Your thoughts on Hume's case against induction?

[Eddie]

Betsy: Knowledge without any contact with reality? How does THAT happen?

When I speak of a priori knowledge as being independent of experience, I mean logically independent, not absent any experience. It seems to me that a priori knowledge is known in a different way to knowledge that is known empirically, although experience is necessary for both forms of knowledge. By “knowledge” here I mean an item of my understanding that I am justified in believing to be the case, and this knowledge is expressed in statements.

The difference between the two is that empirical statements are known/justified by observation, whereas the justification for a priori statements is logically independent of observation, although in both cases experience is the occasion of understanding. The test for distinguishing between the two is whether any state of affairs could render them false.

Take our previous example of swans. The statement “all swans are white" can be falsified by supposing that some black swans may exist. The same cannot be said for 1+1=2. No state of affairs can render this false; it is true whatever possible state of affairs, and the only way the statement could be rendered false would be to change the meaning of the symbols, and that of course would change the meaning of the statement itself. It would no longer be the same statement.

Betsy: If this "knowledge" isn't knowledge of reality, what is it knowledge OF? What do you really "know?"

When I know 1+1=2, I know that a certain relationship exists between the relevant symbols. My knowledge of this relationship allows me to perform all sorts of calculations that can be used in my everyday activities: I can buy goods, plan a journey, keep appointments, bake a cake etc. These are all valuable uses for this type of knowledge.

E

[Eddie]

Fred: “Do you think it is a coincedence that "clarity in thinking, correct reasoning, analysis, organization of information" helps us in dealing with reality?”

Obviously not, but my decimal example referred to a specific system, where the base happened to coincide with the number of digits on our hands, rather than the wider phenomenon of counting. There’s nothing coincidental about counting as a phenomenon, nor about logic as a phenomenon.

Fred: “And how would it be possible to discover anything in reality if we didn't think logically? It is in fact logical thinking which enables us to make these dicoveries.”

Which implies that knowledge presupposes logic. And if logic is itself a species of knowledge, this seems to beg the question. If so, and if we can only discover anything in reality by thinking logically, this implies that logic is itself a logically necessary condition for knowledge, that is, a priori.

Fred: “There is something else which confuses this issue which is our capacity for imagination. We can create ideas which bear little or no relationship to reality (e.g. we can imagine a cow jumping over the moon)…”

That’s true, but imagination not only enables us to think up ways of testing our ideas, but also enables us to have new and creative ideas in the first place. Arguably, our need for survival forces up to focus our minds rather narrowly, whereas imagination enables our minds to soar. Nowadays, we are used to the idea of Newtonian gravity, but in his time the notion was probably rather strange. Similarly with Einstein’s relativity. As with rationality, imagination can be used well or badly.

E

[Tom Rexton]

[...]

Fred: “And how would it be possible to discover anything in reality if we didn't think logically? It is in fact logical thinking which enables us to make these dicoveries.”

Which implies that knowledge presupposes logic. And if logic is itself a species of knowledge, this seems to beg the question. If so, and if we can only discover anything in reality by thinking logically, this implies that logic is itself a logically necessary condition for knowledge, that is, a priori.

[...]

E

In Objectivism, the fundamental unit of knowledge is a concept, which is formed through the differentiation and integration of concrete units or of concepts themselves. In the first level of abstraction, where concrete units are differentiated and then integrated into a concept, the method of differentation and integration is what Ayn Rand called induction:

"the process of observing the facts of reality and of integrating them into concepts is, in essence, a process of induction." (ITOE, chapter 3)

In other words, the process of concept-formation is a process of induction. If induction is a process of concept-formation, does it not follow that the validity of induction cannot be logically proven with a given set of true premises, because all propositions consist of concepts, which are formed via induction? Any logical proof if its validity/invalidity would be a fallacy of "the stolen concept".

If so, then the validity of induction would have the same status as the law of identity. That is, the validity of induction is axiomatic!

