Sorry. :chin:

Presumably you mean formal logic (since the question is logical in its very nature). Formal logic is in an identity crisis imo, due it's failure to explicitly distinguish "necessary" objects that are constructed according to convention and are hence fully specified, from objects encountered in nature that are vague and unspecified.

For example, I can construct a sequence of cakes from a bunch of ingredients by iterating a recipe in my possession. But I can also obtain an identical sequence of cakes by repeatedly pressing a button on a vending machine. Neither logic nor set theory take care to distinguish these two sets, because the process of construction is viewed as being either irrelevant to, or identical to, the meaning of "existence".

Consequently a hideous "bugfix" called "the axiom of choice" was invented in order to accommodate "non-specified" entities, causing mass confusion and yielding ridiculous implications in failing to treat sets and their construction on a case by case basis.

The problem is, this invariance "works" for predictive models and technological problems. The usefulness of the logic is then what matters. Also, there are fields I am sure, that take into account the variance you describe, and put back the subjectivity in the equation, such as quantum mechanics and relativity, etc. — schopenhauer1

Notice that when we point to the invariances of a language like Boolean logic, we are directing ourselves to an inscribed symbolism, something 'physically' present on a page or built into a device. But as I said concerning the way that our sense of the meaing of a symbol drifts the moment we encounter it and then try to return to it the next moment, the evidence of this isnt in the symbol itself but in what happens moment to moment between ourselves and the symbols, in the space between. Its kind of a catch 22.If you believe in the notion of invariance, you can just point to your logical symbol as evidence of it, and if you dont believe in invariance you will also point to those symbols for evidence, but with this 'in-between' space in mind.
The point isnt that logical symbolization is wrong or doesnt work, but that it works not because it is the manipulation of relations between invariant abstractions, but becasue it instantiates a narrative thematics with enough inferential consistency to make us believe in the invariance of its joints. But its the implicative consistency that makes it work. It not only doesnt need invariance, but belief in this concept holds back what our technologies can do, becasue they aren't designed to pick up on and take advantage of this natural drift in sense. instilling greater creative innovation in our machines will require that we explicitly tap into what we now only implicitly understand in our technological languages.

Invariance only works as well as its limitations allow it to, just as Cartesian philosophy 'works' only as well as its limitations allow. This is like saying that those who believe that truth is 'objective' can cite how wonderfully a non-relativistic approach to science solves problems. They cite the wonders of the hypo-deductive method and the linear progress of the sciences. But Kuhnian approaches to science(there is no objective truth), which believe that science is not a linear progression, and that scientific ideas change via revolutions rather than accumulation can argue that their way of understanding also 'works', but differently, and in a way that provides more options for creative advance of thought. This is because "truth is not objective" doesnt mean objectivity is false, it means the idea of objectivity is an island floating on a moving sea, but its adherents cant see past the edge of the island and so see only invaniance. Technologies used to build computing machines work wonderfully, but in a limited fashion.. In order to exceed these limits and accomplish what even the simplest one celled organisms are capable of in terms of intelligence , they will have to modify their vocabulary and methods.

Quantum mechanics and relativity dont question the fundamental basis of an objective causal logic, although they play around with applications of it in terms of specific mathematical models

Conway's game of life was small step in the direction i have in mind.

Thanks for that post, and the other mentions.

Suppose there were a way of looking at mathematics and logic that did not involve the issues you are addressing.

So for example you ask why it might be important to tie maths to logic. To do so requires that you treat maths and logic as if they are distinct. But if maths and logic are much the same thing, it would not make sense to seek to tie them together.

Another example is the puzzles around maths not being based on experience and yet being about things we experience. Perhaps there is something amiss in such an approach. As if one could learn to count without there being anything to count. We count the blocks, then the shapes, then the cats and fingers, doing something that is both the same and yet entirely different each time. How could counting not be something we do within the world? Would you express surprise that when you put one thing with another, there are two things? SO why should you be surprised that other sorts of mathematics are useful?

SO, again, it seems that it is your picture of mathematics that is the source of your disquiet.

