Scientific faith?

[Ragna]

Some days ago I claimed that critical thinking is usually foregone by religion among other things when discussing what atheism is and what atheism is not, and by these claims I got said that me, like many non-theists in the forum, usually engage in hate-speech against Christianity (most likely any religion).

I came across several striking claims about atheism, and not the most impressive of them was:

...the absence of evidence, usually called faith...

This is just another example of ignorant slander. You know nothing of which you speak, nor do you wish to know, since actual knowledge would jeopardize your own faith in scientism.

1. Is it ignorant to claim that faith is belief in the absence of evidence? What is faith then?

2. Does science involve some sort of religious-like faith that actual knowledge can jeopardize? What kind of actual knowledge, and obtained through which methods?

[Adamoriens]

I don't think there's any need to dwell too heavily on validity here (nevertheless, as you will see, I will) since I've acknowledged that such a thing as inductive validity exists (I'll refer to another definition in the literature later). However, a clear distinction should be drawn between deductive and inductive validity. They are two different things, so a common criteria of "validity" cannot apply across all argument forms.

An induction can't be valid? Generalization is a type of induction, and I can imagine some valid generalizations:

1. I have DNA.
2. You have DNA.
3. Therefore, any person has DNA.

For every instance where I said, "induction is by definition invalid," substitute the following meaning for "validity":

In logic, the property of an argument consisting in the fact that the truth of the premises logically guarantees the truth of the conclusion. Whenever the premises are true, the conclusion must be true, because of the form of the argument. Some arguments that fail to be valid are acceptable on grounds other than formal logic (e.g., inductively strong arguments), and their conclusions are supported with less than logical necessity.

This is the most common definition of validity, so it is the one I use. Keeping this meaning in mind, the argument you just presented is invalid; that is to say, it is deductively invalid. It is also inductively invalid, inductive validity being understood as...

...simply that the premisses make the conclusion more probable than not.

The fact that you and I both have DNA is not sufficient grounds to suppose that everyone has DNA.We can determine this by dividing the number of cases in which premisses 1 and 2 are true by the total reference class (in this case, 6.5 billion living humans), resulting in a probability of 3.077 x 10^-10, much lower than the requisite 0.50. This is irrelevant to our discussion, but I point it out because I'm like that.

I can understand where you're coming from because the conclusion doesn't directly "follow", but even if logical validity doesn't apply, there must be a distinction between the condition of the argument applying an induction and it applying a fallacy.

This distinction should not be simply called "validity", because that term is commonly understood to refer to the degree of necessary logical consequence (ie. a deductive relations). I'm not sure that it should even be called "inductive validity", since the failure of an argument to raise its conclusion above 50% probability may not have its cause in a fallacy. But I can't think of an example where this would be the case, so go ahead and use the latter term.

You have changed my example, since the child didn't even know what a tetrahedron is, so he/she can much less have a definition for it. The induction (from particular to general) was devised with the underlying logic that:

1) The child knows that squares have four vertices.

2) The child only knows squares to have this characteristic.

Therefore, in the sight of an unknown shape (a tetrahedron), he mistakenly generalized (generalization is a type of induction) a (deficient) definition of square to cover the tetrahedron, and herein lies the categorical fallacy which renders his logic invalid and therefore his conclusion false.

Fair enough. I retract my claim that purely inductive arguments cannot have formal fallacies, in light of wikipedia:

...an argument can contain a formal fallacy even if the argument is not a deductive one; for instance an inductive argument that incorrectly applies principles of probability or causality can be said to commit a formal fallacy.

Onward:

But as far as I understand "validity" deals with how logically the conclusion of an argument is derived from its premises, while "soundness" deals with the truth value of the conclusion. If an argument which attempts to apply an inductive reasoning fails to do so making a formal or informal fallacy, then the inductive reasoning is not so and the conclusion is derived invalidly (for applying an invalid reasoning), making the argument, as well, unsound.

If soundness were merely the truth-value of the conclusion as you say, then the failure to derive the conclusion validly would be irrelevant; the conclusion might still be true. However, soundness is properly understood as being constituted by both logical validity and the truth of the premisses. At least, that is what wikipedia and a few different logic textbooks are telling me.

