Interesting question. Good answers. Let’s look at how we can ask this question. 😉

Technical Innovation <-> Practical Utility <------> Popular Influence

Successful Technical
Hard to argue that the Russel-Frege-Kripke chain didn’t provide answers but it’s also hard to argue that they weren’t wasting their time. Because Babbage-Cantor-Goedel-Turing produced superior methods and answers.

Failed Technical
The failure of Brouwer(Physics), Bridgman(mathematics), Mises (economics), Hayek(Law), and Popper(Philosophy) to understand that the ‘ideal’ disciplines had failed to include operations as a test of possibility, operational grammar to prevent pretense of knowledge,

Influential and Contributory:
Searle(cognition), Jonathan Haidt(morality), Daniel Kahneman(cognition), Nassim Taleb (probability and cognitive biases). Unfortunately we can’t list Popper(via negativa), Hayek(Social Science = Law), Keynes(Monetary Marxism), Turing, and Rawls who are demonstrably more influential but not living.

Popular Influence But Otherwise Meaningless:
Dennet et all.

1. Categorical Construction:
2. Scientific <----------------> Ideal <-----------------> Experiential
3. Descriptive Causality Experiential Causality
4. Scientific Categories Normative Categories Arbitrary Categories
5. Operational Analytic Literary Conflationary Continental
6. Aristotle Plato (many)
7. 
8. Tends to Result In:
9. Truth Utility Preference
10. Markets, Regulation Command
11. Nash Equality Pareto Equality Command Equality
12. Natural Hierarchy Political Hierarchy Bureaucratic Hierarchy
13. Classical Liberalism Social Democracy Socialism
14. Rapid Adaptation Windfall Consumption Redirected Consumption
15. Hyper Competitive Competitive in Windfalls Competitive when Behind

I would make the following observations:

  1. The continental (German) program has been a failed attempt, since the time of Kant (through Heidegger), to produce a secular, rational, version of Christianity. The French program (Rousseau through Derrida) has been a demonstrably successful program but a devastatingly destructive one. The Abrahamic program’s second revision (Marx, Freud, Boaz, Cantor, Mises, Rothbard, Strauss) has been catastrophic. And between the French Literary, Continental Rational, and Abrahamic Pseudoscientific movements, the attempt to restore the Aristotelian(scientific)/ Stoic(Mindfulness) / Roman(Law) / Heroic(Truth, Excellence, Beauty) program responsible for human progress in the ancient and modern world has been nearly defeated.

  2. The analytic program was exhausted with Kripke, and in retrospect the analytic attempt to produce both formal logic of language, and a science of language will be considered a failure. For example, there is nothing in analytic philosophy that is not better provided by Turing.

  3. The principle function of academic philosophy today appears consist of the self correction of existing errors prior to exhaustion of the philosophical program (termination of the discipline) in the same way that the analytic program exhausted itself. (If you list philosophers and their innovations this is what appears to be occurring. The discipline is exhausting itself as a dead end).

  4. The principal influences on intellectual history are being provided by the sciences. In particular they are eliminating the last refuge of philosophy: the mind. And science is doing so via-negativa: through the incremental definition and measurement of cognitive biases (errors).

  5. Science, if understood as an organized attempt to produce deflationary truthful (descriptive) speech, and the use of scientific categories (necessary and universal), will continue to displace the discipline of philosophy, and the use of philosophical categories, terminology and concepts. And (assuming I am correct), what remains of the discipline of philosophy will be reducible to the continuous refinements of the scientific method’s production of constant descriptive categories, terminology, and operational grammar. And the cross disciplinary adaptation of local categories into universal categories.

  6. Science is less vulnerable to error , bias, suggestion and deceit, in no small part because the common problems of philosophy: suggestion, loading, framing, obscurantism, overloading, and the Fictionalisms (pseudoscience, pseudo-rationalism, and pseudo-mythology(theology)) are prohibited by the demand for Operational language, declared limits, and full accounting of consequences. It certainly appears that since the beginning of the 20th century we have been far busier eliminating errors of philosophy than philosophers have been busy discovering innovations.

