Your thoughts on Hume's case against induction?

[Betsy]

AshRyan: “You claim that induction is invalid. Since all of the premises for deductive arguments must ultimately be gotten by induction, that means that all knowledge is invalid. But if so, that would certainly imply to all of your claims, including your argument that induction is invalid.”

I said that induction is a logically invalid procedure. That doesn’t invalidate knowledge of the external world,

"Knowledge of the external world?" Where did you get THAT from -- if "induction is a logically invalid procedure."

nor does it render the conclusions of deductive arguments invalid, merely more or less provisional.

Provisionally true or provisionally false -- and how can you tell the difference if you reject induction?

What we are seeking in the acquisition of empirical knowledge is a true description of the world. We cannot conclusively claim that our current descriptions really are true

Well, maybe you can't, but I sure can.

(and Rand allows for this with her ‘contextual’ certainty)

"Context" is not a fudge factor. It simply means the PART of reality, usually all that is known, that an idea applies to -- with absolute certainty.

but we can test for falsity.

How do you do that if you reject induction?

A description that is found to be inadequate

How you tell if a description is adequate or inadequate if you reject induction?

can be replaced by another, via a process of conjecture

You mean making things up?

and refutation.

How do you do that if you reject induction?

In other words, what we are seeking in knowledge is the ability to make predictions about the way the world works. In that case, the accuracy of our knowledge is borne out by the success of our predictions,

How can you tell if your predictions have been successful rather than unsuccessful if you reject induction?

rather than resting solely on antecedent evidence. Therefore, it is not necessary to rely on induction to make generalisations about the world.

Really? Then how DO you make generalizations about the world?

AshRyan: “In other words, your argument is a classic example of the fallacy of the stolen concept. As soon as you denied induction (not to mention causality), you automatically lost the argument.

Since I haven’t based knowledge on induction, as above, then I haven’t stolen the concept.

So what have you based knowledge on?

[Fred Weiss]

I said that induction is a logically invalid procedure. That doesn’t invalidate knowledge of the external world, nor does it render the conclusions of deductive arguments invalid, merely more or less provisional.

Oh, but you have invalidated knowledge. If all you have is "provisional", what is that based on? If not knowledge, what? If it, too, is based on the provisional, you are in an infinite regress of guesses, never achieving knowledge.

You are in fact stealing the concept of "knowledge", using it while at the same time denying it. The concepts "guess", "provisional", "conjecture" presuppose the concept of "knowledge" and they are meaningless and baseless without it.

Incidentally, you have no way of judging when a view is "more or less" provisional, again without assuming the very knowledge you are denying is possible.

I highly recommend a book by D.C. Stove, which is available online and which demolishes the Karl Popper view you are espousing:

http://tinylink.com/?XGz2PMvN0X

Fred Weiss

[Eddie]

Betsy: “Predication is identity. When you say "Mary is a parent," you are saying something about the identity of Mary. (You are not saying everything about the identity of Mary and that is why it is not an equality. A thing is all its qualities and not just some of them.)”

The identity principle can be summarised as “a thing is identical to itself”. In that case, “London is the capital of England” qualifies as a statement of identity, because London is equivalent to the capital of England. It is also meaningful to say that the capital of England is London. But ‘Mary’ is not equivalent to ‘parent’, while “ A parent is Mary” doesn’t make much sense. So the statement “Mary is a parent” is not a matter of identity.

Betsy: "Knowledge of the external world?" Where did you get THAT from -- if "induction is a logically invalid procedure."

Perhaps I should recap. As I understand it, the problem of induction concerns the justification for the logical validity of induction. It doesn’t deny that we do as a matter of fact practice induction. (My wording in my previous post was rather careless on this point.) We could not function in the absence of inductive generalisations, and most of the time we act on those generalisations with a fair degree of success. Sometimes, as with the colour of swans, our previous expectations are confounded, but that’s part of the learning process.

So the issue is not an empirical one, and objections based on empirical considerations miss the point of the problem. In science a process of conjecture and refutation doesn’t seek to justify the logical status of induction. Rather, it seeks to test the predictive success of a generalisation.

In the ordinary course of our daily lives we don’t need to be as precise as scientists, since much of the “testing” has already been done, by our forebears, our parents and teachers and the wider society, and we spend a good deal of our formative years imbibing these “tried and true” generalisations.