Induction and deduction, as far as I know, are kinds of reasonings for arguments, not kinds of structures for arguments, so I don't know how correct is it to apply a valid/sound difference here. I'm not any expert in logic, though, and might very well be wrong.

An inductive reasoning has to derive something general from something particular; if it fails to do this appropriately, isn't it invalid logic? What we demand from an induction is it to derive something general from something particular, but these both "something"s have to be meaningful and equally true.

While some dictionaries may still define induction as deriving generals from particulars, that understanding is now obsolete. From the IEP:

An inductive argument is an argument in which it is thought that the premises provide reasons supporting the probable truth of the conclusion.

If if I have stated that there are differences in structure between inductive and deductive arguments, I mean to refer to the relations of their conclusions from their premisses.

That will not be necessary, I think, since your purpose would be to show that such an example is inductively weak. But nowhere have I claimed that religious beliefs are formed on the basis of strong induction, merely that all religious beliefs can be construed as inductions of some sort.

You're missing my point. I'm arguing altogether that I haven't seen any argument for faith through induction which properly resembled any weak or strong induction I can accept, that's why I ask you to provide one. I've only seen errors in category like the one I put above, and there's a huge gap between these three types. If you present an argument that resembles a weak induction, I'll have to change my statement that "faith is not based in a valid induction" (weak induction is, for example: "my hair is black therefore the hair of all people is black"). Do something close to this, for example, for any doctrine.

I cannot provide a valid inductive argument, validity here being understood as greater than 50% probability. However, if weak induction is all that you require, the wiki article offers the following as an example:

1. I always hang pictures on nails.
2. Therefore: All pictures hang from nails.

In kind, I offer:

1. Many of the incidental historical details of the Bible have been confirmed by secular archaeology.
2. The Bible includes reports of miracles as if they were history.
3. Therefore, it is likely that the reports of miracles are also historical details.
4. If the reports of miracles are historical details, then Christianity is true.
5. Christianity is probably true.

As you can see, this is actually a far better argument than the example from wiki, and it also includes a deductive step (4) which may or may not contain a formal fallacy.

An interesting tangential consideration: it may be the case that an inductively valid could be mustered for the truth of Christianity, but we nonetheless might have good reason to suppose it more likely false. Inductive propriety says that the cumulative case must be considered with respect to a given probability, such that we may have good grounds to "push down" the probability that Christianity is true below 50%, a single inductively valid argument for it notwithstanding.

[Adamoriens]

Darn, I saved that mega-post as a draft. I want my ten tokens.

[Ragna]

After reading all that I concede that deductive and inductive validity are two entirely different subjects, but however I had nothing of deduction in my mind when I put the two categories. Also, thanks for the logic lesson, I learnt a lot .

You're also right that soundness implies validity.

But,

I'm not sure that it should even be called "inductive validity", since the failure of an argument to raise its conclusion above 50% probability may not have its cause in a fallacy. But I can't think of an example where this would be the case, so go ahead and use the latter term.

Fair enough. I retract my claim that purely inductive arguments cannot have formal fallacies, in light of wikipedia:

...an argument can contain a formal fallacy even if the argument is not a deductive one; for instance an inductive argument that incorrectly applies principles of probability or causality can be said to commit a formal fallacy.

Let me see, if an inductive argument doesn't contain a fallacy, there's a possibility that the truth of the premises will lead (not entail, though) the truth of the conclusion. That is, there's a chance, be it over or below 50%.

But, if it contains one, which is what until here I meant by "invalid induction" (how do we call it, fallacious induction?), then such possibility is 0%. That is, even if the conclusion turns out to be true, the argument cannot even "lead" to this truth, it will simply "have happened", and therefore the argument will be void.

While you still seem to hold that religious faith through induction falls in the first type, I'll still try to defend that it falls in the second. Also, remember that "religious claims" in this sense won't mean the existence of a cross, or the existence of a tomb, but only those claims only believable by believers in theism.

