Folder 11 part 3 Scientific Methodology
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Scientific Methodology
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Scientific Methodology I. Introduction A. Scientific methodology in general can be taken to mean a study of the rules, principles, or ways followed in science. Here science is taken in the general sense to includphilosophy asas well as the experimental sciences. It doesn't mean to teach the method itself of procedure in the acquisition of science, for this is furnished by logic. It is rather a metaphysical critique considering the value of the knowledge acquired by this method -•-- the stability .of the physical definition. B. However, more precisely by "scientific« we do not mean science in the strict Aristotelian sense, but in the modern sense meaning discursivenon-philosophicalal knowledge, or facts controlled by a method. C. The procedure is by measurement; laws are constructed on the relations between measurements, and these are explained by theories, which are the results of the application of experimental logic. We try to evaluate these. D. Methodology is part of-the philosophy of science which is that body of doctrine in metaphysics which is con- cerned with scientific problems (I-II, 57, 1 & 2). E. There are three groups of questions in philosophy of science: 1. Concerning experimental science in itself -- the inductive method -- this is methodology. 2. Relations between experimental science and the other sciences (e.g. how can experimental science prolong the philosophy of nature?) 3. Judging and using the conclusions of experimental science (e.g. is• exp. science concerned with finality?) F. Methodology is a complement of metaphysics enabling it to proceed to concrete laws, etc. If metaphysics remains in generalities, it is imperfect. G. Ext erimental science must constantly confirm its findings '37770771771777=77 is not true of phil. of nature which although based on experience does not need to confirm constantly its conclusions in experience once they are established. . H. Dialectical prolongation of phil. of nature is of two kinds: 1. That which is subalternated to mathematics; it pro- ceeds by measurement and determinate quantitative aspects. The most rigorous among these is mathe- matical physics which treats of natural being insofar as measurable. 2. That not subalternated to math. although tending toward it (e.g.•biology). The method of mathematical physics is also applied to.biology and psychology, but only insofar as they use certain measureDcnts. : I. Order of course: 1. How are terms defined? 2. The relations between terms --physical laws, their value and elation. 3. Theories. 4. What is auction: is it strictly restricted to ex'er roen a flee? 4. In formulae what comes from _nature and what from r s g ,,-II. How are terms defined? A. In order to characterize a science its mode of defining must be studied (Physics II, 1. 3). This is also held by moderns, Eddington .- to begin physics we must abandon previous definitions and build new ones based on mean surements; a defined in relation to instruments o~f208.126.77.218 m_cas . ,.,..,. We. a• an• .. +t eia sens • es an • eep the common sensibles.. B. (Metaphysics X, n. 1935) measurement is always imperfect • and consequently .also such definitions. Measurements of very small quantities only serves to change the 1 thing measured, e.g. a.small quantity of .water is changed in -temperature by. the temperature of the therometer. 1. Definitions are always variable. 2. They do not attain the nature or essence of the thing but are only signs, attached to the first accident of substance; figure is the sign closest to substantial form. _ C. Physical law -. an algebraic relation between numbers, measurements. They do not ex re s -f. e -, y, IA"al - I but only relation and une on e.g.. they do not say that lessening the pressure is the cause of an increase vu~ap (J1'7,yep 6 in volume) . Is this relation in nature or only in the ?bind? They are based in nature but the univer i 1 ty; is laz '64.4i4 yr n..-by .the ming,, because laws are not perfectly able to be verified in experience. It is impossible ' to apply them directly and completely to reality. They are obtained from reality, but generalised by the mind. ct}1 .1-g.-- RP`°X4a ~ As to certitude, physical laws are merely approximative, not rigorous, for they are of an ideal object which does . not exist. 3,-III. Nature of physical theories. • A. A. Physics tends to unity, tries to synthesize experience into general formulae. This is attained even in laws, but theories represent a vaster synthesis: -- theory : law :; law 4 facts. . B. Theory or hypothesis - qproposition or group of proposi- tions posed to cr.pl,in known laws and • it est new experi- ments. They should imply consequences whit can be de- duced•and compared with other ..sown laws (something simi- lar happens in daily life: a friend is late, we guess a reason to explain this and from this we predict the hour when he will artive) It is not a mere resume of facts of experience, but is on another plane, that of nvcntion or discove of a relit etwce kno f• The hypothesis remedies the inchheence or tr Vl;.