E

[DavidOdden]

Perhaps I should recap. As I understand it, the problem of induction concerns the justification for the logical validity of induction. It doesn’t deny that we do as a matter of fact practice induction.

.....

So the issue is not an empirical one, and objections based on empirical considerations miss the point of the problem. In science a process of conjecture and refutation doesn’t seek to justify the logical status of induction. Rather, it seeks to test the predictive success of a generalisation. 

If you were to explain exactly what you mean by "logical validity", I think you would discover that what you're thinking of is a stipulated circularity. Induction is a valid form of reasoning (and logic is the method of reasoning). I understand that isn't what you mean by "logically valid", but once you say exactly what you do mean, you'll probably discover that by "logically valid", you mean so-called deductive derivations. But that stipulates that inductive generalization is not "logically valid": deduction is simply logic minus induction, so the conclusion that induction is not "logically valid" is a classical example of question begging. Empirical considerations are valid in this argument, except insofar as you try to define a system of logic that precludes using facts.

So in fact the "problem of induction" is, simply, that there is no problem.

[Spearmint]

Eddie: Induction is axiomatic in the same sense that the axioms of identity/non-contradiction/consciousness are - ie you cannot 'prove' it, only demonstrate it by highlighting how any attempt to deny it implicitly affirms it. It is impossible to deny induction without relying on it, since any attempt at human communication is automatically based on its validity. Consider this exchange:

Me: Induction is valid

You: Induction is invalid

Me: Thanks for agreeing with me; valid and invalid are synonyms - they mean the exact same thing

You: Of course they dont - they are opposite and mutually exclusive, any competant speaker of the English language knows this.

Me: No you are mistaken - the word 'invalid' does not mean what you think it does. How can you be sure of its meaning?

You: That is the way the word has always been used in my experience, besides we could appeal to a dictionary if you are not satisfied.

Me: But the fact that the word has always been used this way does not mean that it is still being used in this way now, since induction is invalid. The same applies to dictionaries - they have been considered authoritative in the past, but this says nothing about how they are considered now. Can you give me a logical justification of why that word means what you claim?

What recourse do you now have? To what standard can you now appeal in order to continue your argument?

All you (and Hume) are claiming is that induction is not deduction. Induction cannot be justified via deductive logic, because it has nothing to do with deduction - it is not somehow a 'weaker form' of deduction, it is an entirely seperate form of reasoning. Asking me to justify induction deductively is like me asking you to justify deduction inductively - the request is complete nonsense.

On a sidenote, what is your answer to the "problem of deduction", namely Carrol's Paradox? If your complaint is that inductive claims to knowledge aren't logically valid since induction itself cannot be verified, then surely deductive claims to knowledge are invalid for the same reason?

[Betsy]

Betsy: “Predication is identity. When you say "Mary is a parent," you are saying something about the identity of Mary. (You are not saying everything about the identity of Mary and that is why it is not an equality. A thing is all its qualities and not just some of them.)”

The identity principle can be summarised as “a thing is identical to itself”.

That is not the Objectivist view of identity which is what we are discussing, is it not? I dare you to find any place in anything Ayn Rand ever wrote where she speaks of "A=A" rather than "A is A" or states anything like “a thing is identical to itself” or says that identity means equivalence.

To say that "A is A" simply means that a thing is what it is or it has the characteristics it has. It is a thing equivalent to something OR it is a thing with a certain property or characteristic.

In that case, “London is the capital of England” qualifies as a statement of identity, because London is equivalent to the capital of England.

So does "London is in the UK."

Perhaps I should recap. As I understand it, the problem of induction concerns the justification for the logical validity of induction. It doesn’t deny that we do as a matter of fact practice induction. (My wording in my previous post was rather careless on this point.) We could not function in the absence of inductive generalisations, and most of the time we act on those generalisations with a fair degree of success. Sometimes, as with the colour of swans, our previous expectations are confounded, but that’s part of the learning process.

So the issue is not an empirical one, and objections based on empirical considerations miss the point of the problem. In science a process of conjecture and refutation doesn’t seek to justify the logical status of induction. Rather, it seeks to test the predictive success of a generalisation. 