You provided this definition:

An inductive argument is an argument in which it is thought that the premises provide reasons supporting the probable truth of the conclusion.

And let's use it to determine if it's an induction or some wild fallacy:

1. I always hang pictures on nails.
2. Therefore: All pictures hang from nails.

I can recognize here a generalization, the author inferred the status of all pictures from his experience with this kind of objects. The conclusion is possible from the premise (not "probable", since this is really weak and probable means "likely"). This would qualify for me as a weak induction.

In kind, I offer:

1. Many of the incidental historical details of the Bible have been confirmed by secular archaeology.
2. The Bible includes reports of miracles as if they were history.
3. Therefore, it is likely that the reports of miracles are also historical details.
4. If the reports of miracles are historical details, then Christianity is true.
5. Christianity is probably true.


As you can see, this is actually a far better argument than the example from wiki, and it also includes a deductive step (4) which may or may not contain a formal fallacy.

There are a whole bunch of things I can remark here. First, this are two arguments and not one. The first concludes that miracles are historically reported, and the second concludes that Christianity is most likely true (though I'm not sure a conclusion can be just "likely"). Let's analyze the first one:

1. Historical details of the Bible are true.
2. Miracles are historical details (according to the Bible.)*
Therefore, miracles are true (since they're historical and not legendary).

[You can add "most likely" to the conclusion but that will just make it "most likely" false.]

I don't think this qualifies as an induction, since if the premises were true (which both are), the conclusion would be true (*), I would put it as a deduction or maybe syllogism (I don't know exactly). But, there's a minor detail which renders the conclusion unsound though it's valid. If we count the parenthesis in the premise 2., this turns out to be circular logic. Why are miracles true historical details - because the Bible says so. Why is the Bible accurate? Because Christianity is true - which if I remember well, was your final conclusion.

Now let's go on with the second:

1. Miracles are most likely true (from 1)
2. If miracles are true, then Christianity is true.
Therefore, Christianity is most likely true.

This is plain deduction, and a valid one. The soundness of the final premise will depend on the soundness of 1. (already discussed) since I think 2. is already defined to be true.

I can't see how this qualifies as an "induction". On the other hand, I've seen this kind of induction:

1. Everything has a conscious maker.
2. Plants are (or have the qualities of) things.
Therefore, plants have a conscious maker.

(Though this might actually seem a deduction, it's indeed an extrapolation, though you're open to question it.)

What makes this logic invalid or fallacious? It's the circularity in naming (a fallacy), since the argument is almost a tautology. (Though I'm not sure if it could still be called valid, it's as valid as "A is red because A is red".) When I first put it I was thinking of something like "inductive arguments which can be true (sound) and induction which is necessarily unsound". This is necessarily unsound, because:

1. presupposes the conclusion (if plants are to be taken as "everything").
2. presupposes the conclusion (if plants are not to be taken as "everything").

That is, I implicitly acknowledge the nature of things to plants (or attribute a similar property) in order to conclude that they have a property I entailed to the premises. Even if the statement "plants have a maker" were sound, the argument's conclusion is unsound because it also falls into circular reasoning. Just like if "A is red" were in fact true, my above argument would not be sound logical reasoning for it.

Darn, I saved that mega-post as a draft. I want my ten tokens. Neutral

Ouch PM a mod?

[nygreenguy]

I cannot provide a valid inductive argument, validity here being understood as greater than 50% probability. However, if weak induction is all that you require, the wiki article offers the following as an example:

Im not sure where I get this use of >50% probability. Im not sure that makes an argument valid. I think it depends on the premises.

If I use the argument:
Every swan I have ever seen is white, therefore all swans are white.

While its true the vast majority of swans are white, it only takes one non-white swan to make my argument invalid even though the "probability" of me finding a white swan is 99.9%.

1. Many of the incidental historical details of the Bible have been confirmed by secular archaeology.
2. The Bible includes reports of miracles as if they were history.
3. Therefore, it is likely that the reports of miracles are also historical details.
4. If the reports of miracles are historical details, then Christianity is true.
5. Christianity is probably true.

