I didn ' t move any goal posts . Here ' s what you said The person you responded to literally said The left needs to get a fucking grip obviously referring to whoever suggested that watching Trump on TV ultimately killed this person . Whoever suggested that was Gabriel Roth of the DapKings . Therefore , Gabriel Roth of the DapKings is The Left . Based on what you yourself said . <| sep |> Sad thing is , I feel like some of the high rollers would buy those deals for that price . <| sep |> So , correct is a bit too strong and it was probably me that used that word , tbh . Ever since Cohen proved CH independent of the other axioms , there has been discussion about what axioms to add he proved Choice independent first , and the solution there was to just add it as an axiom . This is far from a unique issue , ZFC doesn ' t say much about infinity it really just has the axiom of infinity which asserts nothing beyond the existence of an infinite set . My feeling that the cardinality of the continuum ought to be aleph 2 stems mostly from arguments Godel put forward suggesting as much . Specifically , he wrote Some considerations leading to the probable conclusion that the true power of the continuum is aleph 2 which can be found in Godel ' s Collected Works , Volume III I don ' t have a legal online source to link to . He also wrote a letter to Tarski which likewise appears in Collected Works Vol 3 stating outright that he believed the continuum should have cardinality aleph 2 in the intended model of set theory . Now to understand why this might be plausible , I have to address how we go about fixing the infinity problem , which necessarily involves assuming new axioms . Broadly speaking there are two classes of proposed additional axioms that are taken seriously the large cardinal axioms which afaik set theorists have essentially already adopted and the forcing axioms . Large cardinals don ' t say much about the continuum , they deal with very large infinities things like inaccessible cardinals , which by definition cannot be accessed using the usual set theory operations . Of course , one might think to just adopt CH as an axiom . And that ' s fine , but it ' s not philosophically justified by anything other than a desire for simplicity . In particular , the easiest model of ZFC to construct where CH ~~ fails ~~ holds is by just adding the axiom of constructibility which asserts that all sets are constructible . But there are sound philosophical reasons to reject that axiom , and in fact the large cardinal axioms are adopted for reasons almost directly at odds with constructibility . Forcing axioms , on the other hand , attempt to constrain how forcing works . Forcing is the method developed by Cohen to product models of ZF where e . g . choice and CH fail to be true . The problem is that ZF by itself can be forced to do almost anything with infinity that ' s not obviously selfcontradictory . So one reasonable solution , and one which Godel at least hinted at , is to adopt axioms that declare what kinds of forcings are allowed . From the point of view that we should add axioms to correct the flaw in ZF that allows forcing , this makes the most sense . One of the forcing axioms , the Proper Forcing Axiom , yields as an immediate consequence that the continuum is aleph 2 . So in this sense , the forcing axioms which are designed to correct the limitations of ZF ' s ability to discuss small infinities lead to the conclusion that the continuum is aleph 2 . To me and Godel afaict this seems the most natural solution to the undecidability of CH . That all said , I should mention that Woodin one of the most significant working set theorists used to subscribe to this line of thinking but recently appears to have changed his tune and concluded that actually CH should be true . CH would follow from his Ultimate L conjecture . I don ' t know the details enough to be able to speak about it , but the set theorists I know are of the opinion that Ultimate L is quite promising it gives all the large cardinals for instance , so there are certainly multiple points of view out there . Edit Pinging ucompletelyineffable to point out where I ' ve made mistakes andor to offer the opinion of an actual expert in set theory on the question . Edit 2 I should probably also mention that the most common formalization of a set theory involving proper classes , NBG set theory , usually includes the Axiom of Limitation of Size that all proper classes are in bijection with the class of all sets . This implies both global choice and the generalized CH , so that ' s another reasonable argument that CH should be true .