On your other suggestion, the theory of evolution is itself a broad expression of mathematical and logical notions; so there is a sense in which seeing an account of logic and mathematics in evolutionary terms is still seeing logic and mathematics in logical and mathematical terms. It's not clear that any philosophical progress has been made here.

I’m struggling to wade through the swamp of words you’ve out out here. Maybe if you stated your issue in terms of what is “fact” and what is a “truth” - in a short paragraph - I’d be able to offer something vaguely constructive?

Also, if you have something to say regarding philosophical relativism and/or psychologism it would help me too.

Thanks

Amplified and seconded!

Thus logic that is metaphysically composed of "natural laws" becomes logic that is creatures composed of the patterns, recognizing the very patterns they are composed of. This might be where Banno was coming from in his idea that logic fits too well- like questioning why a glove fits so well. This also leans towards the idea that logic and math is in fact discovered. — schopenhauer1

And this. Why must logic and maths be either discovered, or invented. Why not both?

That depends on whether or not we’re dealing with ‘facts’ or ‘truths’. Logic is not reliant upon facts. Using logic doesn’t require understanding of logic - understanding of what is true or false does not require experiential facts.

For me this doesn’t seem to have been approached in this thread.

logic is entirely based on definitions and drawing 1 dimension, 2 dimensional, 3 dimensional, 4 dimensional and any higher dimensional relationships between 2 or more defiinitions.

The definition of 5 is (according to the dictionary) is 4 + 1. To know the definition of 5 you must know what the defintion of 4 is.

Does that help you understand?

1 and 0 are hard to define without saying. "i am one person" or there are 0 apples at my kitchen table.

"Logic doesn't require facts" - Only when our process of deduction isn't in question.

Remember, we usually need to verify our proofs via appealing to external facts, e.g. a calculator.

Remember, we usually need to verify our proofs via appealing to external facts, e.g. a calculator. — sime

A calculator is based off of human and actual logic. If humans can't come up with facts that are rational then neither can a calculator or computer.

At some point everyone needs to agree on basic facts. The issue quite often is some problems that need to be solved need to be solved quickly. Most problems if given the right amount of time can be solved with an optimal solution. A SWAT officer doesn't always do the optimal thing because he/she has to make quick decisions. A judge in a court case has alot more time and has a higher probability of making an optimal decision in a court case.

yes, we appeal to external witnesses, such as the operations of computers, or to the opinions of others, in order to conform whether or not our reasoning is tautologous. But this external checking not only confirms whether or not our reasoning is in accordance with our logical definitions, but it also constitutes part of the very meaning of our logical definitions. For the meaning of "ideal" logic must ultimately be witnessed by practical state of affairs, if it is to have public meaning.

So in my opinion, logical necessity is empirically contingent, although not contingent upon the testimony of any particular external witness.

i'll have to re look up what empirical means but that seems to make sense to me.

So for example you ask why it might be important to tie maths to logic. To do so requires that you treat maths and logic as if they are distinct. But if maths and logic are much the same thing, it would not make sense to seek to tie them together. — Banno

Sure that's another way to look at it. I think we have to try to understand why Frege wanted to tie math to logic. I made a "jump" perhaps on why Frege wanted to tie math to a manageable set of axioms and symbolic framework by saying it was due to the idea that logic is more amenable to human reasoning itself.

First let's define logic. Is it purely the forms that were started by the Greeks (notably Aristotle and the Stoics) and later refined by people like Leibniz, Boole, Frege, Russell, Whitehead, Peirce, Tarski, et al? Or is this more "formal logic" of symbols, and relations of the symbols through various methods of inference a specific form of the mere act of inferencing itself?

I think logic as its own genre of inquiry may have culturally started with the Greeks (and other cultural contributors that synthesized with the Greek method etc. etc.), but inferencing itself is simply part of the human animal's capabilities. Our ancestors and tribesman today can inference about a lot of natural phenomena (what causes sickness, what plants have healing properties, etc. etc.) and this inference ability is indeed an informal form of logic. Inferencing from a specific set of circumstances to a broader class (or vice versa), and deducing conclusions from broader notions, are done even at this pre-agricultural level of existence.

