## Wednesday, June 14, 2017

### Induction and universal generalizations

According to Gordon Clark, induction is a fallacy. To take a stock example, if I see a 1000 black crows, that fails to justify the inference that all crows are black, because the 1001st crow might be white.

But there are some problems with that objection:

i) To begin with, is a white crow a crow, or is it a related species? Two different, closely related species.

ii) Let's take a different comparison. Suppose I've only seen white rabbits. But that's because I've only seen rabbits in winter. If I saw rabbits in summer, I'd see brown rabbits.

So it would be invalid to infer that all rabbits are white. That's an unrepresentative sample, based on seasonal variations.

Yet once we take seasonal variations into account, then the reason to believe rabbits must either be white or brown is deeper than observing a sample of rabbits. Rather, that involves the principle of camouflage.

In that event, I wouldn't believe that rabbits are white in winter just because every rabbit I've seen in winter is white. Rather, their pigmentation would be grounded in a principle that's not dependent on counting instances of rabbits.

iii) Take another example: Suppose a 15C American Indian has noticed that solar eclipses only happen at a new moon whereas lunar eclipses only happen at a full moon. What is more, everyone in his tribe has made the same observation. His parents and grandparents have made the same observation. And according to Indian lore, handed down from one generation to the next, that's always been the case. Of course, that, in itself, is insufficient to justify a universal generalization.

Suppose, by contrast, you ask an astronomer. His reason wouldn't be based on repeated observations. Rather, he'd provide an underlying explanation for that observation, based on the relative position of the sun, moon, and earth during solar and lunar eclipses.

A similar example would be the observation that the sun always rises in the east and sets in the west. If all you have to go by is observation, then, in principle, the sun could reverse course. But an astronomer has a differ explanation, based on the earth's counterclockwise rotation.

Scientists observe regularities in nature. But that's just a starting-point. Their belief in the "uniformity of nature" isn't merely based on sampling natural phenomena. Rather, they attempt to go behind the phenomena to discover a mechanism that causes that effect. Therefore, it's simplistic to say inductive logic is fallacious, as if "natural laws" are merely based on repeated observations.

iv) In addition, exceptions wouldn't invalidate the principle, because natural laws have ceteris paribus clauses. An exception is due to the introduction or interference of an overriding cause.

Normally, water can't travel uphill. That generalization isn't simply based on the common observation that water normally travels downhill. Rather, it's grounded in the absence of some additional factor to counteract the force of gravity. But sometimes there are natural factors (e.g. storm surge) or technological factors (e.g. water pumps) that exert a countervailing influence.

In that respect, a white crow is not a real exception to the principle, inasmuch as the generalization is implicitly qualified. All things being equal, all panthers are black, all ravens are black, &c.

Albinism is a genetic condition that produces a different pigmentation. But the generalization allows for differential factors.

In sum, if a Scripturalist is going to attack the principle of induction, he will need to attack the principle of causation that underlies many scientific explanations.

1. "In sum, if a Scripturalist is going to attack the principle of induction, he will need to attack the principle of causation that underlies many scientific explanations."

Bingo! I've been reading a lot of 17th-19th century "evidentialist"/"common sense", etc. material lately, trying in particular to understand why the, broadly defined, "presuppositional" movement is so incensed at folks like Old Princeton, etc. One thing I'm seeing consistently is the importance attached by the pre-Van Tillian (or Kuyper, just trying to pick a convenient marker) of not only Cause and Effect, but in particular of Final Cause. One example of this would be James Buchanan and his emphasis on the importance of Final causes, etc. in epistemology as over against the "intuitionists" of his day (the first generation of German-influenced Anglo-British theologians, etc.) - see his books on Modern Atheism, etc.

A working hypothesis is that far too many post-Kantian, Hegelians/Schliermacherians (boy, that's awkward) seem to share a common target in taking down any perception of causes from effects, etc. Just read last night how Kuyper extolled Schliermacher (and Kant) as, in his words (roughly) "giving theology back to herself, and lifting her out of the mire" (last few pages of the Encyclopedia, the abridged 1898 one).

Do you think you could elaborate further on this? Was Van Til in this camp to any degree? Did folks like Hodge, et al, themselves go to far with induction?

2. I'd say there's a difference between doing inductions within the Christian worldview and doing them outside of it (including atheism, Islam etc.). Given Christian presuppositions, God made kinds and species, has providentially created and sustains general regularity and predictability in nature(though it can be interfered with by angels, demons and God Himself). These types of Christian presuppositions allow Christians to justifiably do inductions and come to certain tentative conclusions that can amount to knowledge.

