1) is a box and (2) has or does not have air in it.

For example, if the ration of X airs to Y airs was 3/4, then X and Y are essential properties to the probability. Both of these can co-exist.

So on one hand we could say overall, there's a 51% chance of no airs vs airs, not considering X or Y. Then we can drill down further, make X and Y a part of our observations, and note that X has a 75% chance of being no air, while Y has a 25% chance of being air. These are two different probabilities, and we could even math them together for an overall probability if we wanted to.

The scenario does not give you a probability of a box being design X or Y and you cannot calculate it given the information for the scenario. So, although you are correct that that probability would be separate from the probability of pulling a BWOA or BWA, you can’t use that probability. That fundamentally changes the scenario if you did.

Once you start including an attribute in your probability, it is now essential to that probability. While you are considering X and Y, you're not considering the how heavy they are right? Anything you don't include in the probability is non-essential. Since you don't care about the weight of each box, it doesn't matter. Once you notice X and Y designs, and start actively noting, "Hey, X's so far have all been with air," then you've created a new probability, and X is essential to that probability.

No. Again you are confusing what is essential to calculating the probability, which in this case is the essential properties, and what is useful for infering what a thing is (when you can’t know that it meets the essential properties).

Although in this scenario weight is not something to consider (to keep things simple), how heavy it is could play a factor into what you guess if you experienced a strong correlation of two distinctly different weights with BWOAs and BWAs a BILLION times. The weight is still an accidental property, but the sheer correlation in the actual world (which can happen) makes it cogent to factor that into consideration since you can’t know by looking at it if it has air or not.

If it is known information that the X or Y is irrelevant to the design, then you cannot make a probability based off of it when referring to the boxes in general

There’s no probability afforded to you of whether has a design X or Y. So correct. But that was never the claim I was making. The billion experiences of X → BWA and Y → BWOA is inductive evidence: it doesn’t give you a probability and that is the whole point.

If it is unknown whether the X or Y is relevant to the air inside of the box, then you could start to note a probability that is again, separate from the box disregarding the design.

No you couldn’t: the antecedent there doesn’t necessitate the consequent. If I am unsure if X and Y are relevant to whether it is a BWA, I don’t thereby gain knowledge of the probability of nor do I gain inference-like knowledge that it does. I think you may be confusing an inductive inference with a probability proper. Unless you know the numerator and denominator (and divide them) then you cannot claim to know anything about what is probable or improbable.

I think the part of confusion Bob is you keep making non-essential properties essential to an induction, but think because its non-essential in another induction, its non-essential in your new induction. That's simply not the case. Once you start including the X or Y as a consideration, it is now an essential consideration for your new induction. That's your contradiction.

There’s no contradiction (that I can see): maybe explain where it is in more detail.

Let me clarify something though: what is essential to the inductive inference is not the same thing as what is essential to the identity of a thing. I think you may be conflating those two here.

Personally, I would say that it is useful and more rational to the inductive inference to go with BWA (in this scenario) (rather than saying it is essential: I am not sure what that would entail, as we are not talking about essential properties there).

I can say the designs are not essential properties of the identity of a BWA and BWOA while holding that the designs, given the inductive evidence and super low probability given of pulling BWOA, are relevant to inferring (guessing) what it is (even though it isn’t an essential property of it). Again, I will refer you to the example of the human drawings.

There is absolutely no contradiction here.

Non essential properties never weigh in or outweigh the probability of something occurring. If they do, they are now essential to that probability

Correct. You keep focusing too much on the probability. The idea is that there is a probability which is calculated independently of the designs, but it is a miniscule difference. Now, couple that with the inductive knowledge that the design is always consistently (a BILLION times) associated non-essentially to the boxes and that knowledge outweighs going off of the probability.

A reason or a factor is a property of something. If you wish to interchange it, its fine. The point still stands.

If by this you just mean that we use the essential properties to calculate the probability, then I agree. But reasons are not properties of the things.

I am saying it is less rational to go with the 1% chance or 0.00000001% chance that it is a BWOA as opposed to a BWA in this specific scenario. — Bob Ross

Only if you consider the X, Y design of the box. In which case, it is now an essential property of your induction, and you've made the separate probability as I noted earlier.

It’s not though. I am saying that there is a strong correlation between this design and this type of box, and I know that this box doesn’t have to have this design--but it has had this design a BILLION times anyways. There’s a difference between something being essential to what a thing is, and it being accompanied by something else consistently.

Bob

I think what you are trying to say is that if one is using something as a consideration of what something is (i.e., its identity), then it should be an essential property: but that just simply doesn't follow from you methodology. I can claim that I distinctly know that a BWA is just a (1) box and (2) has air in it.

I can experience design X with BWAs my whole life and never refurbish its definition to include design X as an essential property: and that is how the scenario is setup. So you can't side-load the designs into the 51% probability because they should be essential properties because in the scenario they are not. If that makes any sense.

The probability was calculated with only the aforesaid two essential properties. The designs were not considered for it.

Bob

I can experience design X with BWAs my whole life and never refurbish its definition to include design X as an essential property: and that is how the scenario is setup. — Bob Ross

True. But if you're going to later include, "I believe property X is a property that indicates it has air," then you've made it an essential property to identifying whether it has air. Basically you're saying its not an essential property, but then in your application, it is. You can claim its a non-essential property within the induction, but then in your application you must show it is. If it was non-essential, then it would have nothing to do with your induction of whether the box has air or not. Once you believe the design pattern does, its now essential to the predictive outcome of the identity despite any belief otherwise.

I can say the designs are not essential properties of the identity of a BWA and BWOA while holding that the designs, given the inductive evidence and super low probability given of pulling BWOA, are relevant to inferring (guessing) what it is (even though it isn’t an essential property of it). — Bob Ross

Introducing different words does not change the outcome. "infer" is "a guess" which is "an induction". So we're right back to the hierarchy again. If you include the "non-essential" property as essential for your induction to the outcome of the box, then it is no longer non-essential to your belief in the outcome of the box's air or not air identity. Again, it does not matter if its non-essential in your original probability identification. You've made it essential in your new one.

Let me clarify something though: what is essential to the inductive inference is not the same thing as what is essential to the identity of a thing. I think you may be conflating those two here. — Bob Ross

It is correct that the essential properties of a known identity, and the essential property of an induction about that identity are not the same. I've said that already by noting that we can hold the original probability while considering this new pattern. Regardless of the pattern of design, we still know that any box has a 51/49 probability in regards to its air. But if we later consider the design in believing whether the box will have air or not, its now essential in that belief. You don't get to decide what's essential or non-essential in application. In application, the design is now essential in your belief on whether it holds air or not. You can deny it, but you haven't proven it yet.