Further, being that logic is much to do about observational patterns (a posteriori) and internal patterns (a priori), both forms of knowledge are innately tapped into, by all humans and cultures in some form (though not formalized and distilled into its own genre and then applied afterwards). Rather a rudimentary form was the basis for the distilled/applied form later on crafted and refined by the Greeks through accumulated cultural learning. These, in turn, cannot be helped to be substantiated in the human as it is necessitated by the laws of evolution/survival that animals either follow patterns of instruction (instinct/most other animals), or recognize patterns of instructions (humans).

@fdrake@StreetlightX you may be interested too.

But its the implicative consistency that makes it work. It not only doesnt need invariance, but belief in this concept holds back what our technologies can do, becasue they aren't designed to pick up on and take advantage of this natural drift in sense. instilling greater creative innovation in our machines will require that we explicitly tap into what we now only implicitly understand in our technological languages.

Invariance only works as well as its limitations allow it to, just as Cartesian philosophy 'works' only as well as its limitations allow. This is like saying that those who believe that truth is 'objective' can cite how wonderfully a non-relativistic approach to science solves problems. They cite the wonders of the hypo-deductive method and the linear progress of the sciences. But Kuhnian approaches to science(there is no objective truth), which believe that science is not a linear progression, and that scientific ideas change via revolutions rather than accumulation can argue that their way of understanding also 'works', but differently, and in a way that provides more options for creative advance of thought. This is because "truth is not objective" doesnt mean objectivity is false, it means the idea of objectivity is an island floating on a moving sea, but its adherents cant see past the edge of the island and so see only invaniance. Technologies used to build computing machines work wonderfully, but in a limited fashion.. In order to exceed these limits and accomplish what even the simplest one celled organisms are capable of in terms of intelligence , they will have to modify their vocabulary and methods.

Quantum mechanics and relativity dont question the fundamental basis of an objective causal logic, although they play around with applications of it in terms of specific mathematical models

Conway's game of life was small step in the direction i have in mind. — Joshs

I think we are actually getting at similar conclusions. Look at my previous post about this here: https://thephilosophyforum.com/discussion/comment/292703.

I too think that the kind of logic that the Greeks crafted, and that was then taken up and further elaborated by people like Frege, logicists, and analytics, were refined and "invariant" versions of the more general inferencing power of the human animal in general. It isn't the only version of inferencing, but a very formal version of it. Tribesman's inferencing works in their environment.

Here is where we disagree, perhaps. The more refined version of logic, which stems from the more general inferencing power, has more efficacy in prediction and technological efficacy. Thus, there is perhaps a realism going on that this more refined version is intuiting. Perhaps there are more refined and elaborated logics that are less "invariant" but that doesn't negate the fact that there is some patterns that are being intuited, be them by old-school invariant styles or new-school variant styles.

What is logic as its own distinct identity?
What is logic before we or anybody else imparts any limitations to it?
What is logic before it was a part of philosophy, of mathematics, before it was designated as something to be taught by somebody, etc, etc? (I'm not asking that we should ignore what has been taught over the years but, as they do in science, let us try to track back and see if we could identify logic as itself. It's like investigating the origin of the universe or an earlier state of our earth, let us track logic and observe what it is or could be as an identity.)

We have this thing we call reason or reasoning and most of the time we imply that to be logic. This may be because, as some people say, everything is an illusion taking place in our mental faculties since nothing can be known outside of it. However, the mind is not self/all-existent, is it? We don't consume foods to feed our minds, do we? (And, if we did, how could those foods exist outside the mind, and as what?)
Also, the concept of others (other things, people, subjects, objects, etc) is always in opposition to the concept of our self-identities. If they were a part of ourselves (our minds), there would be no such opposition, would there?
Another thing is we speak of reasoning about this or that, and we know or realise that our reasons and reasoning can be illogical or limited in relation to logic without negating the faculty or capacity to reason. So, what does that mean?


