In brief, the same word is used with two different meanings. In other words:
The fallacy of Equivocation is a pervading and ubiquitous fallacy. It varies in subtlety from a manifest pun, that would not deceive a child, to a confusion the most subtle, the most difficult to detect, to recognise, and to avoid, of all fallacies; and of all fallacies it is the most frequently perpetrated. Nothing is more frequent in reasoning, and especially in disputation, than the use of a term in two or more senses, without any appreciation on the part of either of the disputants, or of the single reasoner, that it is used in more than one; nor is there any source so fertile of difference of opinion. In fact, difference, that appears to be difference of opinion about facts, is very often, unknown to the disputants, difference about the meaning of words; and no controversy can be useful or fertile, that is not preceded by a definition of the words to be used, and an agreement about the meanings to be attached to them. It is not too much to say, that in most controversies, each party uses some important term, on which the controversy hangs, in a sense different from that understood by the other party; or uses the term, first in one sense, and then in another, without any recognition or appreciation of the equivocation. It requires an effort, and a consider able effort, to adhere to the same meaning in using a word of current and large signification, throughout a controversy that is at all prolonged.Mercier, A New Logic, pp. 366-7.
Consider the following argument, advanced in the context of dialogue on the morality of law: 1) Following the law is obligatory. 2) Failing to do something obligatory is morally wrong. 3) Therefore, failing to follow the law is morally wrong. Anyone to whom this argument is directed might criticize it as committing the fallacy of equivocation, on the following grounds. In the first premise, ‘obligatory’ means legally obligatory. … But in the second premise, ‘obligatory’ means morally obligatory.Walton, Informal Logic, p. 270.
“It depends on what the meaning of the word ‘is’ is.”President Bill Clinton in his Paula Jones deposition, reported in the Chicago Tribune, Sept. 13, 1998 at 19 n.1128.
Imagine an author who sets out to prove that music glorifies violence but who spends most of the book fixated on gangsta rap and then attributes the vices of the latter to music in general. As already noted, this kind of mistake is called equivocation. Dawkins’ rhetorical excesses and inattention to nuanced differences do not just make him susceptible to this fallacy. When he tries to make the case that religion is pernicious, Dawkins moves willy-nilly from an attack on particular religious doctrines and communities to conclusions about religion and belief in God generally.Eric Reitan in Is God a Delusion?, pp. 22.
In early October 2005, Iraq’s parliament made a critical ruling concerning the number of votes required for passage of the newly proposed constitution that was scheduled for a vote later that month. The parliament held that for purposes of ratification,”voters” consisted of those who showed up at the polls and actually voted, but that for purposes of rejection, “voters” consisted of all those who registered voters… Interpreting the second definition of “voters” as “registered voters” had the effect of enlarging the number of voters who had to reject the constitution — two-thirds of those eligible to vote versus two-thirds of those actually voting. Those who opposed the constitution would have been required to overcome those who did not vote. Each “registered” voter who did not appear at the polls, in effect, became a vote for ratification.Bosanac, Litigation Logic, p. 121.
Always, always define your terms and request the same. Identify the word which is used twice, then show that a definition which is appropriate for one use of the word would not be appropriate for the second use.
In 2005, philosopher Nicholas Shackel coined this move as the “Motte and Bailey Doctrine.” (People often call it a fallacy, but Shackel wrote a blog post in 2014 explaining why he calls it a doctrine, and how “a myriad of persuasive fallacies” can be snuck into a motte-and-bailey.) … In rhetorical terms, the bailey is the desired but hard-to-defend controversial opinion. The motte is the less desired yet defensible opinion that nearly everyone agrees with, and which the arguer retreats to if unable to defend the bailey.Stephen Johnson, “The ’Motte & Bailey’ meme” (September 4, 2020).
On agreed upon definitions
It is idle to discuss the advantages and disadvantages of Socialism, until we have settled and agreed upon the meaning that is to be attached to ‘Socialism.’ When one disputant understands by it the organisation and management of industries by the State, and another takes it to mean the equalisation of reward for labour, and a third intends by it the abolition of private property, it is evident that the argument of each will be to the others, beside the mark, irrelevant, and mistaken. It is idle to discuss whether it is right for a clergyman to repel from the communion table (which he erroneously calls the altar) a man who has married his sister-in-law, until we have settled what meaning is to be attached to ‘right.’ Does it mean consistent with statute law? or with canon law? or with the custom of the Church, or of some part of the Church? or with the scruples of the clergyman? or with some code or rule of morality? While the dispute is in progress, any of these meanings may be temporarily uppermost in the minds of either of the disputants, and be shortly replaced by another, without any appreciation, even by himself, that he has shifted his ground; and it is unlikely, unless care is taken both to define the term and to keep to the definition, that both disputants will use the word in the same sense at the same time. A totally different set of meanings clings about the word when the question is asked whether women have a ‘right’ to the suffrage. Is the ‘right’ a legal right, a constitutional right, or a moral right? If a legal right, what is the law that gives it to them? If a constitutional right, what is the meaning of ‘constitutional’? Does it mean consistent with established custom, or consistent with the fiction that taxation and representation go together, or with the principle that they ought to go together? Or does it mean that the granting of the suffrage to women would be beneficial to them, or to the nation? If a moral right, it means consistent with some scheme of morality, but with whose scheme? Yours, or mine, or his? Any discussion that ignores these ambiguities in the meaning of ‘right,’ is barren ab initio.Mercier, A New Logic, pp. 367.