Other Intangible Assets and Goodwill (Finite-Lived Intangible Assets) (Details) - USD ($) $ in Millions	Jul. 02, 2023	Oct. 02, 2022
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	$ 1,161.5	$ 1,182.1
Accumulated amortization	(1,116.2)	(1,123.7)
Total estimated future amortization expense	45.3	58.4
Acquired and reacquired rights
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	966.5	990.0
Accumulated amortization	(966.5)	(990.0)
Total estimated future amortization expense	0.0	0.0
Acquired trade secrets and processes
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	27.6	27.6
Accumulated amortization	(27.6)	(27.3)
Total estimated future amortization expense	0.0	0.3
Trade names, trademarks and patents
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	130.2	124.6
Accumulated amortization	(87.2)	(69.6)
Total estimated future amortization expense	43.0	55.0
Licensing agreements
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	16.9	19.3
Accumulated amortization	(14.6)	(16.2)
Total estimated future amortization expense	2.3	3.1
Other finite-lived intangible assets
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	20.3	20.6
Accumulated amortization	(20.3)	(20.6)
Total estimated future amortization expense	$ 0.0	$ 0.0