â tacts; it is not seen in reality, but is made by the creative imagination. It must make a relation between facts and make predictions. C. Law ceases to be empirical and becmtes rational when it can be attached to a -theory, when we see the wry, when it is not known merely by experiment. Duhem (p.24) does not believe theories to really explain facts; they are logical from which we can deduce laws. We create a theory when we can see relations between symbols and can see in it all known laws. D. Distinction between theory and hypothesis: 1. Jrpothesis has no cont1rmat1oh n expebiment; when corroborated it is a theory (a hypothesis confirmed by,.facq. 2. Hypothesis is the foundation on which $.a theory is built; theory implies a complete form or ensemble.. Hypo. thesis are propositions which enter into a theory (the form which groups and orders hypotheses.) E. Distinction between eneral and '•articular theories - made to avo s fa se pro • ems on e vu ue 01 p • s cal theories. 1. General - not general in the sense that it explains a great5"iumber of facts, but rather that it gives a va: ue and eneral on of • henomena; no ri formu ae or_praaiaigq. These are more • e ;. ve and have greater certitude. 2. particular- a circumstantiated and precise explanation of facts; formulae capable of serving as basis for deductions. These evolve constantly. F. Role of theories - we define them by their role. 1. Explain facts - to make known the reason or motive for facts, .ren-dering them coherent by creative thought. poses a system of equations from which we can deduce laws; gives an origin. The explanation remains sueject to change, but is of value. In math, physics we put laws into a mathematical setting. Our intellect is naturally bent toward deduction in order to see relations between brute facts (those which can not be attached to a theory). As long as they remain un- related, they are incoherent :.w sa k _tQ construct a proposition from which they can be duduced. A theory makes a synthesis and hence ism re intelli- gible than dispersed laws; then we can say that they are explained. ',Save sensible appearances!' - to explain them by propositions whose consequences agree with known facts. (I, 32, 1, ad 2) a certain hypo- thesis can safeguard appearances but this does not mean that perhaps they couldn't be better safeguarded by other hypotheses. 2. Provide means of prediction - (physical criterion) - other phenomena should be able to be deduced. from. it. Scientists look at facts to see if any disagree with the old theory and agree with new. They try to con- firm their predictions in reality. If a theory is good it contains many deductions, some corresponding to known laws, others u mown; some of the latter could be false. The hypothesis has for its object to make new discoveries and advance science. 3. Economy of thought - (logical criterion) - Einstein's theory of relativity Is good because it is simple and logically general, i.e. it explains many facts. A theory should: a. Substitute a formula which virally contains many b. Introduce an order among facts, even if provisional; grôup and make a resume of previous knowledge. c. Awaken thought;- thereby-provoking discovery of things whin-would have remained undiscoveredwithout the theory. 4 G.' Poincare ',Science and Fyrpothesisn, ch. 9: divides hypothesis into three groups: 1. Natural .. forms the common foundation for all physical theories and hence cannot be abandoned (these are really methodological principles), 2. Indifferent — secondary hypotheses which are needed in calculation, but are not themselves criticized, not confirmed or destroyed. • 3. Generalizations ,. those which are confirmed or re. jected by experiment. (hypotheses are not generali-. zations of laws; there is also the intervention of the creative imagination). H. Confirmation of theories ("rverification" _ but must not think that a theory is true) Characteristics of a good theory: 1. Secondary — seep, n_ . tr - . • • - i ly inco- heren ~xelatéd with e . Uleories. (But these are -n ttoo absolute because at first most important theories seemed absurd. Schiller .. 4ypotheses are progressively knocked into shape :..not necessary for it to be correct or probable in the beginning. We cannot compare it with abstract, a priori criteria. B r t_.ie = sentt ei tY at iG suggest._., method to
lae n..,re 1it3 . Note- - also that basic hypotheses
are not directly compared to facts, but only through deductions.) 2. Primary theory is good if it fulfills its role of: a. Simplicity — two things to be considered here: 1. Basic Formulae 2. Deductions to reach reelity .. in modern theories these may be very complex but the basic formulae still be simple. The simpler the theory and - the more it embraces, the more difficult be— come the deductions and mathematical calculations. b. Explaining facts. c, prediction —• suggest new experiments thus opening new paths to science. Pasteur good theories can. surely predict new facts from ,their relation to the old. Bad ones always have to graft on new hypotheses on to the old when new discoveries are made. Good ones keep their unity and coherence; . bad ones become more and more complicated, become impractical and incoherent and :. must be discarded. 3. The r,.~.ti r e g reality is not çe . E cper•iments show It to be as , o no pro,. th;,t it î fl )'tgnrc,ils) rLle. a. Imrrecision of measurements — we can never have precision although we tend toward it. Formulae made from experiments are only approximations and can never include all conditions. Menge in thecriey can result bee:.use a new one can more precisely explain facts. be Sophism of the consequent -- (Sophistics, 167 b 1) The sophism is when we think that the relation of the antecedent and consequent is reciprocal: if A exists then B exists :.if B exists then A exists. If we could say "only if A exists then B e;:ists'1, we could reverse it. But we cannot say this. 5 because it is always possible that another ante- cedent could better explain the conse :u;.nt. (I, 32, 1, ad 2) c, The fact that we can always have better hypotheses lowers the value cf a resolution to the absurd. (i.e.. saying: if proposition B is against experience then A is true). 