As you can see, this is actually a far better argument than the example from wiki, and it also includes a deductive step (4) which may or may not contain a formal fallacy.

I see several fallacies here. First is the term "many". How many? A statistically significant many? Statistics also lend credibility to inductive logic because they evaluate "chance" and error.

Next we have the connection of history and miracles. The events the bible gets "right" tend to be large scale, easily confirmed or falsified details. Miracles, on the other hand, are not in the same category of being easily falsified.

then we have the issue that every other religion can make these exact same claims, and we know that cant ALL be true.

Inductive propriety says that the cumulative case must be considered with respect to a given probability, such that we may have good grounds to "push down" the probability that Christianity is true below 50%, a single inductively valid argument for it notwithstanding.

Im not sure this is a proper application of induction and probability.

[Adamoriens]

Hello Ragna. You'll have to excuse me when I excise sentences here and there from your post, not because they are uninteresting, but for the sake of brevity, or because one of my responses may have addressed several of your points at once.

After reading all that I concede that deductive and inductive validity are two entirely different subjects, but however I had nothing of deduction in my mind when I put the two categories. Also, thanks for the logic lesson, I learnt a lot .

Likewise. I evidently had a monolithic conception of validity.

Let me see, if an inductive argument doesn't contain a fallacy, there's a possibility that the truth of the premises will lead (not entail, though) the truth of the conclusion. That is, there's a chance, be it over or below 50%.

But, if it contains one, which is what until here I meant by "invalid induction" (how do we call it, fallacious induction?), then such possibility is 0%. That is, even if the conclusion turns out to be true, the argument cannot even "lead" to this truth, it will simply "have happened", and therefore the argument will be void.

While I was unsure before, I think now that a non-fallacious inductive argument couldn't ever fall short of 50% certainty, given the fallacy of hasty generalization:

This fallacy is committed when a person draws a conclusion about a population based on a sample that is not large enough.

If this is correct, then a fallacious inductive argument could rise above 0% probability. In short, I think it would be correct for you to label fallacious inductive reasoning as inductively "invalid."

While you still seem to hold that religious faith through induction falls in the first type, I'll still try to defend that it falls in the second. Also, remember that "religious claims" in this sense won't mean the existence of a cross, or the existence of a tomb, but only those claims only believable by believers in theism.

Sure. The existence of God and actions committed by him would constitute the whole of religious claims we are concerned with.

There are a whole bunch of things I can remark here. First, this are two arguments and not one. The first concludes that miracles are historically reported, and the second concludes that Christianity is most likely true (though I'm not sure a conclusion can be just "likely"). Let's analyze the first one:

1. Historical details of the Bible are true.
2. Miracles are historical details (according to the Bible.)*
Therefore, miracles are true (since they're historical and not legendary).

I don't think this qualifies as an induction, since if the premises were true (which both are), the conclusion would be true (*), I would put it as a deduction or maybe syllogism (I don't know exactly). But, there's a minor detail which renders the conclusion unsound though it's valid. If we count the parenthesis in the premise 2., this turns out to be circular logic. Why are miracles true historical details - because the Bible says so. Why is the Bible accurate? Because Christianity is true - which if I remember well, was your final conclusion.

The argument I gave was indeed inductive. I'll present the first three points again and elaborate:

1. Many of the incidental historical details of the Bible have been confirmed by secular archaeology.
2. The Bible includes reports of miracles as if they were history.
3. Therefore, it is likely that the reports of miracles are also historical details.

The first premise refers to geographical and political details within the Bible that have been confirmed by secular archaeology. Say, the Pool of Bethesda or the confirmed existence of Herod Agrippa I. Of course, there are no secular confirmations of miracles, nor could there be; these sorts of things don't fossilize. But we have a sample of correct historical details from which to infer that the Bible's miracles, interspersed as they are with history, are also historical details. So your charge of circularity doesn't stick; I didn't deduce that miracles occurred by assuming that the Bible is true, rather I inferred that the miracles were likely true from the sample of correct secular details.

I cannot provide a valid inductive argument, validity here being understood as greater than 50% probability. However, if weak induction is all that you require, the wiki article offers the following as an example:

Im not sure where I get this use of >50% probability. Im not sure that makes an argument valid. I think it depends on the premises.