But how can you ever say "This is a predictive success" or "This is NOT a predictive success?"

How do you seek to justify the logical status of your conclusions -- with certainty -- about the predictive success or failure of your generalization and what the scientific results really show?

In the ordinary course of our daily lives we don’t need to be as precise as scientists, since much of the “testing” has already been done, by our forebears, our parents and teachers and the wider society, and we spend a good deal of our formative years imbibing these “tried and true” generalisations.

Are you saying you don't really KNOW whether anything is true or not, but you are just taking your forebears, your parents and teachers, and the wider society ON FAITH?

[Fred Weiss]

... In science a process of conjecture and refutation doesn’t seek to justify the logical status of induction. Rather, it seeks to test the predictive success of a generalisation.

That's true, but that's only saying that science is not philosophy. Science doesn't have to - and shouldn't have to - justify logic. That's the job of philosophy.

But the question you raised, the same question raised by others down through the ages - by both scientists and philosophers - is whether science gives us knowledge, real knowledge, i.e. certainty, not just conjectures or guesses.

What constitutes scientific knowledge, i.e. when can we claim that we've achieved it, is a legitimate question. However asking whether we can achieve it at all is not. Evaluating the results of a test may be complicated, but without knowledge, you would have no way of knowing what tests to perform, why those tests rather than some others (and presumably there are an endless number of possible tests you could perform), and what were your results. Regardless of what you might not yet know and are seeking to know, unless you know something, you couldn't even begin, nor could you get anywhere.

Fred Weiss

[Capitalism Forever]

To clear up the confusion about "is" and "equals":

The verb "is" expresses predication; identity is a special case of predication. Examples:

"This car is red." -- predication; you specify one of the car's attributes (namely its color).

"My mother is a teacher." -- predication; you specify one of your mother's attributes (namely her occupation).

"This man is my father." -- identity; you state that the words "this man" and the words "my father" refer to the same person.

Looking at these examples, we can conclude that:

1) If the "is' is followed by an adjective ("... is red"), you have a statement of predication, as the adjective names one of the subject's attributes.

2) The same is true if the "is" is followed by an indefinite noun phrase ("... is a teacher"), because this works just like an adjective: by stating that a subject belongs to a certain group, you specify an attribute of the subject.

3) If the "is" is followed by a definite noun phrase ("... is my father"), we have a statement of identity. This is because by saying that the subject IS a specific thing, you are saying that they are the same thing.

(Incidentally, the above conclusions are a good illustration of inductive reasoning: you observe some examples, propose conclusions to be drawn based on the examples, and validate the conclusions by explaining why they must always be true.)

----

Equality is NOT expressed by merely using the word "is." Equality is expressed by using a phrase like "is equal to," "is equivalent to," "is interchangeable with," "is just as good as," "has the same value as," etc., or by using the = sign.

Equality means that two things evaluate to the same result according to some standard of evaluation. For example, in the statement

2 + 3 = 10 / 2

the = sign means that, in decimal arithmetic, the expression "2 + 3" evaluates to the same number as the expression "10 / 2." Obviously, the two expressions are not identical--one of them is a sum while the other is a quotient--only their values are identical.

As another example, a guy who was trying to persuade me to vote Libertarian once wrote to me this:

Republicans = Democrats = statists

By this, he didn't mean that the GOP and the Democrat party are the same entity. He meant that the Republicans are, in his view, just as statist as the Democrats. I could have replied to him by writing something like:

Libertarians = hippies = losers

[Eddie]

DavidOdden: “If you were to explain exactly what you mean by "logical validity", I think you would discover that what you're thinking of is a stipulated circularity. Induction is a valid form of reasoning …I understand that isn't what you mean by "logically valid", but once you say exactly what you do mean, you'll probably discover that by "logically valid", you mean so-called deductive derivations. But that stipulates that inductive generalization is not "logically valid"…”

In general, I agree. As I understand it, the problem of induction is that induction cannot be validated in the same way as deduction. I’m not saying that induction is invalid as a general form of reasoning, but that it’s a different type of reasoning to deduction, and validated empirically rather than logically.

DavidOdden: “Empirical considerations are valid in this argument, except insofar as you try to define a system of logic that precludes using facts.”