1) There is involved not only proposition B, but also many theories in connection with it. When we contradict B we are not sure that it is really B that is contradicted; it may be one of the other propositions used, All we know is that something is wrong in the ensemble. To attri- bute it to B, we should know with certitude that all the others are o.k. 2) Even if wf:; disprove B we cannot say that A is true because there .may be a C, etc. There are not only two alternatives. A supposition is good when it leads to deductions which agree with reality. d. Einstein theories are not merely determined by exteriF reality; not merely read in experiment, but are creations of the imagination.. (e.g. the closed watch -- we imagine a structure from which we can deduce the observable motion, but we could supeose many kinds of structures, We can never compare our image with the real mechanisms comparison of formulae to reality are not made directly, but through deductions.) e. But a theory is more than a mere logical resume of laws; it must have a certain similarity to reality. 4. Sense of the term Uprobab] t as applied to a iec'ry: a. If we throw dice there is 1:6 probàbility ofgetting number two; also it is probabla that a train arrive at a given time, An event is prob-ble even if it actually does not occur. The uncertainty is with respect to the fact, not the probability. The result is something determinate and precise, there can be no approximation, e.g, nearly number two.. b. But in physics probability is somewhat different. In laws and theories terms have no such precision. Yhat is an atom? The sense of the term elaborates and changes and always remains provisional. We c nnot hold that ttatom" really adequately represents reality, but neither can we say that it does not represent it at all. It is an ap roximaticn in an endless chain of attempts, as a sketch which an artist nbaz renders more and more perfect, but which gives an image of reality. It is not as the arrival of the train which is either completely true or com- pletely false. c. (Meta. XII, lect 9, 2565) movements of stars are known by: 1 Sight 2 Instruments and attentive consideration 13 Declared by reason i,e, a hypothesis, We pose a movement in order and reduce to unity certain movements-which seem irregular and without reason.
6
(n. 2586) does not attribute necessity to his theog4
ries.
$. Practical and speculative truth of theories.
a. (introd. on Soul of DeKoninck - provisional character
of theories p. 75) in constructing theories speculative
knowledge is sought, not merely-their practical value
of changing the world.
b. Two value of a hypothesis:
1) -Instrumental - practical progress in science.
2) Speculative .. attaining truth.
c. We .must not deny the ability of any real explanation,
even if it is approximative.. If so natoms" etc.
would be purely fictive. This is Poincare's position;
he insists on their purely instrumental and arbitrary
nature. They are merely a resume, a logical synthesis
of experimental laws, and . cnnot give the: nature or
real structure of things.
d. This position in all its rigor is not admissible. Phy-
sips studies natural being under its quantitative
aspect. But quantity is the first accident and fun-
damental attribute of material substance, for it
inheres- immediately-in substance (De Anima, III, 707)
Figure is a quality determining quantity; it is very
close to substantial form and the surest sign of a
species (I, 35,' 1.- Physics VI, beet. 5, n. 5).
Physico-mathematical theories because they are about
quantity and figure are close to reality and :,reveal
something of the nature itself.. If not natu itself,
~ M~~ ^ e P a -o -s a egory-ofthe cave • rn ---•
figures on wall, Republic VII)
e. Newton's theory is still good, but is seen to be
restricted. Relativity replaces it in the sense that
it is more vast. Newton's becomes as a part of theory
of relativity.
IV. Life of theories.
A. Discovery of theories
no one' can give infallible rules for
scovering t eorfes. It is necessary to have a capacity
for seeing subtle similarities and rariidly evoking supposi-
tions. This may be called "creative imagination."
1. Scl~ - seems to be equivalent cf the modern "creative
777a 171on, n
a. (I Post. Anal., eh. 35)) 3 4ertia is a vivacity of mind,
a facility to see imvedietcly the middle term which is
t ie ceu se of the connection of subje end predicate
in the conelusioh.
b. Two procedures in the acquisition of science (II-II,
48, art. 1 and 4; Ethics IV, 1219).
1) communicated by another (disciple, virtue of docility)
2) by oneself - ...
invention (virtue of solertia)
a) by syllogism -- application of first principles
to determinate matter (De Veritate 11, 1).
b) by hypothesis -. when we do not know first prin-
ciples, but only certain propositions (I, 32, 1,
ad 2)
7
e) Solertia depends much more on a natur..l gift than
on application (I-II, 64, 1)
d) A ,theory is as a middle term which says the "why"
of physical laws. •
2. Discernment rnment of snalo — a resemblance of relation.
a. Mean g ogyti as used here:
1) (I Parts of Animals, 645 b 4-10) some animals have blood
others have something else playing a similar role.