Non essential properties never weigh in or outweigh the probability of something occurring. If they do, they are now essential to that probability

Correct. You keep focusing too much on the probability. The idea is that there is a probability which is calculated independently of the designs, but it is a miniscule difference. — Bob Ross

And the miniscule difference is irrelevant. Its still 1% more rational. Or .0005% more rational. If X > Y, and no other considerations are made, its always more rational to choose X. It does not matter how small the difference is. Your original claim is that the hierarchy breaks. I'm not seeing how there being a miniscule differences breaks the logic of the hierarchy. That's a personal reason to not want to choose the more rational induction. That's not an argument for saying the probability is less rational.

I feel we're just repeating ourselves on this point. You know I'm very open to conceding whenever I see the logic, but in this case, I do not see a logical point that breaks the hierarchy. If you're going to use a property as a basis for an induction, its essential to the reasoning behind the belief. If you removed the design of X and Y from your second inference, do you have a second inference anymore? No, that inference is based on there being a X and Y design. If you can't remove the property and still hold the induction Bob, its essential to the induction. Unless a new point is made, I don't really see anything to add to this at this point.

I want to get to another point which you made which I think is valid and worth discussing over instead.

There’s no probability afforded to you of whether has a design X or Y. So correct. But that was never the claim I was making. The billion experiences of X → BWA and Y → BWOA is inductive evidence: it doesn’t give you a probability and that is the whole point. — Bob Ross

So here, you are correct. A probability is based off of our knowledge of limits. I've been using it in the generic sense, but depending on the context, the repeated occurrence of X and Y is not one. Here, we do not know the actual limit. You may not remember from the original paper, but I noted that the hierarchy is a basic identifier of inductions that almost certainly could be broken down further.

What we're faced with here is something that is a repeated possibility pattern. Lets say there's a mole in a hole. It comes out of the hole every other day for four days. Does that mean it will do so for the next four? The next forty? We don't know, its only an induction. But the longer the pattern repeats, the more cogent it seems to believe the pattern will continue.

We hold patterns as more persuasive than mere possibilities. If I only observed the mole for two days, I would see it is possible that the mole comes out of the hole, and also possible that it does not for the day. But that's not a probability. Its not a 50% chance that the mole emerges. Its a pattern. Its an observed repetition of possibilities. In other words, its something we applicably know of again and again. Applicably knowing a thing 20 times seems more solid to cogent to believe in it happening again opposed to only seeing its possible one time.

Patterns are a more detailed identity of a cogent argument than possibility alone, yet still less cogent than probabilities. Lets view our cards as an example. We know a jack has a 4/52 chance of randomly being drawn if there is no pattern in how the cards are shuffled. This is the only logical solution. Even if we observe a pattern within the draws, for example, over 10 decks our chance of pulling a jack is 10/52, we still haven't broken the odds if we still applicably know the card shuffling is random. Its like flipping a coin and getting heads 10 times in a row. Its a pattern of success, but not more cogent than the known probability.

The sun rising in the East and setting in the West is not a probability, its a pattern. An extremely long pattern that has remained unbroken. If we consider the box design in relation to whether its an indicator to its identity being an air box or not, this is also a pattern. But a pattern is not more rational than a probability due to the fact that a probability has more applicably known quantities like limitations. That being said, in absence of their being a probability, a pattern is the most cogent inference.

Hello Philosophim,

It is correct that the essential properties of a known identity, and the essential property of an induction about that identity are not the same.

It seems now that you are referring to two things by “essential properties”: what is essential to what one induces something is and what is essential to what that something is. Is this correct?

Firstly, when I say that the design is not an essential property of what they are, I am not referring to “the essential property of an induction about the identity” of them: I am referring to “the essential properties of a known identity”--in this case, the box.

Secondly, I am also not even claiming that the designs are essential to inducing what box it is (which would be the latter thing in your quote), because that would imply that if I didn’t know the design then I couldn’t induce at all what box it is—which is clearly wrong. I am saying that it is a relevant factor. To say it is essential means that I couldn’t decide what it is (inductively) without knowing the designs. If I didn’t know the designs in the example (with all else being equal), then I would go off of the probability.

If by “essential property of the induction” you just mean that I am using designs to make my induction, then I have no problem with that; but that has nothing to do with the substance of the scenario nor does that entail that it is essential to the induction. The point is that the colossally observed pattern of design → box, in this particular context, outweighs going off of the minuscule probability.

If you agree that there is a separation between these two things (which you seem to agree in the above quote), then I don’t know why you said:

True. But if you're going to later include, "I believe property X is a property that indicates it has air," then you've made it an essential property to identifying whether it has air. Basically you're saying its not an essential property, but then in your application, it is

It is not an essential property of the identity of the boxes, but is relevant to inducing which box it is. You are simply noting that, at a minimum, that the designs are relevant to inducing which box it is and then conflating that with my claims that they are not essential properties of the identity of the boxes.

If it was non-essential, then it would have nothing to do with your induction of whether the box has air or not.

This is false. Something being essential means that it cannot be removed, so to say that it is “essential to an induction” is to say you cannot induce either way without that essential factor. However, if the situation changes, then the induction changes. For example, in the scenario where I’ve always experienced gravity pulling things to the ground for 40 years, I am going to induce that the next thing will fall that I drop. However, if it were the case that I’ve experienced gravity not work in those 40 years 500,000 times more than it work, then I would say it won’t fall (all else being equal). Gravity working in the first example is not an essential property of my induction of whether the object will fall when I drop it, because my induction would change if the factors changed. Sure, I wouldn’t have made the same inductive conclusion if that factors changes, but it is not essential to know gravity is working all the time to be able to make an inductive inference in this case.

If you include the "non-essential" property as essential for your induction to the outcome of the box, then it is no longer non-essential to your belief in the outcome of the box's air or not air identity.

This is irrelevant. Again, you just noting that I am using the design in my induction, which doesn’t negate the fact that design is not an essential property of the identity of the boxes.

If that’s all you are saying, then it doesn’t matter for the scenario. You can’t somehow deduce the probability of the designs in the sample of 100, and that was the whole point. Since the person calculated the 51% probability off of the essential properties of the identity of the boxes, which doesn’t include designs, there is no way to know probabilistically which design they will have: it is an induction.

Regardless of the pattern of design, we still know that any box has a 51/49 probability in regards to its air. But if we later consider the design in believing whether the box will have air or not, its now essential in that belief

It is not essential to the belief about the probability, because it wasn’t used in the calculation of it. Just because you use the designs in your inductive inference, does not mean it has any relation whatsoever to the probability of pulling a type of box. That’s a non sequitur.