[Betsy]

Betsy: Knowledge without any contact with reality? How does THAT happen?

When I speak of a priori knowledge as being independent of experience, I mean logically independent, not absent any experience. It seems to me that a priori knowledge is known in a different way to knowledge that is known empirically, although experience is necessary for both forms of knowledge.

If "experience is necessary" then it isn't a priori. A priori means prior to experience.

By “knowledge” here I mean an item of my understanding that I am justified in believing to be the case, and this knowledge is expressed in statements.

Do you mean knowledge of reality? Understanding of reality? Justified in reality? Statements about reality?

The difference between the two is that empirical statements are known/justified by observation, whereas the justification for a priori statements is logically independent of observation, although in both cases experience is the occasion of understanding. The test for distinguishing between the two is whether any state of affairs could render them false.

Take our previous example of swans. The statement “all swans are white" can be falsified by supposing that some black swans may exist. The same cannot be said for 1+1=2.

Sure it can. Arithmetic rules come from experience counting things, although I don't expect you to admit it. Nonetheless, if 1 + 1 doesn't come from reality, where do we get it from? Innate ideas? Fantasy?

If this "knowledge" isn't knowledge of reality, what is it knowledge OF? What do you really "know?"

When I know 1+1=2, I know that a certain relationship exists between the relevant symbols.

A relationship in reality?

Knowledge of this relationship allows me to perform all sorts of calculations that can be used in my everyday activities: I can buy goods, plan a journey, keep appointments, bake a cake etc.

AMAZING!

Since this has nothing to do with reality, it must be a miracle!

[Fred Weiss]

Fred: “And how would it be possible to discover anything in reality if we didn't think logically? It is in fact logical thinking which enables us to make these dicoveries.”

Which implies that knowledge presupposes logic. And if logic is itself a species of knowledge, this seems to beg the question. If so, and if we can only discover anything in reality by thinking logically, this implies that logic is itself a logically necessary condition for knowledge, that is, a priori.

No, it's not begging the question (afterall, begging the question itself presupposes logic) and yes logic is a necessary condition for knowledge. But that doesn't make it "a priori". It makes it axiomatic, i.e. a necessary truth at the base of all knowledge without which knowledge is impossible and which cannot be denied without presupposing it.

But why is it axiomatic, why is it necessary? Because that's the way reality is. Our minds don't make the world consistent with the Law of Non-Contradiction. There is such a (logical) law, and if we are to be logical we must abide by it, because in reality something cannot both be and not be the same thing in the same respect. In other words, it's not that way because we say so or merely because our minds are structured a certain way, i.e. because it's "a priori". It's that way because that's the way it is and has to be.

But if you think that something can both be and not be, etc. then of course all bets are off (literally). But then it's not a priori either and if it were our minds would not be in accord with reality.

Again, don't confuse our capacity for rational/logical thought with rationality/logic itself. That we are capable of rational thought doesn't mean we will be and of course many people aren't. So it is clearly not "a priori" for them. It's a process that has to be exercised. And as you well know, and I'm sure you know people like this, there are people who will tell you that rational thinking isn't all it's cracked up to be and maybe we should rely more on our "feelings", etc. So what's "a priori" for them? They don't get it at all. So where's the "a priori"? Why would it be "a priori" for some and not for others?

Fred Weiss

[Eddie]

Tom Rexton: “If induction is a process of concept-formation, does it not follow that the validity of induction cannot be logically proven with a given set of true premises, because all propositions consist of concepts, which are formed via induction?”

Induction is about making generalisations from particular observations, so it more properly refers to statements or propositions rather than concepts per se. Otherwise, the topic in question is the inability to logically validate induction, so I can only agree with you there.

Tom Rexton: “If so, then the validity of induction would have the same status as the law of identity. That is, the validity of induction is axiomatic!”

The identity claim was the basis of Betsy’s original argument on this issue. I don’t think that an appeal to identity solves the issue, and I stated my reasons many posts back.