This isn't true in non-Christian worldviews. In our contemporary situation, I'd say that atheism and/or secularism (which is closely related) is the reigning ideology. I think Clarkians are absolutely right to attack induction when confronting atheism/atheists. It's unfortunate that they don't limit that to non-Christian worldviews, but they even intentionally undermine the Christian use of induction.

It seems to me one way to undermine causation is to undermine induction. And one way to do that is to attack the reliability of sense experience. My comments regarding Clarkians and experience are the same as for induction. Namely, I think undermining non-Christian sensory experience is good, but bad within the Christian worldview.

Another way of undermining causation is pointing out the fact that apart from the Christian worldview, we can never really know IF causation happens; and if it does, what the cause or causes were that led to the effect. Correlation does not necessarily entail causation. Just because roosters crow before dawn does not entail that they or their crowing causes the sun to rise. Or, maybe the sun does rise because one or more roosters crow. How do we tell how many and which specific roosters cause sunrise?

1. "Or, maybe the sun does rise because one or more roosters crow. How do we tell how many and which specific roosters cause sunrise?"

That's a legitimate question to ask given atheism. In fact, given atheism maybe some events are completely contingent and occur without (and so not being effects at all). Maybe freak things happen in this world. Or as Cornelius Van Til would often say tongue-in-cheek, "Send/submit it to 'Ripley's Believe It or Not'" Or Van Til (citing Aristophanes) would say "Whirl is King, having driven out Zeus".

Alternatively translated:
No, a thousand times no! The ruler of the world is the Whirlwind, that has unseated Zeus.

"There is not, no; for Vortex reigns having expelled Jupiter."

Vortex is king, and has deposed Zeus.

Order is not a given given [sic] atheism. An orderly universe and a non-orderly universe are equally possible given atheism. In fact, calling reality a "uni-verse" is already begging the question. The word "universe" implies UNIty in the diVERSity that we see in the world. There is no God in atheism that can account for unity, or diversity (since atheism is also consistent with pure monism, and not just pure pluralism).

2. typo correction: "That's a legitimate question to ask given atheism. In fact, given atheism maybe some events are completely contingent and occur without [A CAUSE](and so not being effects at all)."

The words "a cause" was accidentally omitted. Also the words in the parenthesis is probably better phrased, "(and so are not effects at all)."

3. Annoyed Pinoy,

Forgive my ignorance. Could you explain how a method of knowing, in this case induction, becomes valid or invalid based on a world view, i.e., lead or not lead to "knowledge"? If the idea is simply that the addition of the world view is by definition a necessary (if not sufficient) component of knowledge, then a) why bother with any particular methodology if the world view is the essential ingredient regardless, and b) how is the world view distinguished from a simple a priori hypothesis that deductively determines the outcome regardless of any investigation at all, as opposed to determining that the world view itself constitutes "knowledge"?

If this comes off as a complex question, feel free to break it down. Looking for "knowledge" here myself.

4. "Another way of undermining causation is pointing out the fact that apart from the Christian worldview, we can never really know IF causation happens"

AP,

I'd suggest to you that the unbeliever can have no less knowledge of x causes y than a believer. What Scripture provides is the justification for the principle of causality, which is not needed to know a particular causal relationship. The object of knowledge would be vastly different.

5. Reformed Apologist,

When you say the following, "the unbeliever can have no less knowledge of x causes y than a believer" and also that the justification for the principle of causality is not needed to have knowledge of a particular causal relationship, I have a question. If we substitute "God" for x and "the World/Universe", etc. for y, would you say your statement still holds for the unbeliever? If not, what is the difference; if yes, are there any appropriate qualifications you would add? Where does the scripture's justification (or the absence of it for the unbeliever) for this particular causal relationship fit in?

Thanks!

6. If we substitute "God" for x and "the World/Universe", etc. for y, would you say your statement still holds for the unbeliever?

Yes, I believe all men know God caused the world.

if yes, are there any appropriate qualifications you would add?

None come to mind.

Where does the scripture's justification (or the absence of it for the unbeliever) for this particular causal relationship fit in?

The professing unbeliever in God the creator knows: "God made me." Let's call that a first order knowledge.

Scripture enables him to know, "God has revealed to me that I know God made me."

Regarding the first order, he can't give an account for the justification of his belief of the truth. In the second instance, Scripture allows him to know *that* he knows.

7. Reformed Apologist,

Thanks for your time. If you still have time (or interest), I have a follow-on question. And please, I am not "going" anywhere with this, just trying to understand, especially in light of what I've been reading in the pre-20th century literature on this.