You don't get to decide what's essential or non-essential in application. In application, the design is now essential in your belief on whether it holds air or not. You can deny it, but you haven't proven it yet.

It is relevant to whether the box has air or not; and this has nothing to do with whether it is an essential property of the identity of the boxes. So I am failing to get what your point is here? You have seemed to veer off into an unrelated observation (but I could be wrong). The probability is still 51% that you get a BWOA, and that BWOA could have design X (despite you experiencing strong evidence to support otherwise).

And the miniscule difference is irrelevant. Its still 1% more rational. Or .0005% more rational.

And this is really what is under contention: for you, it seems as though really strong inductive observations don’t matter if you know a probability and I disagree. If I have experienced a BILLION times design X ↔ BWA and I join a thought experiment where they have 100 boxes (of BWA and BWOA) and they tell me there is a 51% chance of getting BWOA and the box presented to me has design X, then, on the first pull, I am going with it being BWA.

You are saying that having a 1% more chance of getting BWOA is a better bet (inductively) and, consequently, that this box is going to be the first you’ve experienced (out of a previous BILLION) that does not have design Y.

In order for that to be the case, you would have to argue for a really unparsimonious general account of what is happening in the thought experiment. E.g., you would have to argue that perhaps the gamer makers are deceptive, that they have got a hold of a really rare manufactured set of BWOAs without the normal design that is associated with and decided to use those rare ones with you (a normal person), perhaps broke the law, etc. These are just examples, but you get the point.

Now, where I think you are right, is if the probability is not miniscule (e.g., 99% it is a BWOA). Since that calculation is deduced from the sample of 100, then that means there are 99 BWOAs. In that case, I think the probabilistic odds outweigh the experiential evidence of the correlation, and so it is more reasonable to go with BWOA.

I can even make the scenario even more specific to prove my point: imagine that, on top of what has already been said, in this scenario you also have strong inductive evidence that, although there can be a BWOA with design X, it costs an insane amount money to manufacture it with any design other than Y. You, as a normal person, engaging in a basic thought experiment (of pulling a box from 100 sample size) should not expect, given a miniscule 1% difference, that a BWOA has design X.

My point is that the entire situation matters, and it isn’t as easy as saying “probability > possibility” when making informed inductive decisions. If that were the case, then we end up with really unparsimonious explanations of things.

If X > Y, and no other considerations are made, its always more rational to choose X

Correct. But this is a scenario where other considerations are made. So this is irrelevant. If all you knew was that there was a 51% chance of it being a BWOA and all else being equal, then, yeah, go with the probability.

Patterns are a more detailed identity of a cogent argument than possibility alone,

Correct. I am saying that the patterns in this case weigh into the inductive inference: it isn’t as easy as going with the probability for the sake of going with it.

Bob

I hope your Saturday is going well Bob! I think I've been able to pare down our discussion in a more intelligible way this time. Read everything once over and I think it will all come together.

Secondly, I am also not even claiming that the designs are essential to inducing what box it is (which would be the latter thing in your quote), because that would imply that if I didn’t know the design then I couldn’t induce at all what box it is—which is clearly wrong. I am saying that it is a relevant factor. — Bob Ross

Disregarding your first point for a minute, this is what I'm trying to inform you of. A relevant factor is an essential property. A non-relevant factor is a non-essential property in regards to the induction. Anytime you make the design relevant to an induction, a pattern in your case, it is now a relevant, or essential property of that induction. Again, can you make the pattern induction if you ignore the design? No. Therefore it is an essential property of that pattern. .

f by “essential property of the induction” you just mean that I am using designs to make my induction, then I have no problem with that; but that has nothing to do with the substance of the scenario nor does that entail that it is essential to the induction. The point is that the colossally observed pattern of design → box, in this particular context, outweighs going off of the minuscule probability. — Bob Ross

It is what I'm saying. But your claim is not proven. You can include the pattern design in your thinking, but it does not outweigh the known probability. And to this, it must be re-iterated again. This probability is applicably known without the X Y consideration. When you include a new property, then you create a new induction that takes that property into consideration.

We then evaluate that induction. In this case its a pattern. A pattern is less cogent then a probability. This pattern also includes certain properties than the original probability. It is not more cogent than the original probability. However, it is also not fully comparable either. The initial probability does not include the design of X or Y in its consideration. Meaning once we include the X/Y as an essential property in our pattern, we don't have a probability to compare to. We could take the pattern as the most cogent decision if X and Y are essential properties, because there is no probability considered for the X and Y properties. But it does not negate a probability as being more cogent.

So once again, we do not have a lower hierarchy being more rational to pick then a higher hierarchy. What you've attempted to do is make X and Y irrelevant in a probability, say they are then also irrelevant in a pattern, despite them being absolutely necessary to the pattern's conclusion. I'm going to condense the points I made above below in some simple logic.

This is a fair comparable probability and pattern in the hierarchy:

Probability 49/51% of getting either A or B.
Pattern I pull 1 billion A's and 1 billion Bs.

A pattern is not as cogent as a known probability (The probability is not wrong, this would of course be a different discussion)

The more rational belief is that I will pull a ratio of A to B at 49/51%, despite the patterned solution I've seen.

This is another fair comparable probability and pattern in the hierarchy:

Probability of getting either A or B with design X is 75% or Y at 25%
Pattern I always pull an A with X, and always pull a B with Y

In this case, the probability is still more cogent than the pattern. This is because all relevant properties to the conclusion of each induction is being considered.

An incorrect comparable probability and pattern (What your example is doing):

Probability 49/51% of getting either A or B, (X and Y not considered).
Pattern I always pull an A with X, and always pull a B with Y (X and Y considered)

Then you're claiming the pattern is somehow more cogent than the probability.

1. You have not shown that a pattern is more cogent than a probability. To do so, you must resolve a very simple problem.

The probability of a random coin flip is 50/50.
Someone flips a coin ten times randomly and it turns up heads all ten times.
"Randomly" is proven and not doubted.

Why would it be more cogent to predict the next coin is heads rather then saying it could be either on the next flip? Give a reason there, and we can start to question whether a pattern is more cogent than a probability.

2. You are not comparing inductions properly. The first induction does not consider X and Y. You cannot say a later induction that does consider X and Y is more cogent than the first, because the first is a different scenario of considerations. You need to have a probability that does consider X and Y to compare fairly.

I hope this finally clears up the issue! This has forced me to be clearer with my examples and arguments, and I think the entire paper is better for it.

Hello Philosophim,

I hope your Saturday is going well Bob!

To you as well!