Basically, I'm asking, is there logic beyond our reasons or reasoning and what is it?
Obviously, I'm implying that logic does exist beyond our reasons or reasoning. The identity by which I designate it is what is somewhat controversial, if I may say so myself.
To me, logic is the expression of the laws which govern activity in nature. Here, nature being interactive reality and thus the relative aspect or designation of reality. Therefore, logic designates the mode of operation of nature, whether a specific or collective circumstance, depending on the point(s) in focus. It defines the how but not necessarily the why "things" are.

Which brings us to our application or use of logic. We are limited in our expression of reality. This means we are a part of nature. Also, we are limited in our operation of that nature, which means we are a specific circumstance at best even though we may be a collection of lesser circumstances, fundamentally. Basically, we are not the whole of nature.

We can conjure relations/concepts in our minds which connect to and with every possibility extant in those minds. Such a concept we designate as an absolute. It is a concept which connects to all other concepts, contains all other concepts, exists within all other concepts, influences and determines all other concepts and its identity and character cannot be influenced or determined by any or all of the other concepts. It is itself and as such, an absolute. (We know of such - God, Reality, Life, Energy, etc depending on application.)
But, what is the purpose of an absolute concept? My hypothesis is, absolutes are used to set the limits. In analogy, when we know how high a building should go, we are able to calculate how low the foundation should be for the best stability, and vice-versa. Here, stability being the absolute or the determining factor. I think logic is such a determining factor in relation to our reasoning capacities and faculties.

Why must logic and maths be either discovered, or invented. Why not both?

Does the law of the excluded middle not count here? If not should we immediately stop saying “invent” and “discover” and instead say “disineventcover” or some such term?

This depends purely on the view of what are antonyms and what kind of antonyms they are if they are antonyms. Often people confuse ‘absence’ with ‘opposite’ - I don’t think it is fair to claim that the absence of discovery necessarily means invention in the sense that discovery and non-discovery do. So what kind of an antonym is discover and invent? It seems to me that discovery may come about through exploration or not, whilst invention is a purposeful act (always; regardless of the outcome of the inventive act being useful in areas accidentally). If that is agreed then do we commonly say that something is both purposeful and non-purposeful? Obviously not. So we are not dealing with a gradable antonym it seems. Do we say the existence of discovery requires the existence of invention much like husband necessitates wife?

The connection for me seems to be that we invent, by way of refinement of otherwise, tools to assist in the act of discovery. We do not discover an invention or invent a discovery.

What is discovered can be lost and found again. We could burn all the science books on Earth and stop teaching natural science and logic. Regardless, the same laws and rules of discerning patterns in nature will be discovered in future generations not different ones; meaning these things are discovered yet the means by which we apply ourselves practically to human life means we may invent different pathways - if such a dark age were to happen maybe someone would discover some barely untrodden or neglected paths leading to slower or faster progression toward what we have today.

The only point of contention is in the language used. Do we discover or invent methods of investigation, or is that question badly conceived because it misframes the practical use of ‘invent’ and ‘discover’ needlessly conflating them by using common parse in a seemingly technical manner? I would say that we invent methods and continue to use them if they continue to reveal natural rules/laws to us. We don’t know what we’re going to discover and as we’ve been at this game for a long enough, and consistent period of time, it appears that we are ‘inventing’ when really we’re applying past discoveries toward future outcomes that have degrees of deductive validation regarding what we believe/expect to happen due to causal events - yet we don’t adjust our pure mathematics to fit reality because it is abstract; hence ‘pure’.

A hypothetical pure mathematical deduction can be refuted or proven abstractly. Its relation to actuality is irrelevant to the task at hand.