E

[Eddie]

Betsy: “If "experience is necessary" then it isn't a priori. A priori means prior to experience.”

There is a widespread misunderstanding that the term a priori refers to a temporal or psychological priority. As I pointed out in my previous post, a priori refers to logical independence from experience, therefore the term is a matter of logical priority, and not psychology or the temporal flow of events. So it is quite in order that a priori knowledge requires experience, but is not logically dependent on experience.

Betsy: “Do you mean knowledge of reality? Understanding of reality? Justified in reality? Statements about reality?”

Some statements are about the external world and are justified by appeal to that world, eg, some swans are white. Others are justified by the meanings of the terms and their logical consistency, eg, 1+1=2.

Betsy: “A relationship in reality?”

This question refers to my claim that in the case of arithmetic, a relationship, or several relationships, exist between the relevant symbols, viz, 1 plus 1 equals 2, 1 is half of 2, 2 is twice 1, and so on. Empirical or synthetic statements make claims about the world, that such and such is the case. It is therefore possible to specify a state of affairs where such and such is not the case, that is, the statement can be falsified.

The same cannot be said for arithmetical statements. Here is an example. Before me are two swans. I count them: 1+1=2. While my attention is diverted, one of the swans swims out of sight. Does that falsify the statement 1+1=2? Of course not. The statement still holds true, even though it no longer applies to the changed situation, which implies a qualitative difference between empirical and arithmetical statements.

Betsy: “AMAZING! [That one can perform everyday calculations using arithmetic.] Since this has nothing to do with reality, it must be a miracle!”

Amazing, perhaps, but no miracle. A miracle is an outside intervention in the natural order, that is, a supernatural action. But the mind is part of nature; therefore using the mind is a natural rather than supernatural or miraculous activity.

E

[Eddie]

Fred: “…yes logic is a necessary condition for knowledge. But that doesn't make it "a priori". It makes it axiomatic, i.e. a necessary truth at the base of all knowledge without which knowledge is impossible and which cannot be denied without presupposing it.”

I don’t follow. You seem to be saying that logic is a necessary truth. But logic is a system of thought. Perhaps you mean that logical statements can express necessary truths, and that the statements cannot be denied without presupposing them. I would agree with that, but undeniability merely refers to the terms of the statements in question. It is impossible to deny gods or unicorns without appealing to the terms, but that tells us nothing about the reality of the referents of these terms.

Fred: “Again, don't confuse our capacity for rational/logical thought with rationality/logic itself. That we are capable of rational thought doesn't mean we will be and of course many people aren't. So it is clearly not "a priori" for them.”

I’m not making any such confusion, but the distinction I have been drawing is between the form of logical statements and their content. On the wider issue of rationality, or more accurately, the practice of reasoning, this can be done well or badly.

But those who are exposed to the rules of logic will, I believe, understand them a priori, that is, logically independent of experience of the external world, although of course not independently of the specific experience that comprises the learning process. One must be exposed to the discipline of logic in order that a priori understanding can take place; it doesn’t just pop into people’s heads devoid of context. So not everybody knows these sorts of a priori truths.

E

[Bowzer]

There is a widespread misunderstanding that the term a priori refers to a temporal or psychological priority.

That term is itself one big misunderstanding about the nature of knowledge. Read Leonard Peikoff's "The Analytic-Synthetic Dichotomy" in Introduction to Objectivist Epistemology 2nd Ed.

[Tom Rexton]

Tom Rexton: “If induction is a process of concept-formation, does it not follow that the validity of induction cannot be logically proven with a given set of true premises, because all propositions consist of concepts, which are formed via induction?”

Induction is about making generalisations from particular observations, so it more properly refers to statements or propositions rather than concepts per se. Otherwise, the topic in question is the inability to logically validate induction, so I can only agree with you there.

I would argue that concept-formation is a form of generalization--a generalization from particular concrete units or similar concepts.

