Logic in Early Modern Philosophy

With modern philosophy somewhat understood, it's time to pivot and see how logic developed during this time period. First, in the early part of this period, Pascal's wager was an important development, which was followed by the Port Royal Logic. There were also important developments by Kant, Bacon, Hume, Mill, and Llull. Let's see how Aristotelian logic developed during this time!

Script by Luca Igansi

Check out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!

[jolo]

The most confusing class and the worst grade I received in college was Philosophy. I thought it would be interesting and fun, kind of like this. But, i had the most boring and, no, just boring professor that I just couldn't stay connected. Thank you for the second chance for me to at least grasp some knowledge on the subject. 😊

[thomaszack]

Very well done! It connects a lot of the "dots". Thank you.

[nrupenchudasma]

Nice summary... this provides good references to check out.

[alishatruman]

Love videos about Philosophy thanks P. Dave!

[snowmanthegamer]

Thanks for the class sir!! Hope you have a good day! 👍

[JoePalau]

Can't wait to hear about Quince next time!

[vance]

get on the dave wave🏄🏽🌊 teachin em right💪🏽

[rdhealthcare]

I will be self-studying mathematical logic soon. Topics like these feel like they tug at the basis or fabric of other disciplines.

[yedder]

If Pascal’s wager was so good then why isn’t that the only argument people per posing for it make

[readyfireaim]

The existence of quantum entanglement does seem to challenge some of the fundamental assumptions underlying our classical conception of space and time as a 3+1 dimensional continuum. Here's an attempt to mathematically illustrate how entanglement could be seen as contradicting the notion of spacetime as a separable 4-dimensional manifold:

In standard quantum mechanics, the state of a composite system is represented by a vector |Ψ> in the tensor product Hilbert space H = H1 ⊗ H2 of the individual subsystem state spaces.

For two entangled particles, their joint state cannot be expressed as a simple product of individual states:

|Ψ> ≠ |ψ>1 ⊗ |φ>2

But instead takes an entangled superposition form, like the famous Bell state:

|Ψ>= 1/√2 (|0>1|1>2 - |1>1|0>2)

This entangled state vector lives in the full composite Hilbert space and cannot be decomposed into subsystem states. Mathematically, entanglement represents a non-separable holistic structure across multiple "branches" of the wavefunction.

For concreteness, let's consider two entangled particles described by the spin observable S⃗1 and S⃗2 respectively. Their combined spin state is entangled:

|Ψ> = 1/√2 (|↑>1|↓>2 - |↓>1|↑>2)

If we measure S⃗1, say obtaining |↑>1, then the global state is projected via collapse to:

|Ψ> → |↑>1|↓>2

However, this updated state for particle 2 is now correlated with the distant result for particle 1 in a way that appears to defy any "local" space-time explanation based on relativistic fields propagating continuously through a 4D manifold.

The mathematical structure of entangled states seems to transcend the notion of localized objects embedded in a 3+1 dimensional arena evolving smoothly according to local field equations and general relativistic geodesics.

Instead, the instantaneous influence of one particle's state on another's, potentially across cosmic distances, suggests some deeper atemporal interconnectedness that is holistically encoded across the full physical system described by the entangled wave function.

In this way, the basic mathematical structure of quantum entanglement appears to contradict the idea that physical reality can be captured by local objects evolving strictly within a classical 3+1 dimensional spacetime continuum according to local differential equations.

Entanglement hints at a more holistic, non-separable, and potentially atemporal unified structure intrinsic to quantum systems that is simply not capturable within the classical 3+1 dimensional spacetime manifold paradigm alone.

Does this mathematical analysis help illustrate some of the core tensions between the quantum phenomenon of entanglement and the classical notion of spacetime as a separable 4D manifold? The math seems to suggest entanglement represents a much deeper interconnectedness transcending 3+1 dimensional separability.

[brewdog]

See, learning stuff can be fun. Thanks Dave ;)

[lateolabrax]

This is precisely why Kant is the greatest philosopher of all time.

