He did not deny it. He defined it and recognised its limitations.
He rightly asserted that empiricism was inductive, and that induction was really about the probability of reoccurrence through constant conjunction, rather than reliant on an assumption of a priori thinking.

Essay question, right? That is an inductive inference based on (1) having seen many such questions and (2) the fact that it is a very well-written question. However, it could be an original question by a philosophy novice with real insight into the problems cast by Hume. There is no logical means to decide.

Anyway, Hume is regarded as empiricist because he believes that all knowledge begins with experience, and so rejects the notion that there are innate ideas as accepted by philosophical rationalists. However his questioning of the validity of inductive proofs poses a challenge for empiricism, because it means that many of the claims that common sense will take for granted, such as that of ‘the sun rising tomorrow’, have no strictly rational warrant. In fact I think the sceptical implications of Hume’s ideas are reflected by the acceptance of the provisional nature of scientific hypotheses. They’re not regarded as immutable truths, but as working approximations, which however might be subject to revision or even abandonment by the new information. I think for that reason his contribution to modern philosophy has been highly influential.

Thank you both. I am a newbie with an interest in the epistemological development of science. I apologise if this was a bit of a stock question.

So his empiricism rests on his taking experience as the starting point for knowledge instead of basing it on innate ideas or a priori thinking.

If induction is not based on a rational principle then how does one go from a constant conjunction to an assertion of probability?

So his empiricism rests on his taking experience as the starting point for knowledge instead of basing it on innate ideas or a priori thinking. — Perplexed

Yes. Empiricism is about what the world demonstrates and not what principles you hold about it.

If induction is not based on a rational principle then how does one go from a constant conjunction to an assertion of probability?

It's basically repetition; then formulate an hypothesis about what it happening, and see if it sticks. Experimenting to demonstrate the hypothesis' value would be the next step. All inductive knowledge is therefore contingent on replicability and repetition.

In fact I think the sceptical implications of Hume’s ideas are reflected by the acceptance of the provisional nature of scientific hypotheses — Wayfarer

This is of key importance. And is something that science is apt to forget at crucial times. Paradigms tend to get established and hard to shift.
Thomas Kuhn's work has been very influential on this question.
The Structure of Scientific Revolutions

Thank you. I have heard of that book. I'll add it to my reading list.

The difficulty is that if inductive knowledge is purely contingent on repetition then it isn't really true knowledge because no matter how many times we do the experiment it could always fail the following time. This seems to make our claims of knowledge groundless and any assertions of probability merely cumulative of previous experiences and hence subjective or psychological.

True. But nonetheless the findings of science are reliable, and the deeper science is able to describe what seems to be going on the more reliable are the laws that it devises. Alongside all this reliability is the idea that the laws are only as good as their repeated performance and descriptive power.

Undoubtedly it works but as a theory of knowledge it seems to take us into the realm of what I suppose you would call pragmatism or utilitarianism. To say it's true because it works seems unsatisfactory.
Hume new this which is why I wonder if he had a rationalist streak to his epistemology, despite being empirical by method.

To say it's true because it works seems unsatisfactory. — Perplexed

That is all we have.
Deduction can only say it is true because we say it is!!! Deduction is basically playing with definitions; nothing more.

That is all we have. — charleton

That's not true. We also have abduction (leaving aside deduction atm).

Deduction is useful in metaphysics, mathematics and in foreseeing empirical consequences of scientific theories that can be tested in the future. Deduction is also useful because it helps generate coherence and understanding.

Induction means taking a finite sample size, and based on that sample size drawing the probable conclusion that some property that is common to all members of the sample will also be common to all (or most) members of the population. For example, we look at 500 swans, they're all white, so we conclude that most likely all swans are white. Induction allows us to classify things by common features.

Abduction means that we take a list of properties (for example white, long neck, beak, bird) and we associate them with a common name - swan. Then if we see something else which has those properties, we say that it most likely is also a swan. Abduction is the process by which we try to find the best explanation for something.

Induction and abduction don't provide certainty, and deduction cannot tell us something that doesn't already inhere in what we know. So deduction merely clarifies. Induction and especially abduction is what brings new knowledge in.

Deduction is useful when we talk about, for example, God. Because we all have experiences of God and divinity, it's just about clarifying it, and bringing it into focus. *waits for charleton to throw a fit* :D

This seems to make our claims of knowledge groundless and any assertions of probability merely cumulative of previous experiences and hence subjective or psychological. — Perplexed

The universe is inherently probabilistic.. What we observe or measure are approximations. Everything is continuously changing. Knowledge might be viewed as a recognition of patterns that are always subject to change, some changes more likely than others, especially when it comes to the behavior of life forms since life forms are able to make choices and willfully change direction.

Abduction means that we take a list of properties (for example white, long neck, beak, bird) and we associate them with a common name - swan. — Agustino

Sub-category of deduction.

The universe is inherently probabilistic. — Rich

Don't buy into this free will clap trap, as this flies in the face of the massive advances in science of the last 250 years which assert determinism.
Determinism is what makes the universe predictable, and everything we have gaind in understanding has been based on deterministic principles.