Disregarding your first point for a minute, this is what I'm trying to inform you of. A relevant factor is an essential property. A non-relevant factor is a non-essential property in regards to the induction. Anytime you make the design relevant to an induction, a pattern in your case, it is now a relevant, or essential property of that induction. Again, can you make the pattern induction if you ignore the design? No. Therefore it is an essential property of that pattern. .

I don’t have a problem with this: you seem to just be noting that I wouldn’t have made that exact inductive inference without the pattern which, to me, is a trivial fact. If there’s three cards of 2 aces and 1 king and I hedge my bets that I will randomly pull an ace because there is a 66% chance, then, of course, I could not have made that exact inductive inference without the probability because that is what I used: but, my question for you is, why explicate this? What relevance does this have to the scenario I gave you?

I agree that the calculated probability (which is not an inductive inference) is not considering Y and X while the inductive inference about X and Y is; but this doesn’t make it an unfair comparison; and the scenario hasn’t changed because of it: there is a probability you are given and there is an inductive inference you could make either (1) based off of that probability or (2) off of the experiential pattern. In this scenario, they are at odds with each other, so you can’t induce based off of both (as they have contradictory conclusions): so you have to compare them and determine which is more cogent to use. If you think this is an unfair comparison, then please elaborate more on what you mean.

Also, a real example, like my scenario, can’t be negated by saying it is an “unfair comparison” because, in reality, you would have to compare them and choose (as described above). In the scenario, you wouldn’t just throw your hands up and say “UNFAIR COMPARISON!” (:

Probability 49/51% of getting either A or B.
Pattern I pull 1 billion A's and 1 billion Bs.

This is disanalogous because in the scenario you didn’t pull a billion times design X → BWA (and ditto for the other one). I agree that if that were the case then the probability is a better pick.

The point with the scenario is you are coming in with experiential knowledge that shifts how you will play the limited 100 sample game. You, in this example, are talking about knowledge you get by randomly pulling in the limited, small sample game.

Probability of getting either A or B with design X is 75% or Y at 25%
Pattern I always pull an A with X, and always pull a B with Y

This is disanalogous for the exact same reasons as the above one.

Probability 49/51% of getting either A or B, (X and Y not considered).
Pattern I always pull an A with X, and always pull a B with Y (X and Y considered)

Yes, and you can’t just say “unfair comparison”: in the scenario, like the real world, you have to compare them: I specifically made in so that you have to compare them to make an informed decision. You are going to induce it is either with air or not based off of either the probability or the pattern.

Likewise, if you are saying that the probability is a better choice in the scenario, then you are thereby conceding that you can compare them.

Why would it be more cogent to predict the next coin is heads rather then saying it could be either on the next flip?

It wouldn’t. If all you know is that you are performing a 50/50 random coin flip, it doesn’t matter how many times you get heads: it’s the same probability. This is disanalogous to the scenario because your knowledge of the design correlations is not derived from the sample size.

You are not comparing inductions properly. The first induction does not consider X and Y. You cannot say a later induction that does consider X and Y is more cogent than the first, because the first is a different scenario of considerations

The scenario is the exact same: they are both a part of that scenario. In it, you clearly have to choose which you think is more cogent to go off of. You can’t just throw your hands up in the air.

I hope this finally clears up the issue!

I wish it did, but I still don’t think you have addressed the scenario properly. You seem to keep conflating it with a straightforward comparison of a probability vs. knowledge acquired from randomly pulling from a sample: obviously the former is more cogent. There’s no debate in that.

This has forced me to be clearer with my examples and arguments, and I think the entire paper is better for it.

Likewise, this has made me be clearer in my scenario (;

Bob

I don’t have a problem with this: you seem to just be noting that I wouldn’t have made that exact inductive inference without the pattern which, to me, is a trivial fact. — Bob Ross

but, my question for you is, why explicate this? What relevance does this have to the scenario I gave you? — Bob Ross

Your point has been that the hierarchy does not hold and that there are certain instances in which a lower level of the hierarchy is more cogent to hold than a higher one. My point is that you are incorrectly using the hierarchy.

I agree that the calculated probability (which is not an inductive inference) is not considering Y and X while the inductive inference about X and Y is; but this doesn’t make it an unfair comparison; — Bob Ross

Also, a real example, like my scenario, can’t be negated by saying it is an “unfair comparison” because, in reality, you would have to compare them and choose (as described above). In the scenario, you wouldn’t just throw your hands up and say “UNFAIR COMPARISON!” (: — Bob Ross

Ha ha! No, I'm not saying its unfair as in, "I don't like it." I'm saying its not how the hierarchy works. Its been a while since we covered it, but we covered a similar situation a while back.

Probability: A coin has a 50/50 chance of landing heads or tails.
Possibility: The sun will rise tomorrow

We don't compare the two because they don't apply to the same situation, or the same essential properties. We compare coin flip with coin flip with what we know, and sunrise to sunrise to sunrise with what we know. The hierarchy doesn't work otherwise. You're simply doing it wrong by comparing two different identities Boxes without X and Y, and boxes with X and Y, then saying you broke the hierarchy.

there is a probability you are given and there is an inductive inference you could make either (1) based off of that probability or (2) off of the experiential pattern. In this scenario, they are at odds with each other, so you can’t induce based off of both (as they have contradictory conclusions): so you have to compare them and determine which is more cogent to use. — Bob Ross

Sure, and I already pointed out the solution, but I'll be more clear.

If you do not consider the X and Y properties as relevant, you choose the probability. If you consider the X and Y properties as relevant, you do not have a probability that considers the X and Y properties. Therefore you choose the pattern. You're comparing an apple to an orange and trying to say an orange is more rational. You need to compare two apples and two oranges together.

Why would it be more cogent to predict the next coin is heads rather then saying it could be either on the next flip?

It wouldn’t. If all you know is that you are performing a 50/50 random coin flip, it doesn’t matter how many times you get heads: it’s the same probability. This is disanalogous to the scenario because your knowledge of the design correlations is not derived from the sample size. — Bob Ross

The point was to demonstrate that patterns are less cogent than probabilities. We both agree on this then. If that is the case, then if you use the hierarchy correctly by comparing the types of inductions we can make from all the essential properties considered among the inductions, you still choose a probability over a pattern.

Hello Philosophim,

It sounds like you are in agreement with me that the best choice in the scenario is to use the pattern, but you disagree that it is an example of a possiblity outweighing a probability: is that correct?

You say:

If you do not consider the X and Y properties as relevant, you choose the probability. If you consider the X and Y properties as relevant, you do not have a probability that considers the X and Y properties. Therefore you choose the pattern. You're comparing an apple to an orange and trying to say an orange is more rational. You need to compare two apples and two oranges together.

Which indicates to me you are agreeing with me that the pattern is the most cogent choice in the scenario, but you are disagreeing whether that conflicts with the probability. Is that right?