You say the following: "Regarding the first order, he [the unbeliever] can't give an account for the justification of his belief of the truth. In the second instance, Scripture allows him to know *that* he knows."

If the question is "how do I know that I know God is the cause", and if the unbeliever truly has knowledge that God is the cause, and the "final cause" at that, how does this knowledge not cover, or include, the knowledge that God is also thereby the source of this knowledge in God for the unbeliever, just as God is the cause of everything else? Wouldn't this "everything else" include the reason why we have that knowledge at all, as well as our awareness of it?

It would seem from the very idea of Final Cause that identifying this final cause must include and satisfy the condition of "knowing that, how, or why I know." In other words, if knowing is itself also an effect that requires a cause, then this same final cause must also be sufficient grounds for the effect of knowing itself, and hence, I would think, provide its own "justification" for why I know. Otherwise, how is this knowledge (of God) a true, final cause if it does not cover the effect of knowing itself? And this same knowledge of God as cause of the effect of knowing, being "revealed" by the same process of induction from effect to cause, would seem to validate induction in this case as well.

So, let's rephrase the question: if we substitute "God" for x and "I know that I know" for y, would you say your statement still hold? If not, I would say that this is an affirmation of a limitation to induction. If so, how/why should induction be limited in this case?

As to whether or not knowing that God is the cause of my knowing necessarily leads to an awareness of "revelation" vis-a-vis God and my own knowledge, I would think this is where sin, etc. would intrude and Man, while knowing this to be the case, would still deny it, but only inconsistently and at the cost of no longer having a true "final" cause and have to find another, etc. But this effect is a sinful reaction, downstream, if you will, of the prior justified knowledge itself.

Again, I am proceeding on the assumption we are still talking about an unbeliever utilizing induction from nature, etc.

So, in the act of "knowing" (however this awareness can be stated), are we not aware of our knowing as itself an effect that requires a cause? And if we have, as you have already stipulated, at least an “unjustified” knowledge of God as that cause, does not this knowledge also beg a cause, which must by definition be the same God who caused all else?

8. In each case I think you need to tease out and clearly distinguish for yourself the objects of knowledge under consideration. Then it might be helpful to consider the possible source of warrant for those sorts of first and second order beliefs.

For instance, the unbeliever has warrant to believe he's under God's wrath. God has revealed it to him in conscience. But how do I or anyone else know that? Apart from Scripture how would the unbeliever begin to justify in any robust epistemic sense that his belief that he is under God's wrath is indeed warranted, which it is? What complicates things even more is his unwillingness even to admit to his innate knowledge that he's under God's wrath.

I think you're best left to reflection at this point.

9. Reformed Apologist,

Thanks again for your time. I understand you comment about leaving me to reflect, I'm glad to do so. Could I ask a final indulgence for a couple of additional explanations to help me?

1) What is meant by "warrant" in the way you've been using it?
2) When including the idea of warrant, if I understand you correctly, this seems to change the nature of the objects of knowledge (1st vs. 2nd orders of knowledge, etc.) - could you help me understand this a bit as well?

Otherwise, thanks and I'll refrain from posting with you on this again!

10. Warrant (or justification) is the ingredient that must be present for any true belief to be knowledge. It's *not* necessarily the case that whenever one has warrant for his true belief his belief constitutes knowledge. I am justified looking at a clock on the wall in order to know the proximate time. If the clock broke twelve hours before I'd be justified in my true belief but I wouldn't have knowledge of the proximate time.

To your second point, warrant doesn't change the object of knowledge. Rather, the sorts of objects of knowledge can require different sorts of warrant.

11. RA wrote:
I'd suggest to you that the unbeliever can have no less knowledge of x causes y than a believer. What Scripture provides is the justification for the principle of causality, which is not needed to know a particular causal relationship. The object of knowledge would be vastly different.

I agree. That's because he actually lives in God's world and is made in His image. What I wrote I wrote "given atheism". Meaning, if atheists were consistent with their anti-Christian worldview, they wouldn't be able to justify their belief in, and their identification of instances of, causation.

12. To Pip Brandy, regarding your original questions directed to me:

You're asking deep philosophical/theological/apologetical questions which I neither have the intelligence or training to fully answer. Let's start with certain facts (or what I believe are facts):

1. Sense experience and induction by themselves aren't infallible avenues of knowledge as Clarkians abundantly demonstrate. It doesn't logically follow from the fact that I believe I'm seeing a red car that I'm actually seeing a red car. I or We could be dreaming, or in a matrix with our brains (or their real equivalents) in Putnam's proverbial "vat" being manipulated by an Ungerian mad scientist (or by a Cartesian daemon). Atheists appeal to evolutionary reliabilism to explain how our cognitive and sensory faculties are generally reliable. But when you boil down their claims, they are merely hoping that we've evolved so that they are generally reliable. They don't actually demonstrate it. There are also such things as natural (e.g. optical) illusions et cetera. I've already explained how problematic causation is.

