Income Taxes (Narrative) (Details) - USD ($) $ in Millions	3 Months Ended	12 Months Ended
	Dec. 31, 2017	Sep. 30, 2019	Sep. 30, 2018	Sep. 30, 2017	Sep. 30, 2016
Income Taxes [Line Items]
U.S. federal statutory tax rate	35.00%	21.00%	24.50%	35.00%
Discrete net tax expense related to Tax Act		$ 43.8	$ 180.6
Reversal of non-recurring benefit related to U.S. taxation of deemed foreign dividends		56.2
Tax benefit related to finalization of assessment of impacts of Tax Act		12.4
Reduction in equity affiliate income for impacts of the Tax Act			28.5
Provisional tax expense for deemed repatriation tax and additional foreign taxes on repatriation of earnings			392.4
Provisional tax expense for deemed repatriation tax			322.1
Provisional tax expense for additional foreign taxes on repatriation of earnings			70.3
Provisional tax benefit for re-measurement of net U.S. deferred tax liabilities at lower corporate tax rate			211.8
Non-recurring benefit related to U.S. taxation of deemed foreign dividends			56.2
Deemed repatriation tax obligation after application of foreign tax credits		$ 256.8
Period of payment on deemed repatriation tax obligation (in years)		7 years
Deemed repatriation tax obligation in noncurrent liabilities		$ 215.4	184.4
Cash paid for taxes (net of cash refunds)		324.3	372.0	$ 1,348.8
Excess tax benefits from share-based compensation		14.6	21.5	17.6
Tax benefit from restructuring of foreign subsidiaries			(35.7)
Income tax benefit on tax losses from foreign holding company				(111.4)
Goodwill impairment charge				145.3
Goodwill impairment charge deductible for tax purposes				0.0
Deferred tax assets, valuation allowance		92.1	105.0
Tax expense for deemed repatriation tax		373.2
Previously undistributed earnings of foreign subsidiaries and corporate joint ventures		5,800.0
Cumulative undistributed earnings		4,200.0
U.S. Income and foreign withholding taxes estimate		359.6
Unrecognized tax benefits		231.7	233.6	146.4	$ 90.2
Unrecognized tax benefits that would impact effective tax rate		75.0	88.6
Interest and penalties related to unrecognized tax benefits		12.0	(2.4)	3.7
Accrued interest and penalties		19.5	8.4
Additions for tax positions of prior years		14.2	119.2	16.1
Additions for tax positions of the current year		7.8	26.4	47.5
Final audit settlement related to unrecognized tax benefits			43.1
Discontinued Operations, Held-for-sale or Disposed of by Sale | Performance Materials Division (PMD)
Income Taxes [Line Items]
Gain on sale				$ 2,870.0
Foreign Loss Carryforwards
Income Taxes [Line Items]
Deferred tax assets, valuation allowance		42.8
Foreign Capital Losses
Income Taxes [Line Items]
Deferred tax assets, valuation allowance		44.6
Discontinued Operations
Income Taxes [Line Items]
Tax benefit related to settlement and release of reserves			25.6
Continuing Operations
Income Taxes [Line Items]
Tax benefit related to settlement and release of reserves			$ 9.1
U.S. Federal
Income Taxes [Line Items]
Tax credit carryforwards		13.3
Foreign
Income Taxes [Line Items]
Tax credit carryforwards		20.8
Indefinite tax credit carryforwards		5.8
Operating loss carryforwards		352.6
Operating loss carryforwards not subject to expiration		$ 148.9