If I use the argument:
Every swan I have ever seen is white, therefore all swans are white.

While its true the vast majority of swans are white, it only takes one non-white swan to make my argument invalid even though the "probability" of me finding a white swan is 99.9%.

I got the +50% definition from Chapter 11 of Graham Priest's Logic: A Very Short Introduction, found here on Google Books, in which he says:

What is it for an inference to be inductively valid? Simply that the premisses make the conclusion more probable than not.

The rest of your quoted post assumes deductive validity, which is not the subject of this discussion, apart from distinguishing it from inductive validity. Its interesting to note that this standard of inductive validity is very stringent. We certainly trust political polls etc. with far less statistical certainty.

[Ragna]

Hello Ragna. You'll have to excuse me when I excise sentences here and there from your post, not because they are uninteresting, but for the sake of brevity, or because one of my responses may have addressed several of your points at once.

No worries, I understand.

While I was unsure before, I think now that a non-fallacious inductive argument couldn't ever fall short of 50% certainty, given the fallacy of hasty generalization:

This fallacy is committed when a person draws a conclusion about a population based on a sample that is not large enough.

If this is correct, then a fallacious inductive argument could rise above 0% probability. In short, I think it would be correct for you to label fallacious inductive reasoning as inductively "invalid."

Is that an informal fallacy? Sorry but I'm lost here . I would classify a "hasty generalization" as a valid but really weak induction (since sometimes we can't be sure of how big is what we study, like for example for entablishing the Copernican principle), but how can a fallacious inductive argument rise above 0% (without taking chance into account)?

The argument I gave was indeed inductive. I'll present the first three points again and elaborate:

1. Many of the incidental historical details of the Bible have been confirmed by secular archaeology.
2. The Bible includes reports of miracles as if they were history.
3. Therefore, it is likely that the reports of miracles are also historical details.

The first premise refers to geographical and political details within the Bible that have been confirmed by secular archaeology. Say, the Pool of Bethesda or the confirmed existence of Herod Agrippa I. Of course, there are no secular confirmations of miracles, nor could there be; these sorts of things don't fossilize. But we have a sample of correct historical details from which to infer that the Bible's miracles, interspersed as they are with history, are also historical details. So your charge of circularity doesn't stick; I didn't deduce that miracles occurred by assuming that the Bible is true, rather I inferred that the miracles were likely true from the sample of correct secular details.

This is the sort of thing I had in mind to classify as an error in category. You could very brutely generalize "some of the Bible is true therefore all of it is" but that's no different than saying "some swans are white therefore all tables are" (maybe a non sequitur?), because of the implicit categories.

[Adamoriens]

While I was unsure before, I think now that a non-fallacious inductive argument couldn't ever fall short of 50% certainty, given the fallacy of hasty generalization:

This fallacy is committed when a person draws a conclusion about a population based on a sample that is not large enough.

If this is correct, then a fallacious inductive argument could rise above 0% probability. In short, I think it would be correct for you to label fallacious inductive reasoning as inductively "invalid."

Is that an informal fallacy? Sorry but I'm lost here . I would classify a "hasty generalization" as a valid but really weak induction (since sometimes we can't be sure of how big is what we study, like for example for entablishing the Copernican principle), but how can a fallacious inductive argument rise above 0% (without taking chance into account)?

This is running into calculating probabilities, at present beyond my ken. Anyways, a person could make an inductive argument and present the conclusion that such and such an event is likely to happen. But on further examination of his premisses, we find that he took a sample that was too small and made a hasty generalization, leading to a likelihood that was above 0% but below 50%, and thus the argument is both inductively invalid and fallacious.

The argument I gave was indeed inductive. I'll present the first three points again and elaborate:

1. Many of the incidental historical details of the Bible have been confirmed by secular archaeology.
2. The Bible includes reports of miracles as if they were history.
3. Therefore, it is likely that the reports of miracles are also historical details.