Does the law of the excluded middle not count here? If not should we immediately stop saying “invent” and “discover” and instead say “disineventcover” or some such term? — I like sushi

There is a word like “disineventcover” that indicates the mutual dependence of invention and discovery. It's called 'enaction'. To enact a world as a living organism or not to adapt to an already existing world as Darwim thought, nor is it to evolve independently of ones environment, but to adapt to an environment that the organism is continually reshaping in line with its own self-organizing direction. At the level of thinking, enaction means that we neither simply discover a world that is out there independently of our aims, intents and purposes, nor do we fabricate it out of whole cloth. Instead, we discover a world that derives its intelligibility from our pre-exisitng frames of understanding(worldviews, paradigms).

Isn't most of the everyday logic essentially an inductive one. The Goldbach conjecture is an inductive one but while waiting for a deductive proof, it can be assumed to be correct for all practical purposes. Inductive logic often ends with a deductive proof like in the case of Fermat last theorem.

And this. Why must logic and maths be either discovered, or invented. Why not both? — Banno

The problem is, set theory fails to explicitly distinguish 'constructed sets' that correspond to an algorithm known to the logician, from 'discovered sets' encountered externally in the real world, but whose construction is unspecified.

If Set Theory were to insist that all sets can be constructed by an algorithm, then Set theory would also insist that nature is describable by an algorithm, i.e. that a Theory of Everything exists. Yet it cannot ever be known if such a Theory of Everything exists:

Take the example of a vending machine that dispenses a set of items. Should it be the job of set theory to insist that every vending machine has a mechanical implementation, whether or not we know of it's inner workings? Should Set theory automatically assume that every can of coke within the vending machine has a distinct identity before it is dispensed?

Standard non-constructive set theory has a means of specifying an "unspecified set", such as that produced by a mysterious vending machine, namely the Axiom of Choice. But ironically the name of the axiom is a misnomer, because the Axiom of Choice is only useful in mysterious situations where we cannot specify a choice procedure.

As I wrote in earlier posts, according to phenomenology since Husserl, you've got it exactly backwards. Existence is irreducible, and logic presupposes it. There are explanations which precede logic, of which logic is just a historical derivative mode , and not a necessary one. — Joshs

Of course existence is irreducible, insofar as it is not an idea, just as anything cannot be reduced to the mere idea of it. The idea of existence or being is also irreducible, it is the most primordial note of logic, but it cannot be explained in terms of any more "fundamental" notion. So. I have no idea what you mean in claiming that "I have it backwards". I also have no idea what you are referring to when you say that there are explanations which precede logic: all explanations are logical, insofar as they have there own logic. If an explanation is illogical, i.e. if it contradicts itself in gross, that is not merely in nuanced, ways, then it simply fails to be an explanation, or even a coherent statement. You don't seem to be making much sense here, but some examples from you may help.

Differences and similarities are not opposites, they are both implied in every meaning. Invariance is not opposed to change, it is the effect of a constructive activity that maintains itself over time as the same differently. In order to be invariant, a meaning has to reflectively turn back on itself so that it can persist as itself. The effect of exposure to context guarantees that this reflexive move exposes any meaning to alteration of sense. Thus invariance is always the invariance of a meaning whose sense begins to drift at the moment of its turn back on itself in reflection. So the illusion is created of pure invariance only because this continual drift of sense of a meaning is subtle enough that most dont notice it. From this inattention to change within identity was born the concept of pure invariance and the law of non-contradiction. — Joshs

It would help if you addressed what I have actually written. I only quote this whole passage to respond to the litany of irrelevant responses contained in it. I haven't said that differences and similarities are opposites or that invariance is opposed to change. You say it is "the effect of a constructive activity that maintains itself over time as the same differently". It is the constructive activity which is invariant, not the way in which it operates from moment to moment. I have already acknowledged that several times. So, you are just repeating things I have already said in different words and making out as if what I have said disagrees with what you are saying.