2) (Post. An. ch. 8 a 20 ?) there ere analegical genera
of things playing the same role, a resemblance of re-
lation or proportion; a rhythm of thought between
relations: lung : pair :: x : water.
b. Kinds of analogy:
1) that enabling us to posit the existence of something
(un est) :
conditions on earth ---life,
conditions on Mrs ---_life.
We posit as a hypothesis the existence of life on Mars
because of a similarity between conditions on earth
and on Mars.
2) Thet enabling us to posit the nature of something
(quid est) .
ltmg ; air :: x :'water.
7r le conclude to « ho; n _tube of x because. of a ssimile- rity between the two relationships. c. The mind surpasses what experience gives. d, (I Topics, ch. 17, 108 a 8) we should Beek resemblances. . B. Evolution of theories 1. Theories are. pert ected as is a :ketch. If a theory ceases to e edict,it must be replaced because it has become too narrow. This evolution is not bad for science; in fact, it is an essen- tial condition of its development. If evolution ceased, pro- gress woulLi cease. 2. Claude Bernard — too greet faith in theories is scientific superstition. 0. science. must be submitted to facts. Even one well-established minor fact can cause the evolution of even the most logically thought--out theory. • Primacy belongs to facts, not to theories (De Caelo XI, ch. 13, 293 a23) 4. Evolution of theories is not lea:: for science because nothing is lost. Thenew theory embraces new facts and also all the old facts contained in the old theory. The point of departure is always soon, but ie of smaller significance because the new theory is vaster. • 5. F,ddington Mature of the Physical ,;orldt=— we must not base on scientific thcoriee, positions which pertain to other fields, such as philosob,hy or religion. 6. Aristotle's position en ethysic l theories — not merely from historical point of view, but to sock methodological. principles. a. Some moderns reproach Aristotle for not being experimental b but only logical: despising experiments, a mere verbalism or analysis of concepts. -Others hold that he was too ex— perimental end not speculative enough, did not cr. cite enough theories. b. Aristotle is held by scientists such as Darwin to be the father of biology. e. Einstein says that science is merely a purification of daily thought :.methodology is not something secret or unique. d. We must distinguish between: 8 1) Basic ' nrincipl2.1~ 2) 'Practical rtif"iCees of experimentation Basle priri^iples can be had even when artifices are not very developed, or before artifices. Even when artifices are developed we thouic1 reflect on basic principles, e. All theories are formed =..a too narrow experimental base; this is why they are replaced... If scientists waited for' all the facts, he could . never begin. All theories contain arbi- trary postulates.. f. Basic rincit^,ristotle — theories _mus always rerna,in °'uborel naacts e t~•t?nse ex erience. . g. Even i s ,'nia gas c e n e, does not ruin his basic principle. (De Caelo I,. eh. 3, 270 b 5-7) the incor- ruptibility. of the heavenly bodies seems to be upheld by the sense by hump conviction. (St. Thomas. on De Caelo I, lect. 71 n. 6) -.-hug.: n conviction means a certitude based on ob- servations of ,hot't duration of objects far :sway. :.only a prob,.,bility, not ne4 eeeity. The heavens could be perishable, but of such a long duration that we c::nnot observe changes.. h. One can use the experimental method without making expe,:•iments (changing the course of nature), merely by making ob::ervations. In astronomy experiments are not tossible. i. We should,e_ ept a theory to conform to nature, not vice versa. • We must trust primarily experiment, theories only insofar as they conform to experience. To find the value of a theory. we rust en..l=lire as to the conse.iuences of its application. It is not the pincinl a which gives value to the conclusion but • rather he co ... skin which ust f e2 't J. Necessit of experience eeiencew en we cannot construct a general pr ne p c is s due `o a lack of experience, as wa: the case with the Platoniets. We should not base ourselves on purely • dialectical or logical reasons; these are too general or empty. We should base ourselves on proper principles derived from experience. If we fall in this, the conclusions are empty because they tied to ce usos only in appearance (e.g. story of the mule) . Be distinguishes between logical reasoning (common principles) and physical reasoning (proper principles of natur._.l things) --III Physics, ch.. 5, 204 b 4. He also reelized the insufficiency and difficulty of .observation particularly with regard to the hoaveniy bodies. k. Value Aristotle placed in theories -- When further facts are observed, • then ola theories: may have to be changed (De Gen. ^niw._:lium III, ch. I0,. 351 na 19) . le saw theories to be Plausibl,one linens in vhicht49,,mtga„zsaLbeyond facts.