Anyways, you cannot claim that induction is logically invalid, for that would make deduction, too, logically invalid. Any deductive proof of deduction would just beg the question.

Tom Rexton: “If so, then the validity of induction would have the same status as the law of identity. That is, the validity of induction is axiomatic!”

The identity claim was the basis of Betsy’s original argument on this issue. I don’t think that an appeal to identity solves the issue, and I stated my reasons many posts back.

E

The identity claim here is different--I'm talking about the logical status of the validity of induction.

I said it is axiomatic, just like the axioms "existence exists" and "A is A".

[Betsy]

In Objectivism, the fundamental unit of knowledge is a concept, which is formed through the differentiation and integration of concrete units or of concepts themselves. 

Actually, the basic unit of cognition -- the given and the self-evidently true -- is the PERCEPT.

A percept is a group of sensations automatically retained and integrated by the brain of a living organism. It is in the form of percepts that man grasps the evidence of his senses and apprehends reality. When we speak of "direct perception" or "direct awareness," we mean the perceptual level. Percepts, not sensations, are the given, the self-evident.

In the first level of abstraction, where concrete units are differentiated and then integrated into a concept, the method of differentation and integration is what Ayn Rand called induction:

"the process of observing the facts of reality and of integrating them into concepts is, in essence, a process of induction." (ITOE, chapter 3)

What Ayn Rand is saying here is that concept formation is AN inductive process, i.e., a process going from the specific (in this case, specific percepts) to the general (open-ended concepts). There are many OTHER examples of induction, such as forming generalizations, which are NOT concept-formation.

In other words, the process of concept-formation is a process of induction.  If induction is a process of concept-formation, does it not follow that the validity of induction cannot be logically proven with a given set of true premises, because all propositions consist of concepts, which are formed via induction?

Since induction ISN'T a process of concept-formation -- it is a process of going from the specific to the general -- none of that follows.

If so, then the validity of induction would have the same status as the law of identity.

Induction is a type of identification. It is the type that identifies general truths from knowledge of specific entities. In my own theory of induction, when you have shown how your inductive conclusion can be reduced to a statement of identity, then you have validated that particular inductive conclusion. It then has the status of the Law of Identity because it IS an instance of the Law of Identity.

[Fred Weiss]

...You seem to be saying that logic is a necessary truth. But logic is a system of thought. Perhaps you mean that logical statements can express necessary truths, and that the statements cannot be denied without presupposing them. I would agree with that, but undeniability merely refers to the terms of the statements in question. It is impossible to deny gods or unicorns without appealing to the terms, but that tells us nothing about the reality of the referents of these terms.

They are not just necessary truths, they are axiomatic, meaning that they are at the base of knowledge, inherent in knowledge itself, i.e. you couldn't have knowledge without them. Their undeniability consists in the impossibility of denying their truth without presupposing their truth. So denying them in this instance involves self-contradiction.

But those who are exposed to the rules of logic will, I believe, understand them a priori, that is, logically independent of experience of the external world, although of course not independently of the specific experience that comprises the learning process. One must be exposed to the discipline of logic in order that a priori understanding can take place; it doesn’t just pop into people’s heads devoid of context. So not everybody knows these sorts of a priori truths.

Here you are simply equivocating between specific experience and experience in general. True, you don't need to know how to make toast or drive a car before you can grasp the principles of logic. But you do need to have experience, i.e. contact with and knowledge of the real world. Logic afterall is about bringing our thinking processes in accord with reality, right? So how could you possibly know what thinking processes are in accord with reality if you had no contact with reality?

Since logical principles are very broad abstractions, and apply to thought as such, they don't apply to this experience or that experience. They apply to experience in general That is not the same thing as "a priori", independent of or apart from experience.

Fred Weiss

[Betsy]

There is a widespread misunderstanding that the term a priori refers to a temporal or psychological priority. As I pointed out in my previous post, a priori refers to logical independence from experience, therefore the term is a matter of logical priority, and not psychology or the temporal flow of events. So it is quite in order that a priori knowledge requires experience, but is not logically dependent on experience.