I haven't anywhere spoken of "pure invariance", whatever that could even be thought to be. All I can think of at the moment is that it would be absolute stasis, which is impossible, and in regards to which the term 'pure invariance' would not even seem to be necessary and thus appropriate. The idea of pure invariance could only be a purely formal or logical one. Speaking purely logically I could say, for example, that my being myself throughout my life is an example of pure invariance, in the sense that I have not at any moment been anyone else. But of course that is a purely ideal notion, in actuality I am not hermetically sealed off from the world; just in the acts of eating and breathing I am constantly partaking of the world and consequently constantly changing. The invariance consists in the fact that it is I who am changing

But what you likely would not have noticed is that the SENSE of the meaning of the object or word wandered very slightly over that period of time. — Joshs

What, you don't think I would notice that the thoughts and associations stimulated by staring at the object are constantly changing? :roll:

The point about the logical sense of invariance is that, referring to your little thought experiment, I experience myself as staring at the same object throughout. Without the logical sense of invariance that comes from the apparently completely unchanging nature of at least some sensed objects, which establishes their identity, you would not be able to posit the thought experiment involving staring at the same object for a time in the first place.

The only point about non-contradiction is that you cannot coherently say contradictory things applying to the same object at the same time; for example, you cannot coherently say that an object is simultaneously white and black all over.

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Okay, we can say "evolution". But then what is it about evolution that allows for properties to work? Evolution works by way of differential survival rates. Thus, it may be said that it was advantageous for humans to think in these ways. — schopenhauer1

It’s a whole other thread, but I don’t necessarily accept evolutionary accounts of reason. Which is not to say that humans didn't evolve, as we clearly did, along pretty clear (albeit complicated) lines. But when we get to be able to reason and speak, then those abilities really escape the gravity of biology, as it were. (I've been reading about an evolutionary theorist, Kenneth R Miller, whose book The Human Instinct: How We Evolved to Have Reason, Consciousness, and Free Will goes into questions like that. He's not an ID proponent, in fact has testified as an expert witness against ID in US court proceedings.)

I think there's this kind of unthinking assumption that reason evolves, like teeth or tentacles or whatever (to put it crudely) but what see evolving is the capacity to reason - the ability to grasp abstract truths. And I don't think that is accounted for by Darwinian theory as such, as it's not necessarily a question that's strictly biological. (Interesting footnote: neither did Alfred Russel Wallace, who broke from Darwin on this exact question.) So when we perceive necessary truths, etc, we're actually thinking and reasoning in a way that animals generally don't (notwithstanding bee dances, caledonian crows or puzzle-solving octopuses). Hence the Greek definition of 'man as rational animal', which, I think, connotes a genuine ontological distinction.

these patterns were prior to and independent of human conventionalizations of the best ways to recognize them. — schopenhauer1

You're still operating with naturalistic premisses when you say this which, again, you reinforce by re-stating that 'Recognizing patterns becomes the reason why humans can survive'. So, again, this implicitly subordinates reason to survival, (which I *think* is rather similar to what the Frankfurt school criticized as the 'instrumentalisation of reason'.)

We have the picture, or the theory, well attested by evidence, of the ancient universe, before humans evolved, into which we then emerge at a relatively recent time, in geo- and evolutionary terms. That's the modern worldview which is implicitly realist. But what this doesn't see, is that the 'prior truths' that traditional philosophy elucidates, are not themselves a product of this process, but transcend the process. Not 'timeless' in the sense of existing in some 'ghostly ethereal domain' (as we nowadays are inclined to imagine it) but they are foundational to our ability to conceive of time (and therefore develop theories about it) in the first place. So, not temporally, but logically, prior. That is the sense in which traditional philosophy thought them to be nearer the source or ground of being, than what is revealed by sensory perception alone. But what with the abandonment of traditional philosophy, and the concentration on exclusively naturalistic (read: what science can explain) principles, then the original intuition about the significance of the rational intellect proper (nous) has been lost. And one visible consequence of that is the diminishment of the sense of wonder, which, I think, is undermined, whenever we seek to rationalise our abilities in biological terms.

Here's a question that I would genuinely want to get the views from people on PF. Hopefully people understand my question.

Let's assume that there would be an explanation to why we have Russell's paradox and the incompleteness results of Gödel, Turing etc. Hence there would be a central axiom in mathematics, axiom X, that without it we have get into paradoxes and incompleteness results, because we don't take into consideration axiom X, so our logic "breaks down" and we have to settle with ZF-logic or other kinds of logic.