etre used not seokinb thy:., s:?.mo de ree of cex it 1 r ll sciences; . sometime only be possible conclusions can e attained.. For e theory the only necessity is that it mustn't be impossi- ble or inconvenient; i.e. producing conclusions contrary to sense experience. 1. Just because a science posesis priori hypotheses does not mean i that it is bad; in fact, the ion iC mind is characterized by its ability to do this. We can perfectly employ the experimental method even if theories are false and observation imperfect. The method is independent of this. 7. Pascal - experience is the only principle in physics. The ancient theories were good for the amount of experience they hear?. Proofs in physics are effected by enumeration of experience, not by demonstration. 9 C. Role of re son physics . we tr' to determine the respective parts rec.son and experience play in theories. 1. Here we do not mean the reason which deduces from physical theories, but rather, the capacity to create beings of reason, i.e.. those beings whose existence depends on reason (John S.T.; Cursus Phil. I, p. 235; Summa I, 13, 7; 28, 1) There is a double dependence: a. As an effect of reason -. reason :being considered either as an efficient or material cause (e.g. as a habitus depends on reason. for its existence). b. As. an object in the reason the object. has no real existence, but only exists in. the mind . (beings of reason): 1) Negation 2))- Relation a) corresponding to something to reality. b) 2nd intentions, i.e. something as known. 2. In the universality characterizing laws, the intellect sur- passes what is guaranteed by experience. The rational plan is not immediate in reality, but is constructed by reason. (Being of reason .-•- a priori concepts) Experience furnishes certain points of this plan, but there are gaps because not all possible experiments have been made.. The physicist tries - to fill these gaps-by reason -and and -form general laws- and the- ories capable of explaining them. Experience alone does not give universal lakes, nor the reason for them :..reason must intervene, hence science is a mixture of experience and reason, 3. Preconceived idea (a working hypothesis) when we say that the scientist must begin without preconceived ideas we mean that he must be ready to reject any hypothesis which contradicts experience, but not that he should start experiments without having a problem or question to pose.. This is a preconceived idea, a being of reason because formed before experience can • back it. In experiment there are two operations to consider (C. Bernard) a) premeditate, establish or determine a plan of experiment - the . uestion we want answered. (preconceived idea).. b) Read the facts - result of experiment (no preconceived idea) f~. A> >x~ UIca^rjtul i4 s an anticipated,:, a priori, position, a :question ec a e. All hypotheses constitute a question; we predetermine a possible answer (e.g.. is man a rational animal?) err. Role of reason in oranizine experiment - reason attributes phenomena a s rap.. e y w a. cao not have, to laws a universality which they do not have, and to elements a purity which they do not home. This occurs largely by controlling the circumstances in which phenomena take place,. e.g. falling bodies in a vacuum. In nature there is no vacuum; also, a perfect vacuum cannot be produced. It is a being of reason having no adequate correspondence in reality. The scientist creates systems, drops variables, etc. In a sense we can say that physics goes not attain re:.lity,. but an.. abatr.et.ion drawn...fr_om._ra _ .itY yot-its aim is to know reality better. Bodies and elements are idealized; their perfection is owed to the intellect. In measuring, the scientist, as it were, has two instruments: the real one and an ideal one in the mind. He must correct the real with relation to the ideal. o 10 a. Reason universalizes, a law: . 1) By interpolation — e.g. performs experiments on 0 & 2 and guesses at 1., 2) By exterpolation e. e.g. experiments between 0 & 500, than extends curve before 0 and after 500. b. Reason in theory -- seeks the Pwhy" of laws. This cen never be achieved by empiric study. He must postulate by creative imagination certain structures in order to explain laws. Theoric are not directly drawn'from experiment. (Proton is posed only for symmetry's sake, 1944); Many pure beings of reason .are posed for aiding calculus). 5. Justification of this process — science cannot progress without hypothesis. • Those who refuse to go beyond the facts often cannot even attain to the facts because often their discovery depends on hypotheses. It is impossible to create a theory merely by the inductive method. Beings of reason are necessary because of the weakness of the human intellect which cannot directly attain re— k ality. These hypotheses are dangerous only if we consider them ado to representations of reality. This would be idealism. D. EBperiment in physics. 1. experiment has two parts: a. observation of facts - for this it not necessary to know theoriE . be interpretation of facts — can only be done thanks to _theories; must know them and how to apply them.
