There was an Anthony Dodgson born to Myl. Dodgson in HAWKSHEAD, LANCASHIRE, ENGLAND on 20 Nov 1625. This is speculative at best but worthy of noting for future research.
Anthony married Mary Williams, Daughter of John Williams, Sr. on 12 Nov 1651 in Scituate, MA.
He died after 1671 which was the date of birth of his youngest child, Bethia.
Note NI0239History of Scituate, Massachusetts: from its first settlement to 1831 By Samuel Deane published in 1831.
ANTHONY DODSON was in Scituate 1650. He married Mary, the daughter of John Williams, sen. 1651. His land was on the east of John Cowen's, and his house near where the house of late Rowland Litchfield stands. He had Conihassett lands in the right of John Williams, and was much employed as a surveyor, by the partners. His children were Sarah born 1652, Gershom 1653, Mary 1656, Jonathan 1659, Patience, Bethia and Eunice.
Sarah married Thomas Stetson 1671, Margaret married Nathaniel Tilden 1693, Mary married John Booth, jr., Patience married John Pierce, Bethia and Eunice Jiving single 1695, when their mother deceased, and named them in her will.
Gershom was one of the unfortunate men who fell with Capt. Pierce in the Rehoboth battle, 1676. Jonathan married Abigail, daughter of Matthew Gannett, and left a family, viz. Jonathan, Anthony, Deborah, Mary, Sarah, Hannah and Gershoin, born from 1695 to 1704. This family name has long since been extinct in this Town.
. 2 Gershom DODSON b: February 14, 1653/54 in Scituate, Plymouth, MA d: March 26, 1676 in battle at Rehoboth, Plymouth, MA, 1676, w/Capt. Pierce age 23
. 2 Margarite DODSON b: Abt. 1656 in Scituate, Plymouth, MA bp 11/23/1656 IS THIS MARY?
. 2 Mary DODSON b: 1656 in Scituate, Plymouth, MA
..... +John BOOTH m: December 12, 1687 in Scituate, Plymouth, MA
. 2 Jonathan DODSON b: December 20, 1659 in Scituate, Plymouth, MA
..... +Abigail GANNETT b: in Hingham, Plymouth, MA abt 1651 - death date of Abigail indicates may have been 2nd wife d: in Scituate, Plymouth, MA age 44 November 16, 1695 - ch born after this date
* According to Deane, he "was in Scituate 1650. He married Mary, the daughter of John Williams Sr. in 1651. His land was on the east of John Cowen's, and his house [stood] near where the house of the late Roland Litchfield stands. He had Conihassett lands in the right of John Williams, and was much employed as a surveyor, by the partners." 
Sources for Notes:
1. [S365] Pane-Joyce Genealogy, David Pane-Joyce.
2. [S560] History of Scituate, Massachusetts, from its First Settlement to 1831, Samuel Deane, (Boston: James Loring), 263.
This biography is a rough draft. It was auto-generated by a GEDCOM import and needs to be edited.
↑ "England Births and Christenings, 1538-1975," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:JQRZ-W97 : 11 February 2018, Anthony Dodgson, 20 Nov 1625); citing , index based upon data collected by the Genealogical Society of Utah, Salt Lake City; FHL microfilm 476,869.