Would there be any other problems with Frege's ideas (naive set theory) and the idea that mathematics is comes out of logic? Is the set-of-all-sets the only problem?

Logic is the simplicity of functionality; waste energy, per sey.

How a human can command a vehicle. Instead of reducing it to each tiny detail, the logic is the simplified event of a human commanding vehicle. It makes sense.

The universe is deeply seated in Logic, when trying to transfer the analogy to the logic behind day, it won't seem fitting because days are not technology, but natural logic.

It’s a whole other thread, but I don’t necessarily accept evolutionary accounts of reason. Which is not to say that humans didn't evolve, as we clearly did, along pretty clear (albeit complicated) lines. But when we get to be able to reason and speak, then those abilities really escape the gravity of biology, as it were. (I've been reading about an evolutionary theorist, Kenneth R Miller, whose book The Human Instinct: How We Evolved to Have Reason, Consciousness, and Free Will goes into questions like that. He's not an ID proponent, in fact has testified as an expert witness against ID in US court proceedings.)

I think there's this kind of unthinking assumption that reason evolves, like teeth or tentacles or whatever (to put it crudely) but what see evolving is the capacity to reason - the ability to grasp abstract truths. And I don't think that is accounted for by Darwinian theory as such, as it's not necessarily a question that's strictly biological. (Interesting footnote: neither did Alfred Russel Wallace, who broke from Darwin on this exact question.) So when we perceive necessary truths, etc, we're actually thinking and reasoning in a way that animals generally don't (notwithstanding bee dances, caledonian crows or puzzle-solving octopuses). Hence the Greek definition of 'man as rational animal', which, I think, connotes a genuine ontological distinction. — Wayfarer

Sure, weeding out what is an exaptation and what is truly selected for is a tricky area. I am not sure experiments that are/could be done to prove one way or the other. But, we can posit that certainly inferencing ability whether an exaptation that "piggybacked" on an actual selection (better tool-making, increased brain size, better social learning, etc.) did not hurt the animal, and in turn lead to other possible selections that actually refined this ability further. So what once was a "spandrel" (pace Stephen Gould) is now an integral part of the organism. So not only genetic changes, but phenotypic changes that were generally just happenstance, become coopted as a necessary functioning of that organism.

Hence the Greek definition of 'man as rational animal', which, I think, connotes a genuine ontological distinction. — Wayfarer

I actually agree with you/them here, but for possibly different reasons. We are ontological distinct in the fact that our language ability subsumes everything about our cognition. In order to understand "glass has water" we must have the underlying ability to formulate the world into distinct concepts/use syntax etc. How this occurred is another interesting area that has a lot of current imaginative approaches (see Terrence Deacon's "Symbolic Species" approach for example). Certainly to me, it seems there had to be a synthesis of sexual selection, greater need to pick-up social learning already present in our chimp-like ancestors, and tool-making which was evident early on.

You're still operating with naturalistic premisses when you say this which, again, you reinforce by re-stating that 'Recognizing patterns becomes the reason why humans can survive'. So, again, this implicitly subordinates reason to survival, (which I *think* is rather similar to what the Frankfurt school criticized as the 'instrumentalisation of reason'.) — Wayfarer

Yes that is the point. One can say this is a highly anthropic point of view contra speculative realism. That is to say, that patterns had to be apparent to us in order to survive. These patterns, more-or-less had to be "true" in order to maintain our survival, or we would die out fairly quickly or have to find other modes of survival that do not involve leaps in cognitive inferencing, pattern-recognition, and accumulated knowledge. In turn, contingently, through time we turned that inferencing nature on the world itself and have "hit upon" some fundamental patterns of the world that can be harnessed and used for accurate predictions. These patterns aren't arbitrary, or based on contingent circumstances of culture either. Mathematically-derived empiricism works. If one wants to subsume it in the idea that it is only "useful" that also works, as in this case, what is "useful" is what is exactly what is telling us about the world itself.

