Chapter 1: Logic as a Normative and, in particular, as a Practical Discipline

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§4 The theoretical incompleteness of the separate sciences

This section is interesting. The investigator of a science need not know the foundations of his science in order to successfully research it. Like the artist, the investigator follows his trained powers. He thinks and seeks in a particular manner. This however does not require him or her to know or understand the “ultimate grounds” of his discipline. The mathematician need not have a robust philosophy of numbers, only an understanding of their properties and interrelationships. No investigator demonstrates every premise of their arguments. Each science is hence in an incomplete state. This ultimately leaves them theoretically unsatisfying and “not in their entirety raised above all theoretical doubt.” (p. 59).

§5 The theoretical completion of the separate sciences by metaphysics and epistemology

To obtain this goal of a science above “all theoretical doubt” requires a metaphysical type of investigation. Actual reality has many underpinning theoretical presuppositions, such as the existence of an external world, extensionality in space and time, the dimensionality of space and its geometries, causality, and so on. These metaphysical presuppositions Husserl observes pertain to Aristotle’s First Philosophy.

What is perhaps shocking, at least for many Catholics uninitiated in phenomenology, is that Aristotle’s metaphysics is insufficient for our goal of eliminating all theoretical doubt. Husserl writes

Such a metaphysical foundation is not, however, sufficient to provide the desired theoretical completion of the separate sciences. It concerns, moreover, only such sciences as have to do with actual reality, which does not include all sciences, certainly not the purely mathematical sciences whose objects are numbers, manifolds etc., things thought of as mere bearers of ideal properties independent of real being or non-being. (p. 59)

There is a lot in this statement that needs to be unpacked. First, as we have already observed, Husserl claims that Aristotle’s metaphysics is insufficient to eliminate all doubts. The reason is because Aristotelian metaphysics is concerned with actual reality. Aristotelian metaphysics cannot account for objects outside of actual reality. Husserl here contrasts actual reality with those objects that are ideal. At this time what we know about ideal beings according to Husserl is that they are independent of real being and non-being.

Mathematics is an example Husserl provides of objects that are ideal and not real. This is also an indirect critique of Aristotle’s philosophy of mathematics since Aristotle places mathematical objects within real being. Husserl, on the other hand, claims that mathematical objects are ideal beings, independent of real being and non-being.

Even more interesting is the fact that Husserl claims that there are ideal sciences corresponding to ideal beings. Not all sciences pertain to actual reality. This is the fundamental critique Husserl makes against those who wish to hold that Aristotle’s First Philosophy can provide a certainty for all sciences. The science of mathematics serves as one counterexample.

In contrast to these sciences Husserl distinguishes another that is indispensable. The mode of investigation of this other science concerns “whatever makes sciences into sciences” (p. 60). This field is the science of sciences which Husserl calls Wissenschaftslehre, the theory of science.

§6 The possibility and justification of logic as theory of science

Husserl begins this section by observing that science does not consist “of a tissue of acts of knowing” (p. 60). Rather, “science exists objectively only in its literature” (ibid). This is perplexing, science exists only in its “written work”. The reason why Husserl claims this is because it is only in this form that science can be communicated and propagated across millennia, cultures, and generations. The insight Husserl is working with here is that science is something that itself demands to be communicated. Science to be science has to be communicated. In this encounter the work of science is to mold the person into the necessary preconditions for conducting studies towards the goals and aims of that science. It is in this sense that Husserl states “science aims at knowledge” (ibid).

Knowledge however implies the possession of truth. Knowledge requires a correct judgment, but correct judgment alone is insufficient for knowledge: “not every correct judgement, every affirmation or rejection of a state of affairs that accords with truth, represents knowledge of the being or non-being of this state of affairs.” (ibid). Husserl then distinguishes between a narrow and broad meaning of “knowledge”. Knowledge in its “narrowest strictest sense” requires a luminous certainty that what is affirmed is and that is rejected is not. Is and is not here refers to the reality of a state of affairs, such as the Pythagorean Theorem stating that the square of the two sides of a right triangle equals the square of the hypotenuse. This is a truth about the nature and reality of right triangles.

This conception of knowledge with the character of evident or luminous certainty is contrasted to blind belief and vague opining. Knowledge with this character of certainty cannot be conquered by skepticism. Husserl here is concerned about the problem of skepticism and how these two other forms of knowledge cannot survive the attack of the skeptic. These luminously certain truths on the other hand are self-evident such that not even the skeptic in good conscience cannot eliminate.