As with many philosophical issues, one of the difficulties of discussing this issue is one of terminology. Strictly speaking, those who deny the logical validity of inductive reasoning should use a term such “non-inductive inference”, but most people understand induction as generalising from observed particulars, so it’s easier to stay with the term.

I agree that empirical considerations are valid in this argument if they are applied to specific questions about events in the external world. But my comment was directed at attempts to validate induction by formal logic. Appealing to events in the external world will not achieve that validation, for reasons stated, ie question-begging.

E

[Eddie]

Spearmint: “But the fact that the word has always been used this way does not mean that it is still being used in this way now, since induction is invalid. The same applies to dictionaries - they have been considered authoritative in the past, but this says nothing about how they are considered now.”

I said that induction cannot be logically justified, but it can be empirically justified. In the case of dictionaries, their past authoritative status is a reasonable guide to their present performance, but if I want to achieve a substantial validation of their authority I cannot rest on their past performance, since performance varies over time.

What I can do is apply an empirical test, by asking myself: what is the function of dictionaries? Clearly, they are produced in order to present the agreed usage of words. I can test this by taking a set of representative words and comparing them across dictionaries. If there is substantial agreement, I can be confident in the authority of the dictionaries in question.

What I would not do is investigate the “nature” of dictionaries, since that will only tell me that dictionaries supply the agreed usage of words, and I already know that. Nor will that knowledge enable me to “logically” validate the reliability of dictionaries, nor enable me to empirically validate their reliability. Such a procedure is superfluous and a waste of time and energy.

Capitalist Forever: Thank you for clarifying this issue. Unfortunately, people do use “is” equivocally, as your example (3) demonstrates. And this can cause all sorts of confusions.

E

[Eddie]

Betsy: “That is not the Objectivist view of identity which is what we are discussing, is it not?”

As far as I am aware, we are discussing the philosophical notion of identity. If the Objectivist meaning is equivalent to (or “the same as”) the standard meaning, then we are discussing the same (or “identical”) subject. Otherwise, we are talking different meanings.

Betsy: So does "London is in the UK [qualify as a statement of identity]."

“In the UK” is only equivalent to “London” if you want to argue that London encompasses the whole of the UK. As far as I am aware, it does not.

Betsy: “But how can you ever say "This is a predictive success" or "This is NOT a predictive success?" How do you seek to justify the logical status of your conclusions -- with certainty -- about the predictive success or failure of your generalization and what the scientific results really show?”

I’m not seeking to justify the logical status of my conclusions, merely their empirical status. If I predict that Y will occur when I do X, and Y occurs, that is predictive success.

Betsy: “Are you saying you don't really KNOW whether anything is true or not, but you are just taking your forebears, your parents and teachers, and the wider society ON FAITH? ”

No, I’m not saying that. What I am saying is that those who have gone before us have survived and in many cases thrived, so they must be doing something right. That’s not a matter of faith, it’s a matter of fact. Of course this involves a certain amount of trust. Take an historical event: the Battle of Waterloo. I wasn’t present, how do I know this battle actually occurred? I know mainly through reading history books, which I can analyse for internal coherence and the like, but I must also trust that historians are in the main honest chroniclers of actual events.

E

[Eddie]

Fred: That's true [that science tests for predictive success], but that's only saying that science is not philosophy. Science doesn't have to - and shouldn't have to - justify logic. That's the job of philosophy.”

I agree, but what we’re talking about here is a justification for induction, which is an empirical matter, rather than logic, or at least formal logic. The principle of “predictive success” would, I think, qualify as a “meta” principle, and therefore come within the boundaries of philosophy.

Fred: “But the question you raised…is whether science gives us knowledge, real knowledge,i.e. certainty, not just conjectures or guesses. What constitutes scientific knowledge, i.e. when can we claim that we've achieved it, is a legitimate question. However asking whether we can achieve it at all is not.”

I’m not denying that we can achieve knowledge, but I don’t think all knowledge can be equated with certainty. “1+1=2” is regarded as indubitably certain, whereas some modern theories in physics are considered to be much less certain. When it comes to expressions of certainty, both scientific and general, they invariably tend to be hedged with some sort of qualification, akin to Rand’s “within the context of one’s current knowledge”. In the context of that qualification, certainty vs non-certainty devolves to a matter of semantics.

