Skip to content
Carmelics
Topics
Thinkers
Changes
Contributors
Loading account…
Statements
321,452
Perspectives
108,905
Topics
42
Home
/
Original
/
inverse
See Original
Inverse View
It is not the case that A 'lawless' sequence is by definition not constructible through any specifiable procedure, making it mathematically unintelligible on constructivist grounds.
?
Set your confidence on the premises below to see your aggregate.
Reasons For
1 perspective
Reason for
?
1.
Lawless sequences are definable via quantification over infinite choice functions, which constructivism permits as valid mathematical objects.
?
How convincing is this?
Think about whether this reason is strong or weak
2.
Unintelligibility and non-constructibility are distinct: classical mathematics understands uncountable sets without constructive procedures.
?
How convincing is this?
Think about whether this reason is strong or weak
3.
Constructivism itself must countenance infinitary objects (like the continuum); lawless sequences fit naturally within this framework.
?
How convincing is this?
Think about whether this reason is strong or weak
Reasons Against
1 perspective
Reason against
?
1.
Constructivism requires all mathematical objects to be built from explicit operations; lawless sequences lack any constructive specification.
?
How convincing is this?
Think about whether this reason is strong or weak
2.
If a sequence cannot be algorithmically generated or described finitely, it cannot be known or verified by any mathematical agent.
?
How convincing is this?
Think about whether this reason is strong or weak
3.
Mathematical intelligibility requires that objects be surveyable through proof; lawless sequences resist all such demonstrations.
?
How convincing is this?
Think about whether this reason is strong or weak
Next step
Based on where you are in your exploration
Strongest counterpoint
Explore the most compelling reason on the other side.