The green hypothesis is simple and the grue hypothesis is complex.
I simply consider the proposition, attempt to imagine its falsity, and notice that I am immediately involved in a contradiction or some similar incoherence. We are rather concerned with knowledge of unobserved matters of fact. Yet it is in the short run that inductive practice actually occurs and where it really needs justification BonJour Okasha suggests that the Bayesian model of belief-updating is an illustration how induction can be characterized in a rule-free way, but this is problematic, since in this model all inductive inferences still share the common rule of Bayesian conditionalisation.
The first example is clearly inductive, and insofar as it refers to real world objects, it depends on the uniformity of nature.
For induction to be rationally justified, it is not enough that i-arguments are reliable. The first example is clearly inductive, and insofar as it refers to real world objects, it depends on the uniformity of nature.
The most dramatic way to put the point is to say that Hume has shown that common sense and science are matters of faith. The question though is what precisely the something is. An alternative approach inspired by Carnap defines a natural kind to be a set whose members are more similar to each other than each non-member is to at least one member.
So, by the principle of parsimony, which says that we should choose the simpler hypothesis, other things being equal fit with past observations in this case. In a second argument, Hume claims that "It is only after a long course of uniform experiments in any kind that we attain a firm reliance and security with regard to a particular event.
The "new" problem of induction is, since all emeralds we have ever seen are both green and grue, why do we suppose that after time t we will find green but not grue emeralds. Hume himself seems to have thought along these lines. In that case it is theory which first determines what can be observed.
Atomic sentences must be logically independent of each other. Observations are very often the spur to theory formation, as the old inductive method emphasized. Hypothetico-deductivism is the view that theories are hypothesized under no constraints.
Hume does not pretend to know how we came to accept the principle. In the same category, moreover, we find the fundamental hypotheses of the theory of relativity, which theory has led to an unexpected expansion and broadening of the field theory, and to the superseding of the foundations of classical mechanics.
The consequence then is that it is not so important, at least for science, if those inferences would lack a rational foundation. But how, then, can we justify this principle of the uniformity of nature. Shall he cast his net. Try driving a car without making any inductive predictions — How would you point the steering wheel?.
Problem of induction, problem of justifying the inductive inference from the observed to the unobserved. It was given its classic formulation by the Scottish philosopher David Hume (–76), who noted that all such inferences rely, directly or indirectly, on the rationally unfounded premise that the future will resemble the past.
The Problem of Induction. You are hungry and you are about the bite into a hot crusty baguette. But a ‘friend’ stops you and says "Don’t do it. Hume’s Problem of Induction 1.
We naturally reason inductively: We use experience (or evidence from the senses) to ground beliefs we have about things we haven’t observed. Thus, for Goodman, the problem of induction dissolves into the same problem as justifying a deductive system and while, according to Goodman, Hume was on the right track with habits of mind, the problem is more complex than Hume realized.
The New Riddle of Induction. Open Court Publishing. Mar 21, · The problem of meeting this challenge, while evading Hume’s argument against the possibility of doing so, has become known as “the problem of induction”.
Hume’s argument is one of the most famous in philosophy. The "problem of induction" arises when we ask whether this form of reasoning can lead to apodeictic or "metaphysical" certainty about knowledge, as the Scholastics thought.
Thomas Aquinas especially thought that certain knowledge can be built upon first principles, axioms.The problem of induction