In other words, some will take the view that “contextual certainty” equates to plain “certainty”, while others will take the view that it allows for degrees of certainty. Unfortunately, appeal to real world examples doesn’t seem to settle the issue, since the supporters of plain certainty can always interpret “degrees of certainty” to mean “contextual certainty”, and vice versa.

It seems to me that this procedure is self-defeating. A more fruitful question would be to ask what it is that we are seeking when we seek certainty. The answer would presumably be that certainty is required in order that we can act with confidence that our knowledge will produce a desired outcome. But we live our lives in a state of uncertainty. When we wake in the morning, the statement “I will be alive this evening” is by no means certain, and yet we get out of bed and act as if that statement is a certainty.

So a degree of uncertainty is no bar to our acting successfully. It’s only at the boundaries – buying a house, changing jobs – that uncertainty can become paralysing, but even there, we eventually act in the face of uncertainty.

E

[DavidOdden]

As I understand it, the problem of induction is that induction cannot be validated in the same way as deduction. I’m not saying that induction is invalid as a general form of reasoning, but that it’s a different type of reasoning to deduction, and validated empirically rather than logically.

The point that you are missing is that deductive logic cannot be logically validated, in the unempirical fashion you have in mind. What constitutes "valid deductive logic" is determined by fiat (which is why there is a difference between Brouwerians and non-Brouwerians). Nothing in stipulative systems precludes a logic from including universal generalization as a valid rule of inferrence, just as nothing forces the Law of the Excluded Middle to be included.

[Betsy]

As I understand it, the problem of induction is that induction cannot be validated in the same way as deduction. I’m not saying that induction is invalid as a general form of reasoning, but that it’s a different type of reasoning to deduction, and validated empirically rather than logically.

Not quite. Induction is validated by a process that requires BOTH empirical observation AND deductive validation.

[Betsy]

Betsy: “That is not the Objectivist view of identity which is what we are discussing, is it not?”

As far as I am aware, we are discussing the philosophical notion of identity. If the Objectivist meaning is equivalent to (or “the same as”) the standard meaning, then we are discussing the same (or “identical”) subject. Otherwise, we are talking different meanings.

If you are claiming that the "standard meaning" of identity is equivalence, then it is most definitely NOT the same thing as what an Objectivist means.

Betsy: So does "London is in the UK [qualify as a statement of identity]."

“In the UK” is only equivalent to “London” if you want to argue that London encompasses the whole of the UK. As far as I am aware, it does not.

By the Objectivist meaning and use of the term, London does not encompasses the whole of the UK AND "London is in the UK" DOES qualify as a statement of identity.

Betsy: “But how can you ever say "This is a predictive success" or "This is NOT a predictive success?" How do you seek to justify the logical status of your conclusions -- with certainty -- about the predictive success or failure of your generalization and what the scientific results really show?"

I’m not seeking to justify the logical status of my conclusions, merely their empirical status.

If you deny identity, how can you ever justify their empirical status?

If I predict that Y will occur when I do X, and Y occurs, that is predictive success.

If you deny identity, how can you know whether or not Y occurred?

Betsy: “Are you saying you don't really KNOW whether anything is true or not, but you are just taking your forebears, your parents and teachers, and the wider society ON FAITH?  ”

No, I’m not saying that. What I am saying is that those who have gone before us have survived and in many cases thrived, so they must be doing something right. That’s not a matter of faith, it’s a matter of fact.

... or luck, or accident, or coincidence! How do you know?

Of course this involves a certain amount of trust.

Trust? Or is that just another way to say FAITH?

Take an historical event: the Battle of Waterloo. I wasn’t present, how do I know this battle actually occurred? I know mainly through reading history books, which I can analyse for internal coherence and the like, but I must also trust that historians are in the main honest chroniclers of actual events.

Actually, what it takes to know the battle occurred is inductive reasoning, which you deny as valid, on a level of abstraction several levels above the perceptual level, which I have never seen you attain.

[Spearmint]

David Odden:

Nothing in stipulative systems precludes a logic from including universal generalization as a valid rule of inferrence, just as nothing forces the Law of the Excluded Middle to be included.

Upon which point you would immediately be faced with the traditional 'problem' of induction, namely how many observations are required before a universal truth can be taken from a series of particulars, which was the original point being discussed.