How can that be?

If a priori knowledge REQUIRES experience, then it IS logically dependent on experience. If you don't have experience HOW can you have a priori knowledge?

[Betsy]

Some statements are about the external world and are justified by appeal to that world, eg, some swans are white. Others are justified by the meanings of the terms and their logical consistency, eg, 1+1=2.

The meaning of the terms in reality and their logical consistency with reality?

Betsy: “A relationship in reality?”

This question refers to my claim that in the case of arithmetic, a relationship, or several relationships, exist between the relevant symbols, viz, 1 plus 1 equals 2, 1 is half of 2, 2 is twice 1, and so on.

This is true -- in reality -- every time! Ever consider the possibility that we got the idea from reality instead of a priori (A Latin term used by modern philosophers loosely translated as "somehow." )

Empirical or synthetic statements make claims about the world, that such and such is the case. It is therefore possible to specify a state of affairs where such and such is not the case, that is, the statement can be falsified.

Yes, I know that's what you think.

By now I've made my point to almost everyone here. If you don't see it, at least understand that Objectivism totally rejects the analytic-synthetic dichotomy. Instead of arguing further, get a copy of Ayn Rand's Introduction to Objectivist Epistemology and read Leonard Peikoff's essay, "The Analytic-Synthetic Dichotomy."

[mbd28]

How can that be?

If  a priori knowledge REQUIRES experience, then it IS logically dependent on experience. If you don't have experience HOW can you have a priori knowledge?

Interesting thread. I think what philosophers are trying to convey with the concept of "a priori" is not that some knowledge is attained independantly of experience, but rather that its truth value is not dependant on such. In that sense, it is "prior." We obviously learn "2 + 2 = 4" ftrom experience, but that proposition is universally true, not subject to future experiential dis-proof. The ontology of mathematics/logic is a tricky matter for me. Are they mere formal systems that we apply to experience? Do they "constitute" experience in some way? Are they truths that exist independantly in a realm of forms?

[ian]

We obviously learn "2 + 2 = 4" ftrom experience, but that proposition is universally true, not subject to future experiential dis-proof.

What if we find an object on the other side of the galaxy that when you put 2 of them with another 2 there is a flash of light and you get 5? Wouldn't that disprove that 2 + 2 = 4?

[Bowzer]

I think what philosophers are trying to convey with the concept of "a priori" is not that some knowledge is attained independantly of experience, but rather that its truth value is not dependant on such.

Sure, you convey what any philosopher would tell you. That does not change the fact that it is entirely incorrect.

All knowledge is attained from experience and the truth or falsity of all knowledge rests on perception.

[Eddie]

mdb28: “Interesting thread. I think what philosophers are trying to convey with the concept of "a priori" is not that some knowledge is attained independantly of experience, but rather that its truth value is not dependant on such. In that sense, it is "prior." We obviously learn "2 + 2 = 4" ftrom experience, but that proposition is universally true, not subject to future experiential dis-proof.”

In general, I agree. One of the difficulties in understanding the term a priori is that we tend to think of knowledge or knowing only in its psychological aspect, whereas the a priori is concerned with logic. Looking up my dictionary I see that “An a priori proposition is one that can be known to be true, or false, without reference to experience, except insofar as experience is necessary for understanding its terms.” That pretty much accords with what you say above.

Mdb28: “The ontology of mathematics/logic is a tricky matter for me. Are they mere formal systems that we apply to experience? Do they "constitute" experience in some way? Are they truths that exist independantly in a realm of forms?”

I think your first option is the correct one. I tend to see mathematics/logic as tools that we use for particular purposes.

E

[Eddie]

Fred: “They [logical truths?] are not just necessary truths, they are axiomatic, meaning that they are at the base of knowledge, inherent in knowledge itself, i.e. you couldn't have knowledge without them. Their undeniability consists in the impossibility of denying their truth without presupposing their truth. So denying them in this instance involves self-contradiction.”