We don't compare the two because they don't apply to the same situation, or the same essential properties. We compare coin flip with coin flip with what we know, and sunrise to sunrise to sunrise with what we know. The hierarchy doesn't work otherwise. You're simply doing it wrong by comparing two different identities Boxes without X and Y, and boxes with X and Y, then saying you broke the hierarchy.

I honestly don’t understand how I could be misusing the hierarchy if the two options are a probability or possibility (fundamentally).

The probability and the possibility are both being used to infer the same thing, so it is disanalogous to:

Probability: A coin has a 50/50 chance of landing heads or tails.
Possibility: The sun will rise tomorrow

The implication with your example is that they are completely unrelated, but the probability and possibility in my example are both related insofar as they are being used to induce a conclusion about the same question. That’s why you have to compare them.

Another way of thinking of this is that any induction used to infer a conclusion is related to other possible inductions thereof, because they fundamentally are trying to answer the same question. If they were completely unrelated (like you would like me to believe), then one would not be capable of deciding which induction is most cogent to hold.

If you are right that the probability of a pulling a BWOA and the possibility of a BWOA having design X are completely unrelated, then you would not be able to determine which induction to use in the scenario because that requires you to compare them since they are both being used to make an induction about the same question. It’s impossible in the scenario for them to be completely unrelated!

We don't compare the two because they don't apply to the same situation, or the same essential properties.

Just to hone in on this: they absolutely do!!! The question is “does the box have air?” and they are both within that situation that I outlined: to answer that question you must compare them or answer with “undeterminable”. When I said “throw your hands up in the air”, I wasn’t meaning that you don’t like it, I meant figuratively (in a fun way) that you cannot determine which induction to use in the scenario if you are saying those two inductions (which are used to answer the same question) are completely unrelated. There would be, in that case, two inductions that could answer the question which cannot be evaluated as more or less cogent than the other.

The point was to demonstrate that patterns are less cogent than probabilities. We both agree on this then

We don’t agree on this. All your example demonstrated was that patterns extrapolated from random pulls from a sample are not more cogent than probabilities pertaining to that sample. That is not the same thing as proving that patterns are less cogent than probabilities.

Bob

It sounds like you are in agreement with me that the best choice in the scenario is to use the pattern, but you disagree that it is an example of a possibility outweighing a probability: is that correct? — Bob Ross

Correct! This is what I've been trying to get across all along, so I'm happy to see this is cleared up.

Which indicates to me you are agreeing with me that the pattern is the most cogent choice in the scenario, but you are disagreeing whether that conflicts with the probability. Is that right? — Bob Ross

Also correct!

I honestly don’t understand how I could be misusing the hierarchy if the two options are a probability or possibility (fundamentally).

The probability and the possibility are both being used to infer the same thing — Bob Ross

quote="Bob Ross;817572"]The implication with your example is that they are completely unrelated, but the probability and possibility in my example are both related insofar as they are being used to induce a conclusion about the same question. That’s why you have to compare them.[/quote]

Because for one, it has never been that fundamentally the hierarchy is applied without context. If you introduce new properties which are of consideration within the probability, that is a new context. You are not asking the same question. You're not using the hierarchy if you introduce properties in one induction that are not considered in another.

To prove that the hierarchy breaks, you need to show me a comparison of two inductions which both consider all the same properties. Otherwise its just a strawman argument.

We don't compare the two because they don't apply to the same situation, or the same essential properties.

Just to hone in on this: they absolutely do!!! The question is “does the box have air?” — Bob Ross

No, they absolutely don't because you include an X/Y design consideration in your second induction, where this is not considered in the first induction. The first is, "Does the box have air?" While the second question is, "Does the box have air based on its design being either X or Y?"

A^B != A^B & X^Y

That's hard proof Bob. You'll need to disprove the above, and we both know that's not possible.

The point was to demonstrate that patterns are less cogent than probabilities. We both agree on this then

We don’t agree on this. All your example demonstrated was that patterns extrapolated from random pulls from a sample are not more cogent than probabilities pertaining to that sample. That is not the same thing as proving that patterns are less cogent than probabilities. — Bob Ross

Simply prove the coin flip example wrong, and then you'll be able to back that its not proven. Until then, it holds. And again, the hierarchy is when we have competing inductions within the same context. You have not demonstrated that you understand this yet. Please work to understand that first. As a challenge to you to help you do so, take the situation with X and Y properties, then come up with a probability, a possibility/pattern, and a plausibility. Add no other properties, and remove none. Then show if a lower hierarchy results in a more cogent decision.

After, do the same as above, but this time add in the X/Y consideration for all the inductions. All the inductions must now include the X/Y. Then try to demonstrate why a lower hierarchy is more cogent than the higher one. Do this, and you'll have an argument. Don't, and you're not arguing against the hierarchy, but against something else different to the discussion entirely.

Suppose I sit down with a bunch of strangers at a poker game. The dealer deals himself a full house. Then he deals himself four of a kind. Then a royal flush. Then another royal flush. What does your theory say about when I should leave the table?

Hello Philosophim,

I think we have finally pinned down the disagreement: so I am going to focus on that. Which can be summarized on your post as:

If you introduce new properties which are of consideration within the probability, that is a new context.
…

A^B != A^B & X^Y

You can have two induction which use different relevant factors to infer a solution to the same question in the same context. The use of different relevant factors does not change the context.

The context in the scenario includes both the information that the probability of pulling a BWOA is 51% and that you’ve experienced the design correlation which can be used to produce two induction that use different relevant factors in the context to derive a solution.

To summarize:

1. The context does not split into two contexts in virtue of the possible inductions using different relevant factors.

2. You have to compare them, because you must either use one or the other as your inductive inference.

#1, A ^ B & X^Y are a part of the same context: the inductions are what use varying aspects of that context. They are not two separate contexts themselves if they are a part of the same scenario and answering the same question with in that scenario.

#2, It is very clear in the scenario that you have to compare them, so if you are saying that the induction hierarchy is unapplicable then it is useless for practical situations and thusly warrants a new methodology.

You do agree that you are comparing them by saying that you think the pattern is most cogent, right? If so, then you are contradicting your claim that they cannot be compared (because they are different contexts).

You are not asking the same question

Perhaps the scenario wasn’t clear enough: within the scenario you know (1) probability of pulling BWOA and (2) a strong correlation with the designs; this is within the same scenario. The question that is asked is “does this randomly pulled box have air?”, and that question is within that same scenario. Since both bits of knowledge are within the same scenario, you can either to induce a conclusion; but not both (because they contradict each other). There’s no room for you to claim that it isn’t asking the same question.

