more on this theme     |     more from this text

Single Idea 17730

[filed under theme 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite ]

Full Idea

We might arrive to the concept of infinity by composing concepts of negation and finiteness.

Gist of Idea

Combining the concepts of negation and finiteness gives the concept of infinity

Source

Carrie Jenkins (Grounding Concepts [2008], 5.3)

Book Ref

Jenkins,Carrie: 'Grounding Concepts' [OUP 2008], p.166

A Reaction

Presumably lots of concepts can be arrived at by negating prior concepts (such as not-wet, not-tall, not-loud, not-straight). So not-infinite is perfectly plausible, and is a far better account than some a priori intuition of pure infinity. Love it.

The 17 ideas from Carrie Jenkins

17719 Arithmetic concepts are indispensable because they accurately map the world [Jenkins]
17718 Grounded concepts are trustworthy maps of the world [Jenkins]
17717 Senses produce concepts that map the world, and arithmetic is known through these concepts [Jenkins]
17720 There's essential, modal, explanatory, conceptual, metaphysical and constitutive dependence [Jenkins, by PG]
17723 Knowledge is true belief which can be explained just by citing the proposition believed [Jenkins]
17725 'Analytic' can be conceptual, or by meaning, or predicate inclusion, or definition... [Jenkins]
17724 It is not easy to show that Hume's Principle is analytic or definitive in the required sense [Jenkins]
17727 We can learn about the world by studying the grounding of our concepts [Jenkins]
17726 Examining accurate, justified or grounded concepts brings understanding of the world [Jenkins]
17728 The concepts we have to use for categorising are ones which map the real world well [Jenkins]
17729 Examining concepts can recover information obtained through the senses [Jenkins]
17730 Combining the concepts of negation and finiteness gives the concept of infinity [Jenkins]
17731 Verificationism is better if it says meaningfulness needs concepts grounded in the senses [Jenkins]
17732 Success semantics explains representation in terms of success in action [Jenkins]
17734 It is not enough that intuition be reliable - we need to know why it is reliable [Jenkins]
17739 The physical effect of world on brain explains the concepts we possess [Jenkins]
17740 Instead of correspondence of proposition to fact, look at correspondence of its parts [Jenkins]