2. The following would seem at first glance to contradict #1 above. But it doesn't. Irrespective of whether the Christian God really exists, even most non-Christians will admit that the Christian conception of God expects us to know at least some things via induction. Many of God's commandments cannot be obeyed, nor can we be justly found guilty if we couldn't have some true knowledge (not merely opinion) via induction. God has provide us with General Revelation externally and internally. We're surrounded by revelation through and through. He has created and structured the world to be orderly and rationally accessible as well as making us in His rational image with innate knowledge and/or potential (given triggering conditions) for knowing and understanding concepts like: time, causation, space, universals/categories, language, morality, truth, laws of logic, math, His existence, our duty towards etc. He has made our cognitive and sensory faculties generally reliable and adapted to our environment. Given such things as universals, categories, species and the general uniformity and regularity of nature we can know things about the world in which we live. For example that crows normally can fly. Or that things thrown up in the air tend to fall back down. When it comes to science, I lean toward scientific anti-realism and instrumentalism and opperationalism. I doubt we can fully understand the real ontology and mechanics of the physical world. However, within the bounds of the God ordained sphere of our living and acting as God's creatures in His world, we can have an analogically sufficient knowledge of the world and what goes on in it. A knowledge that makes us accountable to Him and that enables us to have and live good and productive lives.

Regarding your specific questions, I'm not sure what you're asking or getting at. Or what your foundational concerns are.

3. Of course inference that is based upon asserting the consequent is based upon a formal fallacy of deduction. But that's the point, isn't it? Inductive inference isn't deduction. Induction is indeed useful though. We couldn't live without it. It's our source of reasoning that informs us of the veracity of an inferfence. Whether inductive inference can bring forth knowledge, it's the internalist constraint they place on knowledge that trips up clarkinans. They should all agree such patterns of plausible inference are useful even while they make much to do about the deductive form of inductive inference.

4. Very good AP. :)

5. Should Thomas have doubted that he knew he touched Jesus after he had touched Jesus? Or, did he not know at all that he touched Jesus and, therefore, should have remained moderately skeptical? Or maybe he knew only way after the fact, when it became a proposition of Scripture that he had touched Jesus. In the like manner, do the heavens declare the glory of God only after learning they do from special revelation? If so, then it would not be the *heavens* that declare God's glory. Wouldn't it have been ill advisable for the saints under both economies to affirm miracles they couldn't have known happened?

1. RA,

This last post about Thomas helps me. This was the point I was getting at about the role that a World View plays in knowledge, etc. Any of the Roman soldiers who had participated in Jesus' crucifixion would have known that it was the same Jesus three days later, just as Thomas did, whether they shared his "world view" or not. They might not have worshiped him as Lord and God, and they might not have been able to explain what had happened, but then that is the role of Special Revelation. But know that Jesus lives? they would have - and true, proper, warranted knowledge it would be! This is the basis of Paul's assertions at Athens and in Corinthians 15.

I like how you ask the rhetorical question - do we know such things "only after learning [them] from special revelation"? I had assumed up till now that this is what you meant, I am glad that you do not. My concern is that far too much of modern "presuppositionalism" strips away all authority and warrant from Natural Revelation in its proper role as ordained by God, and gives all authority/warrant to Special Revelation only. My fear is that Clarkians, and even Van Tillians have, in the words of James Buchanan when dealing with an early 19th century "presuppositionalist", a "morbid jealousy for the honor of [Special] Revelation". This was basically all I was getting at. We are not Quakers (i.e., read the first 3 chapters of Barclay's Apology), nor Socinians (see Charnock on the Attributes of God).

Overall this last post of yours is what I've been trying to emphasize to the younger Van Tillians in my church.

6. Glad I posted it then.

I don't think CVT thought we only can know things revealed in Scripture. Though I do think some have that impression. In a conversation I had with Alvin Plantinga even he said that about Van Til. I voiced my disagreement.

One thing striking about Van Til as an apologist is he operated from the premise that all men know how to count, yet they can't all give an account of their counting. In doing so I believe he distinguished knowledge from the justification of knowledge. We might say he was both an externalist and an internalist depending on the object of knowledge. Unfortunately, to my knowledge is he never fleshed out these things in any great detail.

Keep those young bucks in line. :)