  7. Greek philosophy arose out of the common law of torts. Roman philosophy explicitly functioned on the common law of Torts. The Abrahamic Dark Age (conflating idealism, law, and religion) followed, but we were rescued by the reconstruction of north sea trade and the English common law of Torts (Bacon). And as far as I can determine,

  8. As we have seen with continental and political philosophy, just as we saw with theology, and especially Abrahamic theology, the principle purpose of unscientific speech has been deception, propaganda, the propagation of ignorance, and the conduct of rule, and the expansion of warfare. With theologians and philosophers responsible for more deaths than generals and plagues. Between Zoroaster, Muhammed, and Marx, we have more deaths than all but the great diseases including malaria and the black plague. Philosophers and theologians have done more harm than good, largely functioning as a middle class opposition to the current form of rule.

  9. Philosophical language then is a dead language, and perhaps an immoral one – and rationalism a dead technology. And they will be incrementally combined institutionally and normatively into theology, with Literary Philosophy(Plato and his heirs), merely representing it’s position on the spectrum of Aristotelian/Stoic/Roman/English Law (science), Confucian Reason, French Literary Idealism, Platonic Rational Idealism, Continental and Augustinian Fictionalism, and Abrahamic and Zoroastrian Fictionalism.

  10. The use of non philosophical categories to construct *moral literature* in the French and Italian model will persist forever. Although largely as a means of resistance against the sciences, and the status social, economic, and political status quo.

In this context we have to ask what we mean by Influential, or Great Philosophers, because:
(a) Unless we are talking scientists who function as public intellectuals, philosophers, or Social Critics (practitioners of critique), or Moral Fictionalists (wishful thinkers), it really doesn’t appear that philosophy is a living or useful language or discipline.
(b) it’s hard to argue there are any currently living and working rationalists of any substance. They are largely Moral Fictionalists.

Let’s look at the list:

Dennett, Harris, Hitchens, Dawkins. The atheists. It’s worth noting that Dawkins was correct and Gould was wrong – about almost everything. (Surprisingly). Harris and Hitches practice critique but nothing else.

Zizek practices Critique and has nothing to offer – and is honest about it. I mean, what solutions does Zizek provide? None. And he says so.

Chomsky practices Critique, has nothing to offer – and is dishonest about it. He is an interesting example of how people with high intelligence and verbal acumen can construct elaborate deceptions. Between Chomsky and Paul Krugman, a half dozen people could spend their entire careers demonstrating their use of cherry picking, loading, framing, overloading with incommensurables, straw men, and heaping of undue praise. His insight into ‘universal grammar’ but categories of increasing complexity is largely correct and we can see that in brain structure today. However, he speaks about world affairs by constantly making the error (intentionally), that rational choice is scalable – just as did Marx. And he has no concept of economics whatsoever, and no political statement can be made any longer independently of economics – especially once we understand that the term economics has nothing to do with money and everything to do with the voluntary organization of individuals through the use of incentives provided by money.

Hofstadter is a good example as any, but again, he is a public intellectual and a literary aesthete. Did he really provide any insight that was not visible in the literature of the time?

So in closing, I would say, that:

  1. There are no influential rationalists, because the program is complete and it’s been a dead end. The reasons for this would require I write a tome.
  2. That there are many scientists that serve as public intellectuals, and this will continue.
  3. There remain and always will be a market for moral literature.
  4. That scientific philosophy, if completed, as ‘the discipline of due diligence against ignorance, error, bias, wishful thinking, suggestion, overloading, and deceit, will replace the discipline of philosophy.

But that won’t stop people over invested in a dead frame of reference from attempting to practice it. Why? It’s cheap and science is expensive.

https://www.quora.com/Who-is-the-most-influential-living-philosopher-1