- . theory intervenes in experiment anjresults have no meaning
without reference to theories. . 2. Scientific facts already include a great deal of theory. Facts do not interest the scientist except as verifying or explaining theories. To make the connection between facts and the questions asked.by the physicist already presupposes a body of theories. The common man sees only brute facts; the physicist sees them as scientific facts (ded . ' .l r trim • - menus of theories) As soon as a science is advanced, what is called a ac s ar from being a pure fact. 3. Kinds of facts: a) Occurrences — (e.g. historical. facts) no theory intervenes. ---, b) Mercury boils at 3270 — physical law only approximative; . taken in all its rigor it would apply only to ideal mercury, a being of reason, for reason intervenes to generalize. „t,E, ice_ .4,, .. F z 13z alti=ed. _. e) Light rays curve when passing near the surface of the • sun -- here lixammost it is very complex; the role of 'sim! ale obser- vation is negligible: spots on a negative; t t.j,;, e- 4. Brute facts are es_.the material from whiçh_ .science .5 ...out its scientific facts, - In astr.onory there arcs no p ii facts of ô5-S-6ry tiro those enunciated are already scientific facts.. 5. Difference between common and scientific experience: a) common — the senses state the immediate existence of a fact; complicated apparatus or use of theories is not needed.. Its characteristics are that-it is not very detailed or precise. b) Scientific — is precise and detailed; tries to interpret ob- servation by theories. Scientific is better as to precision and detail but the common is more certain because it concerns only generalities. Sciences of observation and sciences of ex erimentation e reasoning s ' e same, but facts • ave d J'feren or gins. We canse the perimental metho i witi.t .t tmaking. experiments: merely submitting ideas to a criterion oe ac s. es not matter 11 if these'facts came from observation or experiment„ Even if the ancients did not make many experiments this does not mean that they did not understand the experimental method. It is just as valid to use facts bbtained by mere observation. E. Inducation 1. The term "inductive sciences" is usually restricted to the ex- perimental sciences, but the process of induction is not proper tothese alone. Induction is presupposed to all science, even science in the Aristotelian sense. 2. tr-:z "Logic", eh. 21, pp418-.440 - Aristotle's method was deve loped before the scientific method, which is the only valuable one :. it is valueless and is as an encumberingldebris. We need a complete reform in the theory of induction; maintains that Aristotle's logic is tied to his cosmological beliefs. He ignores the Topics and says that Aristotle said that induction is supposed to lead to universal and necessary forms. Dewey holds that induction is an ensemble of operations establishing a generalization. 3. Aristotle (Topics VIII, 105 a 13) induction is progression from. particular cases to the. universal, from singulars known by sensation to universal (156a5) an idea of movement or pro- gression rather than of ratio. 4. Post. An, 81.2 38) (st. - 'homas, lect. 30, n. 4-6) us cannot know the universal except by induction, 5. (Ethics VI, 1139 b 28) all science can be taught;. all teaching proceeds from previous. knowledge either by syllogism or by induction (post. An. I, eh. 1, 71 a 7-10) . 6. Division of induction by consideration of the terms to which it arrives: •
- . To universal concepts - through propositions
1 Ab: olutel univecsa]. - induction is at least inç ireetly t ie .se _at e e ' nitions. Even iî logic does enter in, It combines. general notions obtained by inductions. 2) ppproxi natively universal - in the experimental sciences induction is much longer and more difficult. Cunstruction is interminable ;. a true universal is not attained, but only a provisory and approximate generalization which does not reveal the essential nature. 1 b. To universal ronositions - sual throu h r . a- ,- • #.,: z_z but not always, as in t "w ole Is grey or . an • is partIt. yet even here it i s possible to dispose it in the form of inductive reasoning. 1) Absolute. universal - first principles of science. 2) Ampr oxim.a: r, universal. Base( on common experience (probable) e.g. mother loves her child, b) 3nsed on scientific experience probable) physical laws. 7. Form of induc lion --from E1 po n o v eW õf~Pormal logic. (Albert, I Prior An, Tract I, eh 4, p. 147-8). (Aristotle, II Prior An, ch. 23) . • a. Form - seeing how terms are disposed as to quantity and :quality, and other logical properties. This point of view is presupposed to its application. in particular sciences. This study is common to both dialectician (probability) and sage (certitude) . It is established according to diversity of matter (object under such a form) . From the• formal point of view induction is. either complete or doesn't exist at all. From the material 12 point of view it can be either complete or incomplete. But this ` viewpoint comes after the formal one. b. The study of the form of inducts is related to that of the form of the syllogism and is implicitir],y contained in it. In induc- tion reason does not see the goodness of the formal conclusion and :. it is called an imperfect form of resoning from the for- mal point of view. Knowledge of the figures of the syllogism clears up the form of any kind of reasoning, including induction. c. Certain animals live a long time because they are without bile: A - to live long; B - to be without bile; C - horse, mule. 1) Syllogism: B --A C--B C--A 2) Induction; C --«A C-- B B--A Induction shows that the middle belongs to the major by me:..ns of .the minor,•but in induction the minor plays the role of middle. d. Comparisons: 1) he conclejon__of the syllogism is major premiss in induction am conclusion of induction is major premiss in syllogism. This is necessary because induction has as its aim to furnish conclusions to serve as point of departure in syllogism. 