And one visible consequence of that is the diminishment of the sense of wonder, which, I think, is undermined, whenever we seek to rationalise our abilities in biological terms. — Wayfarer

Perhaps, but there is room in realism with extreme Pythagoreanism (all is math, and we can more-or-less understand some of it, clearly), or Whiteheadian panpsychism, the hyper-chaos theory of Meillassoux, and many other speculative approaches that are "real" in the sense of the theories bieng ontologically grounded rather than focusing on how they epistemically constrained. Of course, I think there is room too for seeing the ontological through the constraints.

Here's a question that I would genuinely want to get the views from people on PF. Hopefully people understand my question.

Let's assume that there would be an explanation to why we have Russell's paradox and the incompleteness results of Gödel, Turing etc. Hence there would be a central axiom in mathematics, axiom X, that without it we have get into paradoxes and incompleteness results, because we don't take into consideration axiom X, so our logic "breaks down" and we have to settle with ZF-logic or other kinds of logic.

Would there be any other problems with Frege's ideas (naive set theory) and the idea that mathematics is comes out of logic? Is the set-of-all-sets the only problem? — ssu

Let's assume that there would be an explanation to why we have Russell's paradox and the incompleteness results of Gödel, Turing etc. Hence there would be a central axiom in mathematics, axiom X, that without it we have get into paradoxes and incompleteness results, because we don't take into consideration axiom X, so our logic "breaks down" and we have to settle with ZF-logic or other kinds of logic.

Would there be any other problems with Frege's ideas (naive set theory) and the idea that mathematics is comes out of logic? Is the set-of-all-sets the only problem? — ssu

I'm not sure if he would weigh in, but that might be a great one for @fdrake, though I am not sure how much he is familiar with Russell's Paradox and Godel's Incompleteness Theorem's impact on Frege's logical project. I think Russell's Paradox and Godel's Incompletness is one example of the flaw in the logic itself. There may be broader criticisms that this approach is erroneous to begin with. Math may not be subsumed in a broader logic.

I think Russell's Paradox and Godel's Incompletness is one example of the flaw in the logic itself. There may be broader criticisms that this approach is erroneous to begin with. Math may not be subsumed in a broader logic. — schopenhauer1

I think that there isn't any flaw in logic. Logic is perfect, we just are not.

The most likely flaw that we have is that we presume natural numbers to be the basis of all math (because from that practical use the field has generated) and also think that we have all the fundamentals of math already at hand. This is our fatal "flaw" here: illogical premises that we are ignorant of.

So we erase the paradox away typically by the axioms of ZF, which however then does contain the axiom of infinity. Then we simply say that what Gödel's imcompleteness theorem refers to has not much if any value. Yet all the incompleteness results do seem to point towards the realm of the uncountable / unprovable yet logical existing. The problem is that people think about this as some kind of attack against math or progress. As one writer called Russell finding the paradox as "a skeleton rattling in the closet far louder than ever before".

We have made such false assumptions before like with the Greeks assuming that all numbers are/have to be rational and were dissappointed to notice that it isn't so.

am I not correct by saying a lot of logic is for clarity?

Getting through the substance of a matter is like decoding logic.

Logic is like mind fodder.

In my earlier post I mentioned, " human driving a car, when functioning, is logic when simplified. Rather than reducing it to the humans cause, it is neutral of cause and effect, as the matter is to be interpreted logically as man moving car, not scientifically but for thought.

Logic is a man-made tool that applies to propositions of a language. If you had no one to communicate with, if you didn't use language, then you wouldn't use logic. That doesn't mean you wouldn't or couldn't function in the world. You don't need logic to know that when you're thirsty you need to drink water, you just know it, you're driven to find water. You don't need logic to know that you must avoid touching fire, after you get hurt you will naturally avoid it.

We get lost inside our minds when we think using language, when we think about the tools we apply to language and wonder why they fit the world so well, but remove the filter of language and you can see the world clearly again, without the artificial problems we create ourselves in our minds.