Did it take till the likes of Lakoff and the 20th-21st century to have truly direct naturalized reasons for logic and math?

Question

I’m finding George Lakoff and cohorts unique (but maybe that’s my lack of looking enough) in that they seem among the first to posit a direct, naturalized account of logic and mathematics, as extended metaphors on basic concepts we learn at young ages.

Quine didn’t hold his, while a naturalist he held logic and math don’t directly answer to the world most of the time:

How is Quine to explain the apparent necessity and a priori status of some truths without appeal to the Principle of Tolerance? Quine’s holism is the view that almost none of our knowledge is directly answerable to experience.

https://plato.stanford.edu/entries/quine/#QuinNatuImpl

Logical positivists wouldn’t have either as math and logic are analytic and a priori, not empirical.

Not Kant either.

Seems like these kind of questions were ignored for a while(?), then back to Aristotle and Plato.

The little I know of them and how they regarded math and logic are that forms are ultimate causes to Plato, and Aristotle relied on the Socratic method/elenchus to posit the law of noncontradiction in his Metaphysics. These are not direct enough to be in the category of Lakoff I think. Winning a Socratic argument (elenchus) isn’t the same as Lakoff is doing (yet Aristotle is a father of science even…), and Plato’s forms are criticized by Aristotle for being too disconnected from the world I believe.

Yet it doesn’t take modern science to imagine what Lakoff is attempting, so why so late coming?. A completely naturalized conceptual metaphor as and for the law of excluded middle and principle of noncontradiction doesn’t seem outrageous. Think of the reasoning in searching for a missing child as your boat capsizes-you know the child must be on the boat or in the water, if you search the boat it’s time to search the water. I’m not using that scenario Socratically I don’t think, I’m saying it because it may point to a natural reason for us having such capacities of thought and reasoning. My instinct upon hearing it is to disengage the Socratic method and take up a new one for this task. Does that distinction make sense?

Answer 1

Thirty-Second Overview of Embodied Cognition as a Philosophical Theory

George Lakoff and the cognitive semanticists as well as embodied cognition might find it's clearest, most popular expression in Philosophy in the Flesh (1999), though there are others such as Shapiro's Embodied Cognition (2019) which more recently articulate more technical theories. From Lakoff and Johnson's work:

This book asks: What would happen if we started with [cognitive science and it's empirical discoveries] and constructed philosophy anew? The answer is that an empirically responsible philosophy would require our culture to abandon some of its deepest philosophical assumptions. p.3

He goes on the next page to offer a host of claims that many philosophers find objectionable:

• Reason is embodied
• Reason is a product of evolution
• Reason is not "universal" in the transcendent sense
• Reason is not completely conscious, but mostly unconscious
• Reason is not purely literal
• Reason is emotionally engaged
• There is no Cartesian dualistic person
• There exists no Kantian autonomous person
• The utilitarian person does not exist
• The phenomenological person is a fiction
• There is no postructuralist person
• There is no Fregean position
• There is no computational person
• There is no Chomskyian person
• A priori philosophizing provides no privileged direct access
• Answers to philosophical questions are inherently based on conceptual metaphor
• Irrefutable facts of the mind introduced by cognitive science are part and parcel of the philosophy of mind

As you can see, that's quite an attack on a broad range of philosophical positions and for some might smack of scientism! Considering that many philosophers are folk scientists and are skeptical of a naturalized epistemology as being philosophy at all, it's little wonder that the position was once considered fringe. These days, there are important movements in philosophy of mind that undergird philosophically popular positions based on cognitive science and physical computation. One very recent publication is Shea's defense of teleosemantics-based (SEP) representational theory of mind (SEP). This sort of stuff is cutting edge science as well as philosophy. From Shea's work:

Ever since the 'cognitive revolution' gave the behavioural sciences the idea of mental representation, one phenomenon after another has succumbed to representational explanation... The recent successes of cognitive science depend on the same insight, while also telling us how representations are realized in the brain, a kind of understanding until recently thought to be fanciful.

Why "Fringe" at All?

The question proper might be best conceived from a Kuhnian framework in that embodied cognition is quite a paradigmatic shift. Lakoff's philosophical stance builds or advanced a number of recent developments in philosophy in the 20th century, but takes a middle-of-the-road approach in a number of debates.

• In terms of linguistic categorization, it purports to advance contemporary philosophy of mind by claiming that thought is primarily conceptual metaphor, and that most philosophical claims are reducible to conceptual metaphors which are the product of representations/misrepresentations based in neural computation. Metaphors We Live By presents the beginning of such an argument following up the developments in linguistics stemming from Wittegensteinian language games by way of the prototypical definition. Many philosophers don't practice theories that embrace Wittegensteinian family resemblance in their metaphysics.
• It takes a middle position on the scientific realism-instrumentalism debate thereby alienating both extreme positions. Scientifically ontological questions and explanation questions are largely reduced to questions of linguistic categorization as in Women, Fire, and Dangerous Things.
• It takes a middle position on the Platonism-intuitionism debate there by denying both extreme positions. Where Mathematics Comes From lays out these positions, and has appendices to reinterpret what it means to be a mathematical theory in semi-physiological terms.
• There is a rejection of truth-conditional semantics in favor of cognitive semantics, which is a very involved philosophical position that requires involved study and a penchant mathematical constructivism, scientific constructivism, and social constructivism all of which borrow heavily from a more contemporary philosophy of language like that goes beyond even that of Szabo and Thomason's textbook. That means to embrace these sorts of philosophical position requires a devotion to furthering the linguistic turn.

None of this should come as a surprise as much of the philosophy of mind comes from 21st century cognitive science which exalts a naturalized epistemology and philosophy of language that goes into demarcating embodied cognition comes from contemporary, upstart philosophical movements.

What are some of the consequences of the position?

• The position essentially sees God as a linguistic construct, just another essentially contested idea and sees cognitive science as the primary epistemological tool.
• The entire Aristotelian and Platonic foundation of Western philosophy is misguided with it's focus on philosophical entities and properties where as conceptual realities are not directly realistic, but rather are closer to being understood by process philosophy (SEP).
• All major philosophical theories are reducible to linguistic frameworks of conceptual metaphors, and therefore are derivative from cognitive linguistic activities.

Conclusion

You asked why is the position so late in coming? Well, George Lakoff and many of his peers reject the foundation of Western philosophy and the notion of the transcendent and objective completely, and instead favor a science-heavy philosophy of mind somewhere between solipsism and eliminative materialism. They not only seek to displace Descartes's "theater of the mind" but also reject Ryle's "category mistake" since they reject monism and dualism and instead posit neural computation as a bridge between mind and body metaphysically by relying heavily on neural correlates of consciousness to draw philosophical conclusions. To reject theology and most of the assumptions of the Western tradition of philosophy going back to the Ancient Greeks is bound to meet resistance, no? One more quote from Philosophy in the Flesh:

We are philosophical animals... The question is clear. Do you choose empirical responsibility or a priori philosophical assumptions? ...We are promoting a dialogue between philosophy and cognitive science. p.551

[Disembodied reason, radical freedom, and objective morality] is assumed in much of Western religion... This view of the person also lies behind the traditional European distinction between the natural sciences and the humanities... [However,] the traditional Western view of the person is, as we have seen, at odds on every point with the fundamental results from neuroscience and cognitive science.

In essence, much of the last 2,500 years of religion and philosophy is wrong! And that sort of claim provokes a lot of disagreement, the sort that Max Planck remarked on in science when relativism and quantum physics was overturning Newtonian physics:

“A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.” ― Max Planck, Scientific Autobiography and Other Papers