Don't buy into this free will clap trap, as this flies in the face of the massive advances in science of the last 250 years which assert determinism. — charleton

It is impossible to find evidence for determinism in science, though some still hold out some hope.

Very simply put, the universe is inherently probabilistic. Period. Hume simply observed this. Quantum Mechanics verified it. Actually, Heraclitus noticed this thousands of years ago.

Actually, Heraclitus noticed this thousands of years ago. — Rich

No doubt building on the lead of the cave man who grunted, "Maybe food will come this way."

No doubt building on the lead of the cave man who grunted, "Maybe food will come this way." — tim wood

No. Just a good observer like many if the ancients whose lives depended upon astute and practical observations. Hume, merely reiterated was is quite obvious to most people who obseve life as it is actually experienced.

Talk of probabilities rather misses Hume's point.

What are the chances that the future will be like the past? Well the future has always been like the past in the past, so if the future is anything like the past, chances are it will be like the past.

One has to assume the conclusion even to reach a probable result.

What are the chances that the future will be like the past? — unenlightened

Zero. Refer to Heraclitus. Something is always different. However, similarities are sufficient for practical purposes in many (most?) circumstances for all practical purposes (FAPP).

chances are it will be like the past — unenlightened

I prefer "similar to the past" FAPP.

One only needs to observe and form a pattern of recognition of what is actually transpiring. There is no leap of imagination to some conclusion.

I like 'like'. I don't prefer 'similar'. Less picking of nits, more thinking about the arguments. The leap is that the pattern continues into the invisible future.

I find it odd that folks are quite happy with 'you can't get an ought from an is', but balk at 'you can't get a will be from a has been.'

Well, in a loose sense, he's making generalizations from observations, and so he is an empiricist.

His arguments regarding causality are sort of different from whether or not he counts as an empiricist. And he builds to them in the first section of A Treatise of Human Nature -- it's not as if he opens with "all inductive inference is invalid!" (or, really, that he concludes that, either). He comes to some queer (to common sense thinking, something he even acknowledges) conclusions, but they are worth reading if you're interested.

Perhaps it's worth noting that inductive arguments are invalid by definition. Validity is defined as the conclusion following from the premises, which would make for a deductive argument.

The leap is that the pattern continues into the invisible future. — unenlightened

It is not a leap. It is brought about by habitual recognition. There are tons of patterns out there, most are of be practical use for practical purposes or are simply not recognized. Perceiving, understanding, and utilizing, and creating new habitual patterns in nature is fundamental because that is precisely what humans (intelligence) do. It is evolution. Babies begin with the process the first time they are fed.

premises, which would make for a deductive argument. — Michael

All premises are inductive, which pretty much invalidates all deductive logic. I actually agree. Everything is subject to change.

It is not a leap. It is brought about by habitual recognition. — Rich

Indeed, habit, as Hume himself says; but it is a leap that reason cannot justify. One might say, by way of analogy, that passion is the boss, habit is the worker, and reason keeps the accounts.

leap that reason cannot justify — unenlightened

Reason would suggest that this exactly what one should recognize. It is definitely keeping accounts of what one is observing.

Talk of probabilities rather misses Hume's point.

What are the chances that the future will be like the past? Well the future has always been like the past in the past, so if the future is anything like the past, chances are it will be like the past.

One has to assume the conclusion even to reach a probable result. — unenlightened

So if we had to make a bet, which option would it be wise or rational to bet on? That the future is like the past, or that it will be different? And why?

So if we had to make a bet, which option would it be wise or rational to bet on? That the future is like the past, or that it will be different? And why? — Agustino

We do have to make a bet, and we do bet that things will go on as before. And it would be unwise to do otherwise. But rationally there is no reason to do so; except that there is nothing else to go by.

We do have to make a bet, and we do bet that things will go on as before. And it would be unwise to do otherwise. — unenlightened

When you say that it would be unwise, don't you really mean that it would be irrational? It would go against our reason? I mean certainly if you saw someone making the opposite bet, you'd say they have lost their mind wouldn't you?

But rationally there is no reason to do so; except that there is nothing else to go by. — unenlightened

I think what you really mean is that there is no necessity that the future will be like the past. Sure, in that way, induction cannot be justified through deduction if that's what you were intending to do. However, you must concede that it is overwhelmingly more likely, given the evidence, that the future will be like the past. We have a lot of data points indicating this trend. There is no necessity that the trend will continue, but we have no reason to doubt that it will. Therefore it is irrational to doubt it in the absence of a reason.

However, you must concede that it is overwhelmingly more likely, given the evidence, that the future will be like the past. — Agustino

No, I don't have to. You have to provide some evidence or argument that does not assume what it seeks to prove.

No, I don't have to. You have to provide some evidence or argument that does not assume what it seeks to prove. — unenlightened

So when you have a trend that seems to indicate something, do you bet that the next data point will be different or the same as the trend? You have reason to presume that the next data point will be X (since that's what the trend indicates) and no reason to presume it would be anything else.