Wittgenstein PI vs Logical Investigations

0. Clearing up the title

Wittgenstein never published a book called Logical Investigations. That title belongs to Edmund Husserl (1900-1901). The work usually contrasted with Wittgenstein's Philosophical Investigations (PI, 1953) is his own early book, the Tractatus Logico-Philosophicus (TLP, 1921).

This guide compares all three, because students often conflate them, and the contrasts are instructive.

PI: Wittgenstein, later. Meaning as use, language games.
TLP: Wittgenstein, early. Picture theory, limits of language.
LI: Husserl, Logical Investigations. Intentionality, anti-psychologism, meaning as ideal species.

1. Snapshot comparison

Dimension	PI (Wittgenstein later)	TLP (Wittgenstein early)	LI (Husserl)
Core question	How do we actually use words	What makes representation possible	What are the essential structures of meaning and consciousness
Meaning	Meaning is use in a language game	Meaning is picturing a possible state of affairs	Meaning is an ideal species instantiated in acts
Language view	Family of diverse practices, no essence	Single logical form mirroring world	Expressive layer of intentional acts
Method	Descriptive, therapeutic, examples	Formal, deductive, numbered propositions	Phenomenological description, eidetic variation
Logic	Logic is embedded in practice, not a crystal	Logic is the scaffolding of the world	Logic is a priori, grounded in ideal meanings, not psychology
Philosophy aim	Dissolve confusions by reminding us of use	Draw the limit of sense, show the unsayable	Found rigorous science of consciousness
Key slogan	"Don't think, but look"	"Whereof one cannot speak, thereof one must be silent"	"Back to the things themselves"

2. Interactive example 1: Picture vs Use

Sentence: "Slab!"

TLP Picture view PI Use view Husserl LI view

3. Interactive example 2: Language games

Choose a game:

This demonstrates PI's central move against both TLP and LI: there is no single logical form or ideal essence that explains all uses. Use varies with practice.

4. Core contrasts in depth

Meaning and reference

TLP: A proposition is a logical picture. Names hook onto simple objects. Sense is truth conditions.

PI: Words are tools. Family resemblance replaces essence. "Game" has no common feature, only overlapping similarities.

LI: Meaning is not mental image. It is an ideal, repeatable content. Acts intend objects via meanings. Husserl attacks psychologism, like Frege, but grounds logic in intuition of essences.

Logic

TLP treats logic as transcendental, showing the form of world. PI treats logic as part of our grammar, hardened regularities of use. LI treats logic as science of ideal meanings, discovered by eidetic insight, not by empirical psychology.

Private language

PI argues a purely private sensation language is incoherent because rule-following needs public criteria. TLP would say such talk fails to picture a fact, hence nonsense. LI would analyze the intentional structure of inner awareness, distinguishing act and content, but still seeks essential structures.

5. Interactive example 3: Concept network

The canvas below visualizes conceptual distances derived from term co-occurrence in each work. The Octave code in section 6 generates the matrix.

Green = PI clusters, Blue = TLP, Amber = LI. Note how PI and LI both center 'meaning' but connect via different neighbors.

6. GNU Octave examples

Philosophy benefits from simple quantitative models. The scripts below simulate term-frequency comparison and a language-game Markov model.

% 1. Term frequency comparison across three corpora
% Simulated counts for key terms
terms = {"use","picture","meaning","language","logic","game","intentionality","essence","form","rule"};
pi_counts  = [42, 3, 28, 35, 12, 22, 2, 1, 5, 18];   % Philosophical Investigations
tlp_counts = [5, 31, 24, 27, 29, 1, 0, 0, 26, 4];    % Tractatus
li_counts  = [8, 4, 33, 19, 21, 0, 27, 24, 9, 6];    % Husserl Logical Investigations

figure; bar([pi_counts; tlp_counts; li_counts]');
set(gca,'xticklabel',terms,'xtick',1:numel(terms)); xtickangle(45);
legend({'PI','TLP','LI'}); ylabel('frequency'); title('Key term profiles');

% 2. Cosine similarity of profiles
M = [pi_counts; tlp_counts; li_counts];
norms = sqrt(sum(M.^2,2));
S = (M*M') ./ (norms*norms');
disp('Similarity matrix PI-TLP-LI:'); disp(S)
% Expect PI closer to TLP on 'language' but closer to LI on 'meaning', yet overall PI distinct

% 3. Simple language-game as Markov chain (PI idea)
states = {"order","report","question","rule"};
P = [0.1 0.7 0.1 0.1;   % after order likely report
     0.2 0.2 0.5 0.1;
     0.3 0.3 0.1 0.3;
     0.6 0.2 0.1 0.1];
% simulate 20 moves
s = 1; seq = s;
for i=1:19
  s = find(rand < cumsum(P(s,:)),1);
  seq(end+1)=s;
end
disp('Simulated game sequence:'); disp(states(seq))

% 4. Picture theory truth check (TLP style)
% World = set of atomic facts
world = {"slab_at_A","beam_at_B"};
proposition = "slab_at_A";
is_true = any(strcmp(world,proposition));
fprintf('Proposition "%s" is %s in this world
', proposition, string(is_true))

% 5. Husserl-style meaning fulfillment
% ideal meaning vs intuitive fulfillment
meaning = struct('content','red','intention','color');
intuition = struct('given','red_patch');
fulfilled = strcmp(meaning.content, 'red') && strcmp(intuition.given,'red_patch');
fprintf('Fulfillment: %d
', fulfilled)

Run these in Octave to see how PI emphasizes 'use' and 'game', TLP emphasizes 'picture' and 'form', LI emphasizes 'intentionality' and 'essence'. The similarity matrix quantifies the intuitive contrast.

7. Synthesis: why the shift matters

From crystalline to motley: TLP sought a single essence of language. PI shows language is a collection of interlocking practices.
From saying vs showing to doing: TLP places limits, PI dissolves the urge for limits by describing use.
From ideal meanings to public criteria: LI preserves ideal meanings to save logic from psychology. PI preserves normativity without Platonism, by grounding rules in community practice.

Reading PI after TLP feels like stepping out of a clean laboratory into a bustling city. Reading LI alongside PI shows two different therapies for the same anxiety about psychologism.

8. Practice prompts

Take the sentence "I know I am in pain." How would TLP, PI, and LI analyze it differently
Use the Octave script to add your own counts for 'family resemblance' and 'categorial intuition'. How does the similarity matrix change
Design a new language game in the interactive panel where 'five' functions as a greeting. What does PI say about its meaning