2) fi inor - n l' o 7 sm is middle in induction and middle in sy ogism in minor in indùétto . 3) In syllogism the _eonn.ection between extremes is established by the middle which is a tAuo universa , while in induction 'the major is attributed to the middle by the minor `which plays the role of middle .- Thes n er _ennI ueratied-_.s.ingulars. - e. Induction is imperfect because its middle is neLeeereeempeeiall, and also, what saves as a middle does not have t to position among the terms ;. The conclus on is not immediately seen. • f. In induction the minor premiss is affirmative and B is particular. yet we conclude to a universal affirmative :. the conclusion. does not seem true. It would be false from the viewpoint of logical form to arrive at a v :lid universal proposition as a conclusion. We must suppose on the side of C that t pl ta, that C contains all animals without bile, c tkuaL R no gr tite en r exts91, thus mak + . eiticn co t3.ble Jwe se vet e q.,çi ,Vi . .P?fi,NAt ..:gcav .z_on f _the pï•â `s-itionn.2- ïi.s conversion makes possible the formal consequen- ce w -Could not exist unless there were a comelete enumeration of singulars. Having_hillegomplete enumeration B has no greater .? . h conclusion th inhr tirEi i. • g.. But doescYnet,~i nco lû tï ÿ our posing tees: Peet ° aliisi"? This does not concern us here, for this comes from material induction; in formal induction we merely eosit it. All inductive reasoning must possess a note of universality in its form (Ipoat. An led. 4) he who proceeds by .induction from singulars to universals does not demonstrate by necessity because enumeration is not complete. h. The form of i nductio4s not tr._nsposed to the syllogism. They arc, two irreducible forms. Induction has no true middle term; it is merely an enumeration, What we do is use the same matter which was under the form of induction and then rearrange it in syllogis- tic form. However, this syllogism is not a strict one, for its conclusion is not a mediate one p owed through a middle term. Its conclusion is immediate because it is the same proposition 13 obtained by induction from the ennumeratien of singulars. Induc- tion is a• form of argument which in order tovvalid as to form requires complete enumeration of singulars. le- 8. M tter of induction singulars are furnished by experience; these forma the basis for induction. Certitude of induction is divisible according to its matter. a. Certain induction 1) complete enumeration .-the singulars examined are few is possible:. sality exists _ and form. :. conclusion is cer a ugh not truly scientinriTTS strict sense because it iu not kncreledge by causes; it does not give us the universal ratio. The enumeration is cause of certain knowledge of the thing, but not.of the thingitself. 2) incomplete enumeration A it is not necessary to examine all • singulars n order o s;.15/- lithe whole is greater than its part." If we multiply cases it is morp_to_illnAtgetheeprinci4les than to Tirove it. t is not-haseil -the enumeration as such. It-IT3-;7rissen s. . -The mind sees it to perta n o all singulars even to theee not enumerated. It is equivalent to a tetal enweration even though it is not made. Universality is had both on the side of the matter and of the form, Whereas in dialectica/ induction we have only formal_univeesality (et sic de but-as to matter only an approximated or constructed universality. .iZrtieae 'Ttion. is and comp ete mere Y ethe_o.ccasian...f eresel . ug P ..1.P.AiRla gi' Prope itions arrived at in this way are: • a comMen—and general propositions (s, isn es) b) •n r sri E$. Induction s guided by dialectics (Topics, ch. 2, 101 a 34), the most proper function of dialectics is to enable us to find first principles by facilitating induction. b. Probable induction — here propositions are not necees;.ry even if cnunc1=n .a universal form for such universality is merely constructed and approximative. As universal it 1:3 a being of reason. Two kinds of such propositions: 1) Those based on xximkila common experience (e.g. mother loves her child) . Z) Those based on scientific experience — physical laws. In both K inds the incertitude of the matter impedes certitude and univo._. s a lity as to matter. c. In which measure are we justified in adding "et sic de alias"? In dialectical induction assent and conelusion are based solely on the repetition of experience. The conclusion is posed as uni- vee sal, not because it is confirmed by experience but .mere1 cause_ADej l..:.c ..than,... ogre°.• iez Tf no }iine s its th con_ rai y elvi if :suf ~i ei-eut•-1 W. b ~,:s? ",~.enut a ratio. s have been made we must consider tho universal ee attained (Topics, 157 b 33) . All propositions seemingly true of all or most cases must be taken as principles accepted by all (Topics 105 b 10) To refuse to do this would be foolish (1G0 bl) In dialectical induction the diffi- culty is to pose a subject or universal representing the singular which is not too broad or too restrained. It is not formal univesti- sality which is difficult, but material universality. 9. Physical laws are acquired by induction. Is it the same with theo- ries? It is impossible to construct a theory on a purely inductive system. In theory we do not go step by step from laws; the creative imagination enters in. F. 14 More precise study of induction in the experimental sciences. 