[Betsy]

I’m not denying that we can achieve knowledge, but I don’t think all knowledge can be equated with certainty.

Actually, I doubt you think ANY knowledge can ever be certain. Correct me if I'm wrong, but isn't your position that NO inductive generalization is EVER valid?

“1+1=2” is regarded as indubitably certain, whereas some modern theories in physics are considered to be much less certain.

... with good reason. Some of those theories are dead wrong and others are still awaiting a proper causal explanation.

When it comes to expressions of certainty, both scientific and general, they invariably tend to be hedged with some sort of qualification, akin to Rand’s “within the context of one’s current knowledge”.

"Context" is not a "hedge." It is the definition of the PART of reality a concept, idea, statement, etc. applies to. When I say, "Things like this yellow citrus fruit are very sour," the context is lemons, not watermelon. Except for the axioms, every idea, statement, concept, and generalization applies to some parts of reality but not others, so specifying WHICH part is necessary.

In the context of that qualification, certainty vs non-certainty devolves to a matter of semantics.

... for those who are playing word games. For those of us who are investigating reality in order to find true and certain answers to our questions and problems, it devolves into exploring and analyzing things and their characteristics until we reach a point where we find an answer which reduces to an identity in the Objectivist sense.

In other words, some will take the view that “contextual certainty” equates to plain “certainty”,

It does.

while others will take the view that it allows for degrees of certainty.

Because it can lead to confusion, I never use the term "degree of certainty." Instead, I use "probability" which is what most people really mean when they say "degree of certainty."

Unfortunately, appeal to real world examples doesn’t seem to settle the issue, since the supporters of plain certainty can always interpret “degrees of certainty” to mean “contextual certainty”, and vice versa.

No. "Certainty" (except for axiomatic truths) always means the same thing as "contextual certainty" since all items of knowledge pertain to some PART of reality but not ALL parts of reality.

"Degrees of certainty," on the other hand, means something completely different. It means probability, NOT certainty.

It seems to me that this procedure is self-defeating. A more fruitful question would be to ask what it is that we are seeking when we seek certainty. The answer would presumably be that certainty is required in order that we can act with confidence that our knowledge will produce a desired outcome.

No, the answer is because living successfully, in fact, in reality, requires acting on ideas which are TRUE.

But we live our lives in a state of uncertainty.

SOME people do because they have so much to be uncertain about.

Others, like me, are constantly observing and thinking about reality until we know enough to BE certain -- and we live our lives in a state of certainty.

[Spearmint]

Betsy:

No. "Certainty" (except for axiomatic truths) always means the same thing as "contextual certainty" since all items of knowledge pertain to some PART of reality but not ALL parts of reality.

Forgive me for butting in here, but I think this is the main aspect of your disagreement. Would you not say that there is something approaching a 'contextless' degree of certainty about a truth such as "1 + 1 = 2", or "A is A"? If you are going to reply that these count as 'axiomatic', then I would suggest that you and Eddie are actually in agreement, but he is using the phrase 'logical truths' to describe what you refer to as 'axiomatic truths'. If you are claiming that axiomatic truths are 'more certain' than other truths (which is what I interpret you as saying here), then this would be almost equivalent to the standard claim that deductive truths are more certain than inductive ones, only with slightly different terminology. Hume used the phrase "relations of ideas" to describe your 'axomatic truths', but I'm starting to suspect that the labelling is the only major difference.

[Betsy]

Forgive me for butting in here, but I think this is the main aspect of your disagreement. Would you not say that there is something approaching a 'contextless' degree of certainty about a truth such as "1 + 1 = 2"

Not in that case. "1 + 1 = 2" can only be applied to PART of reality, i.e., things which exist in discrete, similar, countable units. Thus 1 apple plus 1 apple equals 2 apples, but what applies to apples doesn't apply to "justice" or "happiness."

or "A is A"?

This is axiomatic. As a result, far from being "contexLESS," it is OMNI-contextual. It applies to ALL and to EVERY part of reality.

If you are going to reply that these count as 'axiomatic', then I would suggest that you and Eddie are actually in agreement, but he is using the phrase 'logical truths' to describe what you refer to as 'axiomatic truths'.