[nirmalmishra]

DAVE, I'm thinking to join as a member so as for homework help exclusively. Is that a good idea. Can you manage to have some time for that?

[nihilgeist]

It's not Pascal's wager, it's the Prisoner's Dilemma and a Nash Equilibrium.

[readyfireaim]

Dear Academic Community,

I am writing to bring to your attention a critical foundational issue that has the potential to upend our current understanding of physics and mathematics. After carefully examining the arguments, I have come to the conclusion that we must immediately reassess and rectify contradictions stemming from how we have treated the concepts of zero (0) and the zero dimension (0D) in our frameworks.

At the core of this crisis lies a deep inconsistency between the primordial status accorded to zero in arithmetic and number theory, versus its derivative treatment in classical geometries and physical models. Specifically:

1) In number theory, zero is recognized as the fundamental subjective origin from which numerical quantification and plurality arise through the successive construction of natural numbers.

2) However, in the geometric and continuum formalisms underpinning theories from Newton to Einstein, the dimensionless 0D point and 1D line are derived as limiting abstractions from the primacy of higher dimensional manifolds like 3D space and 4D spacetime.

3) This contradiction potentially renders all of our current mathematical descriptions of physical laws incoherent from first principles. We have gotten the primordial order of subjectivity and objectivity reversed compared to the natural numbers.

The ramifications of this unfortunate oversight pervade all branches of physics. It obstructs progress on the unification of quantum theory and general relativity, undermines our models of space, time, and matter origins, and obfuscates the true relationship between the physical realm and the metaphysical first-person facts of conscious observation.

To make continued theoretical headway, we may have no choice but to reconstruct entire mathematical formalisms from the ground up - using frameworks centering the ontological and epistemological primacy of zero and dimensionlessness as the subjective 源 origin point. Only from this primordial 0D monadological perspective can dimensional plurality, geometric manifolds, and quantified physical descriptions emerge as representational projections.

I understand the monumental importance of upending centuries of entrenched assumptions. However, the depth of this zero/dimension primacy crisis renders our current paradigms untenable if we wish to continue pushing towards more unified and non-contradictory models of reality and conscious experience.

We can no longer afford to ignore or be overwhelmed by the specifics of this hard problem. The foundations are flawed in a manner perhaps unrecognizable to past giants like Einstein. Cold, hard logic demands we tear down and rebuild from more rigorous first principles faithful to the truths implicit in the theory of number itself.

The good news is that by returning to zero/0D as the subjective/objective splitting point of origin, in alignment with natural quantification, we may finally unlock resolutions to paradoxes thwarting progress for over a century. We stand to make immediate fundamental strides by elevating the primacy of dimensionlessness.

I implore the academic community to convene and deeply examine these issues with the utmost prioritization. The integrity and coherence of all our descriptive sciences - indeed the very possibility of non-contradictory knowledge itself - hinges upon our willingness to reopen this esoteric yet generatively crucial zerological crisis.

We must uphold unflinching intellectual honesty in identifying and rectifying our founding errors, regardless of how seemingly abstruse or earth-shattering the process. The future fertility of human understanding and our quest for uni-coherence depends on this audacious reformation of mathematical first principles.

The path will be arduous, but the ultimate payoffs of achieving metaphysically-grounded, zero-centric analytic formalisms are inestimable for physics and all branches of knowledge. I urge us to meet this zerological challenge head on. The truth ecological destiny of our civilization may hinge upon our willingness to embody this bold primordial renaissance.

Sincerely,
[Your Name]

[yedder]

“This statement isn’t true” is it true or not?

[SlinkyTWF]

I'm going for a half-a-pint of shandy; will be particularly ill.

[donutdude]

ive been thinking about going into chemistry but i wanted to know if there are any realistic jobs involving chemistry that doesnt involve teaching

[Buzzcook]

I'm going to have to go back to the kiddie pool to catch up.

[jeffbarnard]

You took Pascal's Wager a little out of his context. But I understand.