1. The method followed to make an induction in the experimental sciences bases itself entirely on enumeration as such. How does one m:..ke a • good enumeration? They.try to isolate. one particular thing from bthers and then make a generalization on it. a. Procedure .of simple enumeration - simply count the instanceswhen a pi:enot non happens. NO effort is made to find exceptions or make phenomena vary. But this procedure is a little childish and its conclusions p:ecarious; sometimes based on insufficient number of case, and only the most obvious ones. It does not consider the ensomblé of circumstances, nor establish that other factors have no barring on the conclusic.n. b. Rules for induction - certain terms are used: antecedents and con- sequent cause (efficient) and effect. Now, "cause" is not used much but is replaced by the idea of relation which is vaguer. ' Laws of mathematical physics era not mention efficient causality. John f tu.rt Mill has 4 methods which presuppose a general p~=inci- ple: if all other circumstances remain the some and-if one cannot discard or quantitatively change a factor without changing the effect, then this factor is the cause. of or related to the effect; and inversely, if we remove or change the factor and no change occurs in the effect, thon such a, factor- is not connected ;, we must study 'effects (phenomena) in circumstances as variable as possible. 1) Rule 11:. method of concordance - when one antecedent (A) is common to all effects (a) then it is the cause of (a) which is 9ought. This rule tries to establish that such :;. relation is connt nce, and that• other factors are not pertinent with respect to this effect (negative aspect). In its positive aspect it gives severel ensew',les to support the generalization. The weakness of this method is that it is difi'icult to eliminate fortuitous coincidences. 2) Rule 2 when two effects have the same antecedents excepting one, ten this one is the cause sought. Thedifficulty is to suppress an antecedent which is truly unique, i.e. without s ' sing at the s:_me time more than one antecedent. 3) ,3• concomitant variations - when a, phenomenon varies and ,~ en only one of is _~ te;ecden s varies in the same peopor- tion, this antecedent is the cause sought. We must determine up to what limit variation takes place. 4) Rule 4• method of residues -. one presupposes a complex ante- cedent which is the cause caf, a complex conse:iuent.. If we can: a sign all ele exits but one of the antecedent, then the re- IJeini ag e e!:rerrt of the cone ïuent correspond: to the remaining element cf the antecedent. The difficulty is to see that only one antecedent remains; things are not always clear cut. e.g. If A BC D then b c d These rules are more useful for destroying... for any particular thing . One well-established fact can destroy the universality of a generalization, whereas no number of instances can confirm it, for they are mere enumerations. These rules are more a method of verification rather than a means of suggesting new experiment. 15 2. Methodolo ical orinciale •of induction. in spite of their number and vas:• e y, exper men s ear on a limited number of cases 2. our formulae (physical laws) include even cases not submitted to experiment: extrapolation -.-from a limited number we arrive at a general affirmation. To do this we must base ourselves on the principle of induction. This is not necessary to assure the goodness of the formal consequence. of induction. (use net sic de aliis". This principle is not necessary when enumeration is complete, when propositions have essential predicates, or with first principles. It is needed when enumeration is not complete and conclusion is based on the enumeration as such. This principle does not enable us to arrive at a proposition which is certain and rigorously universal, but enables us to progress and proceed to an approximative universal; it is a supplement on the side of matter, of the singulars which are always insufficiently enumerated. It doesn't express a law of nature, but only a law of the-intellect's progress. It allows genuralization and progress of science toward unity, but doeSnot confer certitude to the conclusion, The principle is that... not completely ... This principle cannot be; .discovered or verified by experiment. This would be a vicious circle, for experiment already presupposes this principle. This principle is based on another and rToro vast methodological principle: hn 1 1 o the unity it of .... an extension Of this principle. ... It a scientific. fact based on previous experience, buL this leads us to the vicious circle. This does not mean (that it precedes all experience; it does not come before common experience (less precise, but more certain than scientific experience). Poincare says that the best justification AMP for this principle is that we cannot do without it. POSSIBLE DISSERTATION TOPIC General interest: the nature of the art of teaching, chiefly its essential, and not its introductory or concluding, activity. Reason for interest: a. It bears a relationship to the art of logic, which is the method of all science. (Logic seems to be the solution for many of the current problems in teaching and learning.) b. I have had direct experience with only a few good teachers. Many other teachers whom I have had seem unaware of what the art of teaching should be. Even conversations with teachers whom I have not had in class reveal that they do not know what is the essential activity they must perform in order to teach others. (My position in our college is the training of teachers.) Possible specification of interest: An analysis of some section of a writing (?) of St. Thomas in relation to the teaching procedure (method) used so that the readers would be able to arrive at the proper conclusion. This analysis would illustrate (for the instruction of those reading the thesis) the meaning of the principles essential to the art of teaching. Naturally, these principles would have to be examined at length.