The blind belief and baseless opinion is contrasted to knowledge in a wide meaning. Knowledge in its wide meaning for Husserl means that this knowledge has a “mark of the presumed state of affairs or for the correctness of the judgement passed by us” (p. 61). Knowledge in the narrowest meaning has the mark of “correctness in inward evidence” and is an immediate intuition of the truth itself. This gives us some further details concerning what is “luminous certainty”. Knowledge in the narrowest meaning is defined as “being inwardly evident that a certain state of affairs is or is not”.

Knowledge in the wider meaning has inner evidence of high to low degrees of probability for correctness based upon these marks of the states of affairs. These serve to distinguish the reasonable from the unreasonable, and both from opinion. If our knowledge possesses any probability, then no matter how high of a degree of probability for the least likelihood of error, it must be distinguished from those truths that are indubitably so. Knowledge in the narrowest meaning therefore “counts as the absolutely fixed, ideal limit which the graded probabilities for the being P of S approach asymptotically”. Knowledge in the wider meaning with its probabilities approaches and gets closer to indubitable truths, but notice that Husserl used the term “asymptotically”. Asymptotically means that there will never be an intersection of wider knowledge with the narrowest meaning of knowledge. Any degree of probability immediately places it within this wider meaning. The narrow meaning of knowledge absolutely forbids any and all probability. Knowledge in the wider meaning can infinitely approach indubitable truths but never become such.

Now Husserl observes that science requires more than simply mere knowledge. If one were subscribed to Today I Learned on Reddit, he or she would learn several random facts, but this does not mean he has a scientific understanding. Random bits and groups of knowledge do not constitute as a knowledge of science. One needs to have a “systemic coherence”, that is, “finding grounds for one’s knowing, and suitably combining and arranging the sequence of such groundings.” (p. 62).

The aim of any science is not simply obtaining bits of knowledge or information, but finding knowledge “in such degree and form as would correspond to our highest theoretical aims as perfectly as possible.” (ibid). Husserl states that

The essence of science therefore involves unity in the whole system of grounded validation: not only isolated pieces of knowledge, but their grounded validation themselves, and together with these, the higher interweavings of such validations that we call theories, must achieve systemic unity. (ibid).

There are three ideas here that I emphasized. The first is the term “essence”. Husserl introduces the term here without explaining it. We will have to wait and see what he means by this term. As a historical note, there is fierce debate what Husserl means by essence given that Husserl underwent his own developments after the Logical Investigations. We abstain from this discussion. The second term is “grounded validations”, which is the subject of the next section.

The third term is “systemic unity”. This is an important feature of science. Science cannot be random, chaotic, or ordered according to the whim of man who then acts as its architect. “Science neither wishes nor dares to become a field for architectonic play.” (ibid).  Science is not an invention of man, but is “present in things, where we simply find or discover it.” (ibid). Science is a conquest of the realm of truth with knowledge. The realm of truth is ordered, “unified by law”. This requires that sciences be systemic to “reflect the systemic connections of those truths” and to progress from known truths to higher ones. Husserl calls this a ladder.

Husserl next expands upon what he means by “inward evidence”. Husserl states that inward evidence “is no gift of nature” (p. 63) which I take to mean that Husserl is rejecting the Cartesian notion of innate ideas, that some concepts we are simply born with by nature.  A characteristic of inward evidence is that it stamps a state of affairs as having real being or as absurd with no being at all. This inward evidence for Husserl is limited to a few “primitive facts”. Husserl also notes that this inward evidence cannot be induced from propositional thought, even if it brings about a judgment.

Therefore there is the need of science to have grounded validations in order to pass from these immediate truths to higher truths to make science and the theory of science, logic, even possible.

§7 Continuation. The three most noteworthy peculiarities of grounded validations

Husserl now turns to three characters of grounded validations. First, grounded validations have “a fixed structure in relation to their content.” (p. 64). One cannot start with a biological fact to obtain a mathematical truth for example.

Second, the connections of grounded validations are “not governed by caprice or chance, but by reason and order, i.e. by regulative laws.” (ibid). Arguments follow certain syllogisms. If A is B and B is C, therefore A is C, is a syllogism that can express a multitude of arguments. Syllogisms are “class concepts”. These have the character of a priori, and so any argument that follows these class concepts with valid premises are necessarily so.

These class concepts are a form that “resides in our modes of validation” that validates all of these arguments that follow these forms of logic.