I’m not sure what you mean by “they” here. An axiom is generally understood to be a statement for which no proof is required, and occurs as the premise of an argument, whereas logical truths are the conclusions of arguments. Perhaps you are referring to the principles of logic, and that to deny them involves a contradiction, in which case I would agree, but I also think they’re rules of language and inference rather than statements about anything.

Fred: “Here you are simply equivocating between specific experience and experience in general. True, you don't need to know how to make toast or drive a car before you can grasp the principles of logic. But you do need to have experience, i.e. contact with and knowledge of the real world. Logic afterall is about bringing our thinking processes in accord with reality, right? So how could you possibly know what thinking processes are in accord with reality if you had no contact with reality?”

I’m not equivocating; my example of learning the principles of logic was merely an illustration. Nor am I disputing that experience is necessary for knowledge. But in its broadest sense, logic is about the structure and principles of sound reasoning. As I mentioned previously, a priori knowledge requires experience, so contact with the external world is a given, but logic is not justified by appeal to the external.

E

[Fred Weiss]

...the principles of logic...they’re rules of language and inference rather than statements about anything.

They are statements about whether your thinking is in accord with reality

If they are not that what is their point?

...logic is about the structure and principles of sound reasoning. As I mentioned previously, a priori knowledge requires experience, so contact with the external world is a given, but logic is not justified by appeal to the external.

Then it has no point. Do you think it is just a game, a flight of fancy? What?

As to the "a priori", see my previous comments. Logic is not a priori. It is entirely based on, derived from, and validated by experience. The reason why logic is valid is because: that's the way reality is. It is not something which we impart to reality or is it anything we possess innately at birth. Yes, we have the capacity for rational thought but we also have the capacity for running. That doesn't make rational thought a priori anymore than running is.

Fred Weiss

[Betsy]

Logic is not a priori. It is entirely based on, derived from, and validated by experience. The reason why logic is valid is because: that's the way reality is.

Many philosophers claim that since logic is not derived from PARTICULAR observations, it is not derived from observation.

What they miss is that logic can be derived from ANY observation because it applies to ALL observations.

[Spearmint]

Many philosophers claim that since logic is not derived from PARTICULAR observations, it is not derived from observation. 

What they miss is that logic can be derived from ANY observation because it applies to ALL observations.

How can logical principles be derived from observation? Logical principles are necessary to do the deriving in the first place, this argument is going to descend into circularity...

[Fred Weiss]

How can logical principles be derived from observation? Logical principles are necessary to do the deriving in the first place, this argument is going to descend into circularity...

Not if you grasp that they are axiomatic.

Axiomatic does not mean "not derived from observation". The observation in this instance, which is all it can be, is ostensive. That and the fact that any attempt to deny them is self-refuting.

Fred Weiss

[Spearmint]

Not if you grasp that they are axiomatic.

Axiomatic does not mean "not derived from observation".

How can they be derived from observation? We dont 'know' the law of identity yet, how can we possibly derive either it or anything else? If someone 'knows' no principles of logic whatsoever, by what means could he possibly derive anything?

[Bowzer]

How can they be derived from observation? We dont 'know' the law of identity yet, how can we possibly derive either it or anything else? If someone 'knows' no principles of logic whatsoever, by what means could he possibly derive anything?

Knowledge is built in a progression from the implicit to the explicit. A child is thinking logically long before he learns the explicit rules guiding his thought during that time. The fact that an item of knowledge is implicit does not mean that it is useless or baseless. From IToE (p. 159)

The "implicit" is that which is available to your consciousness but which you have not conceptualized. For instance, if you state a certain proposition, implicit in it are certain conclusions, but you may not necessarily be aware of them, because a special, separate act of consciousness is required to draw these consequences and grasp conceptually what is implied in your original statement. The implicit is that which is available to you but which you have not conceptualized.

See the section "Implicit Concepts" in the Appendix to IToE for more discussion.