Obviously, the inductions themselves are using different relevant factors, and so they don’t reach the same exact conclusion (in this case) nor do they have the same reasoning behind them; but that doesn’t matter: you have to compare those two inductions to see which is more cogent to hold.

Think of it this way. You say that the pattern is more cogent in the scenario, but I say it is the probability. If you also hold that you can’t accurately compare them, then you can’t claim my conclusion (to the same question within the same scenario) is less cogent. As a matter of fact, you wouldn’t be able to justify you own claim that it is cogent at all. Do you see the problem here?

Otherwise its just a strawman argument.

I honestly think this is an iron man argument, and your hierarchy is being demonstrated to break here. I think you agree that the pattern is more cogent, so we are getting closer to seeing why.

You are just noting that the inductions themselves don’t use the same factors, but that is irrelevant to the dilemma: which are you going to use to make your educated guess? The one that is more cogent. But, wait, according to you, they can’t be compared! So, according to you, you could only say it is undeterminable. Do you see what I mean?

Simply prove the coin flip example wrong, and then you'll be able to back that its not proven

This is unproductive to say this. I already addressed this: in the coin flip example you are right, but it doesn’t imply that probabilities are more cogent than possibilities. The antecedent does not imply the consequent that you want it to.

For example, if I claimed “giving someone a hug is always worse than killing them” and tried to prove it with the example:

1. A person is skinning your wife alive.
2. You go give them a hug.
3. That was worse than if you would have killed them (to defend your wife).

You could agree with the example and disagree that it proves the claim I made: no problem.

In logic, you are a committing a fallacy of a claim about the some to the all, and I can demonstrate it in a predicate logic:

∃y∃x (Prob<x> & Poss<y> & Better<this: x, than: y>) ⊬ ∀y∀x (Prob<x> & Poss<y> & Better<this: x, than: y>)

Thusly, I can completely agree with you on the coin example and claim that that is insufficient to prove that all probabilities are better than possibilities. You asking for me to disprove it disregards what I am telling you my position is: you would have to provide a proof that ever probability is better than a possibility, which is clearly unafforded by your example.

After, do the same as above, but this time add in the X/Y consideration for all the inductions. All the inductions must now include the X/Y.

They don’t. In real-world practical (and theoretical) scenarios, there are a range of possible inductions one could use that are (1) competing and (2) using different factors of that context. One has to pick one as the most cogent inference. Period. If you hierarchy cannot handle this scenario, then it isn’t complete enough.

Bob

You can have two induction which use different relevant factors to infer a solution to the same question in the same context. The use of different relevant factors does not change the context — Bob Ross

No, you cant in the instance I noted. You usually do fair readings, but this time you're not. I've told you how the theory works, you don't get to say my own theory doesn't work the way I told you!

You know I have no problem admitting when I'm wrong or you've made a good point. In this case, you're telling me the theory I made should be something different. That's a straw man. If you don't like the theory that's fine. But insisting it is something it is not is wrong.

I've asked you to do the induction breakdown in my last post so you would understand. Until you do so, you won't have understood the hierarchy theory. Your reticence to do so indicates to me you're more in attack mode than discussion mode. It's ok, I've done that myself. On the next post do the breakdown I asked and then I know your criticisms will come from an understanding. As it is, this is all a strawman, intentional or no. List those first, then see if your criticisms still hold.

Suppose I sit down with a bunch of strangers at a poker game. The dealer deals himself a full house. Then he deals himself four of a kind. Then a royal flush. Then another royal flush. What does your theory say about when I should leave the table?
9h — RogueAI

A good question! Before I answer, I want to make sure you've read the theory first. To do so, use the terms for knowledge and inductions in the paper and tell me from your viewpoint what the theory would conclude. At that point I will either agree with or correct you. But if you haven't read the paper and understand the ponts first, you won't have the ability to understand the answer. Don't be lazy or insist that you have, prove that you have and we'll discuss

Hello Philosophim,

You usually do fair readings, but this time you're not. I've told you how the theory works, you don't get to say my own theory doesn't work the way I told you!

I apologize if I am misunderstanding you! To better understand what you are saying, let me ask you these:

1. In the scenario I gave, is the possibility or the probability what you would go with (or perhaps neither)?

2. Do you agree with me that if you decide one over the other that you are thereby comparing them?

3. Do you agree that all the possible inductions for a question within a context are thereby within the same context as each other?

In this case, you're telling me the theory I made should be something different. That's a straw man...But insisting it is something it is not is wrong.

Although I think I understand what you are saying, it isn’t necessarily a straw man to point out that a theory needs to be revised; and that is what I am trying to convey.

From your perspective, you just disagree with that; but that doesn’t make it a straw man argument.

I am going stop here for now because I need to know your answers.

I look forward to hearing from you,
Bob

And I should clarify for question #3 that by "question" I am referring to the same asked one within the context. Of course, I could ask question X in context Y and question X in context Z, but I am asking you if you think that all possible inductions formulated for answering question X in context Y are within the same context. If that makes any sense.

I will refurbish it in the original post.

Not a problem Bob! My smiley face did not go through on that statement. My internet is down so I'm having to type these on the phone for now. Again, I will gladly answer your questions and points, but to make sure we're on the same page, first answer with the exercise I posted earlier. Here is is again.

Take the situation with X and Y properties, then come up with a probability, a possibility/pattern, and a plausibility. Add no other properties, and remove none. Then show if a lower hierarchy results in a more cogent decision.

After, do the same as above, but this time add in the X/Y consideration for all the inductions. All the inductions must now include the X/Y. Then try to demonstrate why a lower hierarchy is more cogent than the higher one.

Once we have those examples, we can use those as a base of discussion, as that will accurately represent the hierarchy of inductions.

My internet is down so I'm having to type these on the phone for now.

Absolutely no problem! I will answer your questions, but my questions aren't related directly to yours; so if you could answer them as well that would be much appreciated!

Take the situation with X and Y properties, then come up with a probability, a possibility/pattern, and a plausibility. Add no other properties, and remove none. Then show if a lower hierarchy results in a more cogent decision.

My situation is an example of this, and to keep it simpler I excluded a plausibility: do you want me to add in a plausibility as well? I think it will just clutter up the discussion adding it in.

After, do the same as above, but this time add in the X/Y consideration for all the inductions. All the inductions must now include the X/Y.

To do that, in my scenario, we would have to add in the idea that each box has a 50.001% of it being a BWOA and design Y, and you've experienced design X <-> BWA and design Y <-> BWOA a billion times. I just don't see the relevance of this, as it is no longer the same scenario, but that is my answer.

Bob

Take the situation with X and Y properties, then come up with a probability, a possibility/pattern, and a plausibility. Add no other properties, and remove none. Then show if a lower hierarchy results in a more cogent decision.