Wherever we ascend by an establishing argument from given pieces of knowledge to new ones, a certain form resides in our modes of validation, which is common to countless other validating arguments, and which stands in a certain relation to a general law that allows us to justify all these single validations at one ‘go’. (p. 65)

Third, the forms of validation which are the the subject of logic are free of all scientific field limitations. It is not as if one logic applies to biology and another to psychology; rather, the same and one logic applies to all sciences. “We may in fact say of all other types of syllogism that they may be so generalized, so purely conceived, as to be free of all essential relation to some conceivably limited field of knowledge.” (ibid).

§8 The relation of these peculiarities to the possibility of science and the theory of science

This section is a continuation of Husserl’s observations from the last. One interesting side note Husserl makes is that man is “all too little disposed to turn everyday matters into problems”, (p. 66) that is it appears that the human condition is such that we prefer a surface explanation without a rigorous probing into the nature of things. I am reminded of the example of Socrates here challenging the streets of Athens with his questions about virtue, justice, piety, etc.

Husserl in this section gives an extended argument that validating arguments must have forms and be lawful. One immediate consequence if the opposite were true is that then there could be no science. No method of argumentation could serve as a paradigm for right reason. The imbecile and the intellectually gifted would both be in the same situation for there would be no logic by which one could say a proposition P is true or absurd according to the state of affairs. Summarizing his argument, Husserl writes:

If all this shows that it is regular form that makes possible the existence of sciences, so, on the other hand, it is the wide degree of independence of form from a field of knowledge that makes possible a theory of science. Were there no such independence, there would only be coordinated logics separately corresponding to the separate sciences, but no general logic. (p. 67-68).

This independence Husserl is referring to is the independence of form from the many manifestations of a syllogism. If A is B, and B is C, then A is C is a form with many propositional statements forming valid arguments. The form here however has its own inward evidential character and apriority apart from the propositional arguments corresponding to its form, and hence why the form is independence of any particular sciences and belongs to a general logic.

§9 Methodical modes of procedure in the sciences are in part validatory, in part auxiliary devices towards validations

This section Husserl outlines several methods for validating arguments. Validatory methods include abbreviations and substitutions. Auxiliary methods include clearly defining terms to avoid ambiguities, nomenclature, classification, and algorithms.

§10 The Ideas of Theory and Science as problems of the theory of science

Building off of what was said earlier in §6 concerning the systemic nature of science, Husserl notes that science is not concerned with mere validations, for such validations can appear in isolation. Science requires a coherent unity and system of validations.

Since this is the case, logic, the theory of science, must therefore analyze

sciences as systemic unities of this or that sort in other words, with the formal features that stamp them as sciences, with the features that determine their mutual boundaries and their inner articulation into fields, into relatively closed theories, with the features which fix their essentially different species or forms etc. (p. 70)

Furthermore, the task of logic as the theory of science includes not only separating valid from invalid arguments, but also valid from invalid theories and sciences. It is interesting to note here that some sciences are actually not sciences but pseudosciences. This further requires investigation into a science’s methods and procedures.

§11 Logic or theory of science as normative discipline and as technology

From what has been thus far said, Husserl concludes that logic, the theory of science, is a normative discipline. All particular sciences are distinguished from logic in that they are mental creations directed to a particular end and are judged by that end, (cf. p. 70-71). Logic distinguishes itself by seeking to “search into what pertains to the genuine, valid science as such, what constitutes the Idea of Science…” (p. 71).

Logic separates itself as a normative discipline precisely because logic measures the empirical sciences and how well or lackluster they are approaching their ideals.

For it is of the essence of a normative science that it establishes general propositions in which, with an eye to a normative standard, an Idea or highest goal, certain features are mentioned whose possession guarantees conformity to that standard, or sets forth an indispensable condition of the latter. (p. 71).

§12 Relevant definitions of logic

Husserl next briefly mentions some definitions of logic mostly based upon the notion that many have held that logic is a technology, such as a “technology of judgment, of reasoning, of knowing, of thinking”, all of which Husserl labels as misleading, (p. 72). One particular point that was fairly entertaining is the criticism against those who believe that logic is to be defined as a technology of an activity, like painting and singing. If we think about the act of singing itself, this has many types of requirements alien to logic, such as how to breathe, posture, and other variables required to be a good singer. Admitting that logic is such an activity admits many “doctrines wholly alien to it”, (p. 72). (Note that Husserl credits Bergmann for this type of criticism against this definition).

Husserl also mentions Schleiermacher’s definition of logic, that logic is a technology of scientific knowledge. The problem with this definition, according to Husserl, is that such does not take as its aim the rules for the demarcation, delineation, and construction of the sciences.