Since the source you offer in your post cites cognitive science, I'm going to offer the second-generation cognitive science of George Lakoff to characterize mathematical conceptualization. As a theory, it draws from Lakoff's views in cognitive semantics and is fully fleshed out in his Philosophy in the Flesh wherein he offers the full scope of his and colleagues' position that he labels embodied realism which is a flavor of embodied cognition. His work on conceptual metaphors is quite extensive, however, he ventures into mathematics in his and Nuñez's Where Mathematics Comes From (WMCF).

I won't be able do justice to the theory here, but it starts with the idea that fundamental concepts are formed in discrete units of neurological computation. If you're familiar with computational neuroscience, you'll know there has been many excellent efforts to characterize how small neural networks can be modeled. Neurological computations as a basis of language has the benefit of aligning with NCCs. I would argue at this point in cognitive science, to see the mind as a product of anything other neural and chemical activity that captures the essence of the changes of state in the body is naive.

WMCF doesn't get into the nitty gritty of neural encoding or calculus-based description of dynamical systems. It waves it's hand in the air just pays tribute philosophically. What it does do is start with the idea that mathematics is essentially an aspect of experience that traces its formal semantics to four fundamental neural capacities, called the Fundamental Conceptual Metaphors. For instance, the Metaphor of Containment is the claim that our ability to see experience space as volumetric is what underlies the notion of a set. The Metaphor of Infinity is very much similar to the mathematical constructivist notion that infinity is a potential infinity generated by iteration. Our ability to track motion in our environment underlies the notion of the infinitesimal and the epsilon-delta definition because the latter is an infinite point-wise description of continuous motion along a plane. And so on.

No, and logical positivism died because it lacks critical insights into how humans form concept systems. Post-positivist thinking is far more productive in this arena. I'll offer you one such system.

Since the source you offer in your post cites cognitive science, I'm going to offer the second-generation cognitive science of George Lakoff to characterize mathematical conceptualization. As a theory, it draws from Lakoff's views in cognitive semantics and is fully fleshed out in his Philosophy in the Flesh wherein he offers the full scope of his and colleagues' position that he labels embodied realism which is a flavor of embodied cognition. His work on conceptual metaphors is quite extensive, however, he ventures into mathematics in his and Nuñez's Where Mathematics Comes From (WMCF).

I won't be able do justice to the theory here, but it starts with the idea that fundamental concepts are formed in discrete units of neurological computation. If you're familiar with computational neuroscience, you'll know there has been many excellent efforts to characterize how small neural networks can be modeled. Neurological computations as a basis of language has the benefit of aligning with NCCs. I would argue at this point in cognitive science, to see the mind as a product of anything other neural and chemical activity that captures the essence of the changes of state in the body is naive.

WMCF doesn't get into the nitty gritty of neural encoding or calculus-based description of dynamical systems. It waves it's hand in the air just pays tribute philosophically. What it does do is start with the idea that mathematics is essentially an aspect of experience that traces its formal semantics to four fundamental neural capacities, called the Fundamental Conceptual Metaphors. For instance, the Metaphor of Containment is the claim that our ability to see experience space as volumetric is what underlies the notion of a set. The Metaphor of Infinity is very much similar to the mathematical constructivist notion that infinity is a potential infinity generated by iteration. Our ability to track motion in our environment underlies the notion of the infinitesimal and the epsilon-delta definition because the latter is an infinite point-wise description of continuous motion along a plane. And so on.

Since the source you offer in your post cites cognitive science, I'm going to offer the second-generation cognitive science of George Lakoff to characterize mathematical conceptualization. As a theory, it draws from Lakoff's views in cognitive semantics and is fully fleshed out in his Philosophy in the Flesh wherein he offers the full scope of his and colleagues' position that he labels embodied realism which is a flavor of embodied cognition. His work on conceptual metaphors is quite extensive, however, he ventures into mathematics in his and Nuñez's Where Mathematics Comes From (WMCF).

I won't be able do justice to the theory here, but it starts with the idea that fundamental concepts are formed in discrete units of neurological computation. If you're familiar with computation neuroscience, you'll know there has been many excellent efforts to characterize how small neural networks can be modeled. Neurological computations as a basis of language has the benefit of aligning with NCCs. I would argue at this point in cognitive science, to see the mind as a product of anything other neural and chemical activity that captures the essence of the changes of state in the body is naive.

WMCF doesn't get into the nitty gritty of neural encoding or calculus-based description of dynamical systems. It waves it's hand in the air just pays tribute philosophically. What it does do is start with the idea that mathematics is essentially an aspect of experience that traces its formal semantics to four fundamental neural capacities, called the Fundamental Conceptual Metaphors. For instance, the Metaphor of Containment is the claim that our ability to see experience space as volumetric is what underlies the notion of a set. The Metaphor of Infinity is very much similar to the mathematical constructivist notion that infinity is a potential infinity generated by iteration. Our ability to track motion in our environment underlies the notion of the infinitesimal and the epsilon-delta definition because the latter is an infinite point-wise description of continuous motion along a plane. And so on.

Since the source you offer in your post cites cognitive science, I'm going to offer the second-generation cognitive science of George Lakoff to characterize mathematical conceptualization. As a theory, it draws from Lakoff's views in cognitive semantics and is fully fleshed out in his Philosophy in the Flesh wherein he offers the full scope of his and colleagues' position that he labels embodied realism which is a flavor of embodied cognition. His work on conceptual metaphors is quite extensive, however, he ventures into mathematics in his and Nuñez's Where Mathematics Comes From (WMCF).

I won't be able do justice to the theory here, but it starts with the idea that fundamental concepts are formed in discrete units of neurological computation. If you're familiar with computational neuroscience, you'll know there has been many excellent efforts to characterize how small neural networks can be modeled. Neurological computations as a basis of language has the benefit of aligning with NCCs. I would argue at this point in cognitive science, to see the mind as a product of anything other neural and chemical activity that captures the essence of the changes of state in the body is naive.

WMCF doesn't get into the nitty gritty of neural encoding or calculus-based description of dynamical systems. It waves it's hand in the air just pays tribute philosophically. What it does do is start with the idea that mathematics is essentially an aspect of experience that traces its formal semantics to four fundamental neural capacities, called the Fundamental Conceptual Metaphors. For instance, the Metaphor of Containment is the claim that our ability to see experience space as volumetric is what underlies the notion of a set. The Metaphor of Infinity is very much similar to the mathematical constructivist notion that infinity is a potential infinity generated by iteration. Our ability to track motion in our environment underlies the notion of the infinitesimal and the epsilon-delta definition because the latter is an infinite point-wise description of continuous motion along a plane. And so on.