Sorry, I meant air and no air situation first without the X/Y's. Missed it on the phone, but I have access to a computer again. I wanted you to walk through it yourself as I thought it would help you understand. I'll just do it here however. I will answer your questions btw, I just understand that they are directly related to mine, and we cannot discuss them until this one point is understood. Lets slowly build this up so we have solid footing each step of the way.

An example of the hierarchy
Probability 49/51% of getting either A or B.
Pattern I pull 1 billion A's and 1 billion Bs.

We can compare them because all the properties considered for the induction are the same.

Another example of the hierarchy:
Probability of getting either A or B with design X is 75% or Y at 25%
Pattern I always pull an A with X, and always pull a B with Y

Again, we can compare them because we're involving the same properties in both inductions.

An example that is NOT the hierarchy:
Probability 49/51% of getting either A or B.
Pattern I always pull an A with X, and always pull a B with Y

We cannot compare them using the hierarchy, because while some of the properties are shared, not all of them are in regards to the inductions that are made.

Its that simple Bob. Your example does not address the hierarchy. The second induction involves X and Y where the first induction does not. You are trying to compare apples to oranges when the hierarchy only allows you to compare apples with apples, and oranges with oranges. You cannot use this as an example to show that the hierarchy is wrong, because its not addressing the hierarchy. There is no debate on this. This is what the hierarchy is.

If you understand this, we can move on. Understanding this does not mean that you believe the hierarchy is adequate, useful, etc. It does not mean your example cannot be discussed as its own situation. But you must understand this definition and its application before we move onto any more questions. If you don't, we're not talking about the hierarchy. If you understand this, then I will address your previous questions.

Hello Philosophim,

An example of the hierarchy
Probability 49/51% of getting either A or B.
Pattern I pull 1 billion A's and 1 billion Bs.
…
Another example of the hierarchy:
Probability of getting either A or B with design X is 75% or Y at 25%
Pattern I always pull an A with X, and always pull a B with Y
…
An example that is NOT the hierarchy:
Probability 49/51% of getting either A or B.
Pattern I always pull an A with X, and always pull a B with Y

I understand what you are conveying, but this just segues into my questions because if you are saying that the inductive hierarchy doesn’t apply (like in your last example one above), then, by my lights, it is useless (since it cannot be applied) for practical examples. My scenario is an example of that. But to not get ahead of myself, please answer my previous questions directly.

Bob

I understand what you are conveying — Bob Ross

Great! This absolutely had to be understood before I addressed your questions. Now let me get to them! If I miss any of your questions or points in this answer, please redirect me and I will address them.

1. In the scenario I gave, is the possibility or the probability what you would go with (or perhaps neither)? — Bob Ross

Lets use the hierarchy to answer the question. First, it is understood that within the hierarchy, we choose the most cogent induction within a comparable set. But what if we're missing a higher level of cogency? For example, what if I only have a pattern and no odds to consider? At that point, the pattern is the most cogent to choose from.

Hierarchy 1 Just A and B
Probability 49/51% of getting either A or B.
Pattern (Not available)

Hierarchy 2: A and B and X or Y
Probability (Not available)
Pattern I always pull an A with X, and always pull a B with Y

As you can see, in the first example, we have a probability and no pattern established yet. Even if we had a pattern, we would choose the probability.

In the second example, we do not yet have a probability involving A and B and X or Y.

So which do we rationally choose if we have two hierarchies? That depends on what you find essential in pulling the boxes. If you consider the X/Y distinction irrelevant, then you would choose the probability in example one. If you find the the X/Y distinction relevant, then you would choose the pattern in example two because you do not have a probability to compare in the hierarchy. You can compare hierarchies depending on what properties you find essential to your induction, but you cannot cross parts within hierarchy 1 and 2 together to compare.

2. Do you agree with me that if you decide one over the other that you are thereby comparing them? — Bob Ross

No. You may be comparing the properties, but you are not comparing the h1's probability with h2's pattern.

3. Do you agree that all the possible inductions for a question within a context are thereby within the same context as each other? — Bob Ross

I'll need more details in what you mean by this. If you mean considering all the relevant properties to that hierarchy, yes. If you mean comparing hierarchies with different relevant properties, no.

by my lights, it is useless (since it cannot be applied) for practical examples. — Bob Ross

I hope this shows that it is not. You still have to evaluate your inductions and make sure they are accurately evaluated and compared. If you cannot cross hierarchies, you still have a rational conclusion based on the highest tier of inductive argument you have within that hierarchy comparison. To my mind, there is also no rational argument for handling inductions in any way in philosophy. I would say what I have is a pretty good foundation to start.

Hello Philosophim,

I understand better what you are arguing, but, in light of it, I think, by my lights, that is a concession that the hierarchy does not function (as I thought it was intended) in this scenario; and here is the crux of it:

That depends on what you find essential in pulling the boxes.

Correct me if I am wrong, but you seem to be admitting that these two inductions (which pertain to answering the same question in the same context) cannot be evaluated with respect to each other to decipher which is more cogent because you are generating two different hierarchies for them; and you are expressing this in the form of saying that it is up to the person to define what they think is essential. However, this is very problematic.

Firstly, unless there is some sort of separate criteria in your methodology for what one should consider essential, then it seems like, according to your methodology, a truly arbitrary decision of what is essential. I am ok with the idea of letting distinctive knowledge be ultimately definitional: but now you are extending it to applicable knowledge.

Secondly, because it is an arbitrary decision whether one wants to include the X and Y designs into their consideration, the crux of the cogency of their induction is not furnished nor helped by your induction hierarchy and, thusly, your methodology provides no use in this scenario. I think you are agreeing with me here implicitly by admitting that you had to generating to two competing but completely uncomparable hierarchies. This is a clear demonstration of the inapplicability of your methodology to determine cogency of inductions.

Thirdly, I find that it would actually be less cogent to go with the probability (in that scenario) and someone merely saying they don’t want to include the designs as essential doesn’t seem like a rational counter. The strong pattern, in this case, clearly outweighs using the miniscule probability. So I think that, as far as I am understanding it, using this methodology in this scenario can lead people to making an irrational decision (in the case that they arbitrarily exclude their knowledge of the patterns).

To me, this is the cost of claiming these two inductions as uncomparable, and it seems way too high to me to accept.

Would you at least agree that this scenario demonstrates how your methodology affords no help in some scenarios?

The bridge between them cannot be made (according to you) and so you have to arbitrarily pick which hierarchy to use.

Bob

Correct me if I am wrong, but you seem to be admitting that these two inductions (which pertain to answering the same question in the same context) cannot be evaluated with respect to each other to decipher which is more cogent because you are generating two different hierarchies for them; and you are expressing this in the form of saying that it is up to the person to define what they think is essential. — Bob Ross

Yes, this is correct.

