Question: Which English philosopher did Henry Seymour believe authored plays under the pseudonym of William Shakespeare?

Context paragraphs:
Henry Seymour, Lord Beauchamp: Henry Seymour, Lord Beauchamp (c. 1626 – 14 March 1654) was an English nobleman, third son of William Seymour, 2nd Duke of Somerset.

Baconian theory of Shakespeare authorship: The Baconian theory of Shakespearean authorship holds that Sir Francis Bacon, philosopher, essayist and scientist, wrote the plays which were publicly attributed to William Shakespeare.  Various explanations are offered for this alleged subterfuge, most commonly that Bacon's rise to high office might have been hindered were it to become known that he wrote plays for the public stage.  Thus the plays were credited to Shakespeare, who was merely a front to shield the identity of Bacon.

Lord Henry Seymour (naval commander): Lord Henry Seymour was a younger son of Edward Seymour, 1st Duke of Somerset by his second wife Anne Stanhope.  Aboard HMS "Rainbow" he commanded the 'Narrow Seas' Squadron of ships that took part in the Battle of Gravelines against the Spanish Armada in 1588.  Controlling the seas off Dunkirk they joined the main British fleet (the 'Western Squadron') near Calais on 6 August, adding about a third to the total size.

English ship Rainbow (1586): Rainbow was a galleon of the English Tudor navy, built at Deptford Dockyard by Peter Pett (the first of that name in this extensive family), and launched in 1586.  Commanded by Lord Henry Seymour, a younger son of Edward Seymour, 1st Duke of Somerset by his second wife Anne Stanhope, she fought against the Spanish during the Singeing the King of Spain's Beard and the Spanish Armada, including the Battle of Gravelines in 1588.

Henry Seymour (secularist): Henry Albert Seymour (1861–1938) was a British secularist, individualist anarchist, gramophone innovator and survey author, and Baconian.  He published the first English language anarchist periodical in Britain and is credited, in 1913, with introducing the Edison disc into the country.

William Seymour, 3rd Duke of Somerset: William Seymour, 3rd Duke of Somerset (1654 – 12 December 1671) was the son of Henry Seymour, Lord Beauchamp and Mary Capell.

Lord Henry Seymour (politician): Lord Henry Seymour (15 December 1746 – 5 February 1830) was a British politician, the second son of Francis Seymour-Conway, 1st Marquess of Hertford.  He was known as Hon. Henry Seymour-Conway until 1793, when his father was created a marquess; he then became Lord Henry Seymour-Conway, but dropped the surname of Conway after his father's death in 1794.

Antrim by-election, 1869: The Antrim by-election of 1869 was fought on 21 August 1869.  The by-election was fought due to the death of the incumbent MP of the Conservative Party, George Henry Seymour.  It was won by the Conservative candidate Hugh de Grey Seymour.

Norris Castle: Norris Castle is located on the Isle of Wight and can be seen from the Solent standing on the northeast point of East Cowes.  It was designed by the famous architect James Wyatt for Lord Henry Seymour.  The estate adjoins the neighbouring Osborne House, country home to Queen Victoria, which also includes the nine-hole Osborne Golf Club.  On the other side of Norris Castle sits the Spring Hill estate, bought by William Goodrich in 1794.  Norris Castle was built in 1799 and sits in 225 acres of land, with a mile of waterfront.  The Castle is a Grade I listed building.

Henry Seymour (16th-century MP): Sir Henry Seymour (c. 1503 – 5 April 1578) was an English landowner and MP, the brother of Jane Seymour, queen consort of Henry VIII, and consequently uncle to Edward VI.  He was created a Knight of the Bath after his nephew's coronation.

Supporting paragraphs: Henry Seymour (secularist) Baconian theory of Shakespeare authorship
Answer: Sir Francis Bacon