The first premise refers to geographical and political details within the Bible that have been confirmed by secular archaeology. Say, the Pool of Bethesda or the confirmed existence of Herod Agrippa I. Of course, there are no secular confirmations of miracles, nor could there be; these sorts of things don't fossilize. But we have a sample of correct historical details from which to infer that the Bible's miracles, interspersed as they are with history, are also historical details. So your charge of circularity doesn't stick; I didn't deduce that miracles occurred by assuming that the Bible is true, rather I inferred that the miracles were likely true from the sample of correct secular details.

This is the sort of thing I had in mind to classify as an error in category. You could very brutely generalize "some of the Bible is true therefore all of it is" but that's no different than saying "some swans are white therefore all tables are" (maybe a non sequitur?), because of the implicit categories.

You'll recall that I carefully presented it as an inductive conclusion; some or most of the Bible's historical details are true, therefore it's likely that the miracles described as history also occurred. Where is the non sequitur? More to the point, why does it matter? A false or weak inductive argument is still an inductive argument.

[Ragna]

This is running into calculating probabilities, at present beyond my ken. Anyways, a person could make an inductive argument and present the conclusion that such and such an event is likely to happen. But on further examination of his premisses, we find that he took a sample that was too small and made a hasty generalization, leading to a likelihood that was above 0% but below 50%, and thus the argument is both inductively invalid and fallacious.

You'll recall that I carefully presented it as an inductive conclusion; some or most of the Bible's historical details are true, therefore it's likely that the miracles described as history also occurred. Where is the non sequitur? More to the point, why does it matter? A false or weak inductive argument is still an inductive argument.

If you remember, when I proposed the "valid" and "invalid" categories, I did so including both weak and strong as "valid".

You claimed that the first example was invalid, and I asked the reason for doing so (the reason why "hasty generalization" is a true logical fallacy when the total field is not knowable - because otherwise we'd be explicitly ignoring available data, or toying with a non-representative study, consciously). I'd consider it a valid, weak induction. One of the kind of "there are no fish in this glass of water, therefore there aren't any fish in the sea".

On the other hand, the second is one I would place as "invalid", for the reason I expressed in my comment: it jumps from a category (historical) to another category (mythical), which can only be legitimately (non-fallaciously) compared if considered historical, which would presuppose the conclusion.

[Adamoriens]

If you remember, when I proposed the "valid" and "invalid" categories, I did so including both weak and strong as "valid".

You claimed that the first example was invalid, and I asked the reason for doing so (the reason why "hasty generalization" is a true logical fallacy when the total field is not knowable - because otherwise we'd be explicitly ignoring available data, or toying with a non-representative study, consciously). I'd consider it a valid, weak induction. One of the kind of "there are no fish in this glass of water, therefore there aren't any fish in the sea".

For now, then, I guess we're not using the definition of inductive validity by Priest that I quoted earlier?

On the other hand, the second is one I would place as "invalid", for the reason I expressed in my comment: it jumps from a category (historical) to another category (mythical), which can only be legitimately (non-fallaciously) compared if considered historical, which would presuppose the conclusion.

On the contrary, to segregate miracles as myth and everything else as history presupposes, it seems to me, that miracles have not occurred. The Bible contains a narrative which has been partially confirmed as historical by secular archaeology (so the argument goes), so one could argue inductively that, given the Bible's success so far, it is reasonable to expect that the miracles described also occurred.

[Adamoriens]

On the other hand, the second is one I would place as "invalid", for the reason I expressed in my comment: it jumps from a category (historical) to another category (mythical), which can only be legitimately (non-fallaciously) compared if considered historical, which would presuppose the conclusion.

On the contrary, to segregate miracles as myth and everything else as history presupposes, it seems to me, that miracles have not occurred. The Bible contains a narrative which has been partially confirmed as historical by secular archaeology (so the argument goes), so one could argue inductively that, given the Bible's success so far, it is reasonable to expect that the miracles described also occurred.

A second thought. Perhaps you are challenging my assumption that miracles, like more mundane historical events, are even possible? If so, then I would respond like this: it is logically possible that God exists and that he can influence the natural world. If this is true, then it is logically possible that miracles have occurred.