I realize that. I just wonder where Eddie gets his "logical truths" from. I get my axioms from observing reality -- every little bit and all of it.

If you are claiming that axiomatic truths are 'more certain' than other truths (which is what I interpret you as saying here), then this would be almost equivalent to the standard claim that deductive truths are more certain than inductive ones, only with slightly different terminology. Hume used the phrase "relations of ideas"  to describe your 'axomatic truths', but I'm starting to suspect that the labelling is the only major difference.

I am claiming that any assessment of truth ought to be based on observation of reality, which we can know by means of our senses, and that any, every, and all observations implicitly rest on an inescapable fact of reality: that everything that is, is what it is.

[DavidOdden]

Upon which point you would immediately be faced with the traditional 'problem' of induction, namely how many observations are required before a universal truth can be taken from a series of particulars, which was the original point being discussed.

That would depend on the relevant facts, so there isn't a universal number like "100". A single observation suffices, if the conclusion non-contradictorily integrates with all knowledge. So as I say, what's the problem?

[Spearmint]

Not in that case.  "1 + 1 = 2" can only be applied to PART of reality, i.e., things which exist in discrete, similar, countable units.  Thus 1 apple plus 1 apple equals 2 apples, but what applies to apples doesn't apply to "justice" or "happiness."

Not really - "1 + 1 = 2" applies to relations of concepts, ie our concepts of number. Saying "1 + 1 = 2" isnt the same as saying 1 apple added to 1 apple gives 2 apples - theres a difference between grasping the truth of "1 + 1 = 2" in an abstract sense, and applying it to a material part of reality. In some cases adding 1 object to another object doesnt give 2 objects, for example adding a sugar cube to a cup of water, but this doesnt alter the fact that "1 + 1 = 2", always and forver.

I realize that. I just wonder where Eddie gets his "logical truths" from. I get my axioms from observing reality -- every little bit and all of it.

I assume he means relative to a set of axioms. The premises of a deductive argument are (generally) obtained via induction, and then the consequences follow via deduction.

[Eddie]

DavidOdden: “The point that you are missing is that deductive logic cannot be logically validated, in the unempirical fashion you have in mind.” What constitutes "valid deductive logic" is determined by fiat (which is why there is a difference between Brouwerians and non-Brouwerians). Nothing in stipulative systems precludes a logic from including universal generalization as a valid rule of inferrence, just as nothing forces the Law of the Excluded Middle to be included.”

As I understand it, logical validity relates to the form of an argument, and providing a deductive argument follows the correct form, it is valid, so there’s no need for an appeal to empirical truths to establish validity. An example would be: All mice are black; all black things are blind; therefore all mice are blind. But inductive arguments do not follow this form, and are therefore in that sense logically invalid, but can be justified empirically.

E

[Eddie]

Betsy: “By the Objectivist meaning and use of the term, London does not encompasses the whole of the UK AND "London is in the UK" DOES qualify as a statement of identity.”

In that case, we are talking at cross-purposes.

Betsy: “If you deny identity, how can you ever justify their [conclusions] empirical status?”

I haven’t denied the notion of identity, nor that a thing is what it is. Empirical conclusions are justified, well, empirically, that is, by observation.

Betsy: “... or luck, or accident, or coincidence! How do you know?”

This comment relates to my view that the survival of the human race to date indicates that our forebears were not totally wrong about what is needed to survive and thrive. The short answer is that as any gambler knows to his regret, luck, accidents and coincidence do not persist over the long term, and we’re talking a very long term here.

I’m not saying we should take everything on trust. As for my knowing anything, I know in the standard way, by observation and reasoning. But the world’s a big place, and nobody can have first-hand knowledge of everything, so much of our knowledge is a matter of trust. When I want to cook a meal, I consult a cookbook. I don’t spend a lot of time learning about the physics of cooking or practices of animal husbandry and agriculture. I trust that the cookbook has taken these factors into account, and my judgement of its worth depends on the result.

Betsy: “Actually, what it takes to know the battle occurred is inductive reasoning, which you deny as valid, on a level of abstraction several levels above the perceptual level, which I have never seen you attain.”

You would need to indicate which real-world observations lead you to the conclusion that the Battle of Waterloo actually occurred. Texts, of course, do not constitute real world observations.