Firstly, unless there is some sort of separate criteria in your methodology for what one should consider essential, then it seems like, according to your methodology, a truly arbitrary decision of what is essential. I am ok with the idea of letting distinctive knowledge be ultimately definitional: but now you are extending it to applicable knowledge. — Bob Ross

I'm not quite sure what you mean by extending it to applicable knowledge, but I'll state what I see. We know that definitions are fully within our own choice. Of course, once we accept those definitions, then we must apply them. But the standard for applied knowledge does not change. You are simply using a definition in one scenario, then a different definition in another. Also understand that we're talking about inductions here. You won't know the outcome until you apply the induction itself. After you establish the identities in front of you, the hierarchy helps you organize your beliefs that you could apply, and which belief out of those inductions seems most rational to take.

Secondly, because it is an arbitrary decision whether one wants to include the X and Y designs into their consideration, the crux of the cogency of their induction is not furnished nor helped by your induction hierarchy and, thusly, your methodology provides no use in this scenario. — Bob Ross

First, the arbitrary decision of how you define identities is not a rule of the hierarchy, that's simply our capability as identifying minds that can discretely experience. The hierarchy arises from this knowledge, not the other way around.

If you think about it carefully, you'll realize the hierarchy is a stable way to evaluate the immense freedom of the human minds ability to identify. Recall that one such action that shapes the identities we choose is how useful they are to us. Same with things such as avoiding death or harm. Identities that have too few properties, or evaluate something as non-essential when it is essential to a person's benefit will not be very good identities to have.

The hierarchy's rules apply no matter what identities you ultimately decide on in the end. Further, understanding that the hierarchy means you need to consider all of the properties, may allow you to catch that you haven't fully explored an induction. If I start looking for a pattern of X, Y, and Z, then realize my probability I was holding only involved X and Y, I can then consciously realize that I should be looking for a probability of X, Y, and Z if I can.

This is immensely useful. Again, to my mind there is no other method in philosophy that can measure inductions in such a way.

Thirdly, I find that it would actually be less cogent to go with the probability (in that scenario) and somehow merely saying they don’t want to include the designs as essential doesn’t seem like a rational counter. The strong pattern, in this case, clearly outweighs using the miniscule probability. So I think that, as far as I am understanding it, using this methodology in this scenario can lead people to making an irrational decision (in the case that they arbitrarily exclude their knowledge of the patterns). — Bob Ross

And yet did you not come to a rational conclusion? Using less essential properties in you inductions results in broader outcomes. If I go through a forest and say, "All wood like plants with leaves are trees," its going to be very easy to point out trees. If I introduce other properties that divide trees into types, or bushes and other plants, its going to be much more difficult for me to point out specific trees, but I will be more discerning in my findings.

Taking the probability in the first case ignores every single other property of the box besides the fact its a box and has air or not. After pulling literally two billion boxes and noticing there was a 100% match of design to air or not air, it seems silly not to consider it. You're still hung up on comparing that pattern to the probability though. You can't because you're not considering the same properties in both instances. It doesn't work that way. Stop it Bob. :D

The two can coexist as separate sets in your mind. We do this every day. Genuinely, what is wrong with holding the probability of 49/51 for boxes with air and out air, then also considering there is a pattern where X and Y are considered? The most rational is to take both into account and assume that 49% of the boxes we find will be with air, and we believe that all of these boxes will have the X pattern.

The fact that people can misunderstand, misuse, or make mistakes in applying a methodology is not a critique on the methodology. Do we discount algebra because it takes some time to learn or master? No.

Would you at least agree that this scenario demonstrates how your methodology affords no help in some scenarios? — Bob Ross

No. The scenario was fine, you just misunderstood and misapplied the hierarchy. It had been a while for both of us, so no worry! The puzzle for me was in explaining the answer in a way that was clear. The example allowed me to show you how to apply the hierarchy, demonstrate to you the decisions you have available to you, and come to a rational outcome. That's pretty useful. Now is the hierarchy useful in places its not meant to apply to? Of course. Its a tool, and like any tool it has its places where its shines the best and places where it reaches its limitations. But I see nothing here which show a contradiction within the hierarchies claims, or has broken it in any way.

Hello Philosophim,

I see what you are saying, but the problem is that there is not means of determining the cogency when comparing:

After pulling literally two billion boxes and noticing there was a 100% match of design to air or not air, it seems silly not to consider it.

According to the entirety of your methodology (and not just the hierarchy), there is no justification for this claim you have made here. You can’t say it is less cogent, even when it seems obvious that it is, for a person to say “no it doesn’t seem silly to just go off of the probability”. Without a clear criteria in your view, the vast majority of scenarios end up bottoming out at this kind of stalemate (because the hierarchy is unapplicable to the situation).

You're still hung up on comparing that pattern to the probability though. You can't because you're not considering the same properties in both instances. It doesn't work that way. Stop it Bob. :D

I totally am (; I mean:

The most rational is to take both into account and assume that 49% of the boxes we find will be with air, and we believe that all of these boxes will have the X pattern.

You can’t say this if you generated two separate, uncomparable hierarchies and there is nothing else in the methodology that determines cogency of inductions! Philosophim, you are admitting it is more cogent and that there’s absolutely no justification in your methodology for knowing that!

I 100% agree with you that it is most rational, but the problem in your view is you cannot justify it.

Let’s make the danger in having no means of determining cogency of the inductions more clear in this scenario: imagine that if you guess incorrectly they kill you. Now, we both agree that the obviously more cogent and rational move is to bet it is a BWA; but imagine there’s a third participant, Jimmy, who isn’t too bright. He goes off of the probability. Now, he isn’t misapplying your methodology by choosing to go off of the probability: he carefully and meticulously outlines the hierarchies involved in the context just like you, and realized (just like you) that he cannot compare them and is at a stalemate. He decides that he will use the probability.

We are both witnessing this irrational decision, and we want to help Jimmy not make a collosally dangerous mistake here in his reasoning; but, according to your methodology, what are we to cite as his mistake in his reasoning? What is it philosophim?!? Absolutely nothing. He did everything by the books.

The fact that people can misunderstand, misuse, or make mistakes in applying a methodology is not a critique on the methodology. Do we discount algebra because it takes some time to learn or master? No.

But, Philosophim, Jimmy isn’t misapplying your methodology—it just doesn’t afford an answer to what is the most rational and cogent decision between the inductions! The mistake is in the lack of usefulness of the methodology, not Jimmy’s application of it!

What justification would you give to Jimmy to try and save him?

Bob