Betsy: “Actually, I doubt you think ANY knowledge can ever be certain. Correct me if I'm wrong, but isn't your position that NO inductive generalization is EVER valid?”

No. I said induction cannot be logically validated, but inductive generalizations can be empirically justified.

Betsy: "Context" is not a "hedge." It is the definition of the PART of reality a concept, idea, statement, etc. applies to. When I say, "Things like this yellow citrus fruit are very sour," the context is lemons, not watermelon.”

Since a claim that is contextually certain can in fact turn out to be mistaken, “contextually certain” in effect boils down to probability, so the distinction is just a matter of semantics. One might then ask what is the purpose of adopting a phrase such as contextual certainty rather than probability, and in my view it simply adds a veneer of certainty where none exists. And if ‘contextual certainty’ does equate to ‘certainty’, as you claim, why not, in the interests of economy, just drop the ‘contextual’?

E

[DavidOdden]

As I understand it, logical validity relates to the form of an argument, and providing a deductive argument follows the correct form, it is valid, so there’s no need for an appeal to empirical truths to establish validity. An example would be: All mice are black; all black things are blind; therefore all mice are blind. But inductive arguments do not follow this form, and are therefore in that sense logically invalid, but can be justified empirically.

Yes and no. That is, "valid" is defined in terms of formal properties in a derivation, but what these properties are, are not given a priori. Within the realm of "deductive" logics, some derivations are valid in some systems, but not in other systems (hence certain proofs that are valid under garden variety predicate logic as they teach in Logic 101 are not valid for Brouwerians, namely the ones that depend on (AV^A). Inductive generalization is a rule of inference in some logics (esp. nonmonotonic logics) and thus in the sense you are using "valid", induction is valid. The syntactic concept of "valid" that you're thinking of does extend to normal reasoning. When I pointed out to you a short while ago that your notion of validity being restricted to "pure deduction" is circular, this is what I was referring to. From a formal POV, "deduction" simply refers to a specific set of rules of inference or axioms that convey properties about "ands" and "ors" and quantifiers, plus metarules pertaining to allowed and disallowed assumptions. But it is a completely arbitrary stipulation to allow a derivation that asserts a false premise, and disallows the rule of inductive generalization. It is just as natural -- no, more natural -- to requre that all derivations must be founded on true premises -- not false ones, and not arbitrary ones. In fact, that is a fundamental statement of logic in Objectivism: conclusions must be derived by applying logic to true statements -- to knowledge -- and not to false statements or arbitrary statements which are neither true nor false. This delimts what is a valid derivation -- your mouse example is invalid, because not all mice are black nor are all black things blind. So while I'm aware of the existence of types of formal logic that would label such a derivation "valid" and I grant you that this is the most common construal of the concept in academic studies on logic, it is not how ordinary logic works and is also is not the only variety of academic logic on the market. I'm also aware of (and practise) a different formal logic where such a derivation is invalid; and where inductive generalization is a rule of inference, so inductively based proofs are perfectly valid.

In fact, they are pretty much the core of what a valid derivation is about. Setting aside the fact that all mice aren't black, you cannot stipulate that statement ex nihilo -- it is not axiomatically true. You cannot arbitrarily introduce an untrue statement and derive anything valid. So you would first have to prove the universally quantified claim, which has to be done inductively.

[DavidOdden]

Since a claim that is contextually certain can in fact turn out to be mistaken, “contextually certain” in effect boils down to probability, so the distinction is just a matter of semantics.  One might then ask what is the purpose of adopting a phrase such as contextual certainty rather than probability, and in my view it simply adds a veneer of certainty where none exists. And if ‘contextual certainty’ does equate to ‘certainty’, as you claim, why not, in the interests of economy, just drop the ‘contextual’?

The expression "contextual certainty" is redundant: simply saying "certainty" suffices because the basis of certainty (knowledge) is always contextual (nobody is omniscient: we all have specific knowledge. In addition, statements are true of specific things). The difference between probability and certainty regards a crucial difference in knowledge. If a conclusion is merely "probable", that means that there is a lot of evidence for accepting the conclusion, but there is still some fact that casts doubt on the conclusion. Once you have dealt with that fact that seemed to cast doubt -- and therefore there remains no doubt -- then you are certain. "Certain" and "probable" are related, but they are not the same.